Microsoft Word - 8300INTR.DOC

8300INTR.DOC TI-83 Intl English, Title Page Bob Fedorisko Revised: 02/19/01 2:32 PM Printed: 02/21/01 9:05

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TI-83

GRAPHING CALCULATOR

GUIDEBOOK

TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR,

Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas

Instruments Incorporated.

IBM is a registered trademark of International Business Machines Corporation.

Macintosh is a registered trademark of Apple Computer, Inc.

Windows is a registered trademark of Microsoft Corporation.

8300INTR.DOC TI-83 Intl English, Title Page Bob Fedorisko Revised: 02/19/01 11:26 AM Printed: 02/19/01 1:46

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Texas Instruments makes no warranty, either expressed or

implied, including but not limited to any implied warranties of

merchantability and fitness for a particular purpose, regarding any

programs or book materials and makes such materials available

solely on an “as-is” basis.

In no event shall Texas Instruments be liable to anyone for special,

collateral, incidental, or consequential damages in connection with

or arising out of the purchase or use of these materials, and the

sole and exclusive liability of Texas Instruments, regardless of the

form of action, shall not exceed the purchase price of this

equipment. Moreover, Texas Instruments shall not be liable for any

claim of any kind whatsoever against the use of these materials by

any other party.

This equipment has been tested and found to comply with the

limits for a Class B digital device, pursuant to Part 15 of the FCC

rules. These limits are designed to provide reasonable protection

against harmful interference in a residential installation. This

equipment generates, uses, and can radiate radio frequency energy

and, if not installed and used in accordance with the instructions,

may cause harmful interference with radio communications.

However, there is no guarantee that interference will not occur in

a particular installation.

If this equipment does cause harmful interference to radio or

television reception, which can be determined by turning the

equipment off and on, you can try to correct the interference by

one or more of the following measures:

• Reorient or relocate the receiving antenna.

• Increase the separation between the equipment and receiver.

• Connect the equipment into an outlet on a circuit different

from that to which the receiver is connected.

• Consult the dealer or an experienced radio/television

technician for help.

Caution: Any changes or modifications to this equipment not

expressly approved by Texas Instruments may void your authority

to operate the equipment.

Important

US FCC

Information

Concerning

Radio Frequency

Interference

Introduction iii

8300INTR.DOC TI-83 Intl English, Title Page Bob Fedorisko Revised: 02/19/01 11:26 AM Printed: 02/19/01 1:46

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This manual describes how to use the TI

83 Graphing Calculator. Getting

Started is an overview of TI

83 features. Chapter 1 describes how the TI

operates. Other chapters describe various interactive features. Chapter 17

shows how to combine these features to solve problems.

83 Keyboard

..........................................

83 Menus

.............................................

First Steps

...............................................

Entering a Calculation: The Quadratic Formula

..........

Converting to a Fraction: The Quadratic Formula

........

Displaying Complex Results: The Quadratic Formula

....

Defining a Function: Box with Lid

.......................

Defining a Table of Values: Box with Lid

.................

Zooming In on the Table: Box with Lid

...................

Setting the Viewing Window: Box with Lid

...............

Displaying and Tracing the Graph: Box with Lid

.........

Zooming In on the Graph: Box with Lid

..................

Finding the Calculated Maximum: Box with Lid

..........

Other TI

83 Features

.....................................

Turning On and Turning Off the TI

....................

Setting the Display Contrast

.............................

The Display

..............................................

Entering Expressions and Instructions

...................

83 Edit Keys

..........................................

Setting Modes

...........................................

Using TI

83 Variable Names

.............................

Storing Variable Values

..................................

Recalling Variable Values

................................

ENTRY

(Last Entry) Storage Area

........................

Ans

(Last Answer) Storage Area

.........................

83 Menus

.............................................

VARS

and

VARS Y

VARS

Menus

.........................

Equation Operating System (EOS

)

.....................

Error Conditions

.........................................

Table of Contents

Getting Started:

Do This First!

Chapter 1:

Operating the

TI-83

iv Introduction

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Getting Started: Coin Flip

................................

Keyboard Math Operations

..............................

MATH

Operations

........................................

Using the Equation Solver

...............................

MATH NUM

(Number) Operations

........................

Entering and Using Complex Numbers

...................

MATH CPX

(Complex) Operations

.......................

MATH PRB

(Probability) Operations

.....................

ANGLE

Operations

.......................................

TEST

(Relational) Operations

............................

TEST LOGIC

(Boolean) Operations

......................

Getting Started: Graphing a Circle

.......................

Defining Graphs

.........................................

Setting the Graph Modes

.................................

Defining Functions

......................................

Selecting and Deselecting Functions

.....................

Setting Graph Styles for Functions

.......................

Setting the Viewing Window Variables

...................

Setting the Graph Format

................................

Displaying Graphs

.......................................

Exploring Graphs with the Free-Moving Cursor

..........

Exploring Graphs with

TRACE

...........................

Exploring Graphs with the

ZOOM

Instructions

...........

Using

ZOOM MEMORY

..................................

Using the

CALC

(Calculate) Operations

..................

Getting Started: Path of a Ball

...........................

Defining and Displaying Parametric Graphs

..............

Exploring Parametric Graphs

............................

Getting Started: Polar Rose

..............................

Defining and Displaying Polar Graphs

...................

Exploring Polar Graphs

..................................

Chapter 2:

Math, Angle, and

Test Operations

Chapter 3:

Function

Graphing

Chapter 4:

Parametric

Graphing

Chapter 5:

Polar Graphing

Introduction v

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Getting Started: Forest and Trees

........................

Defining and Displaying Sequence Graphs

...............

Selecting Axes Combinations

............................

Exploring Sequence Graphs

..............................

Graphing Web Plots

......................................

Using Web Plots to Illustrate Convergence

...............

Graphing Phase Plots

....................................

Comparing TI

83 and TI

82 Sequence Variables

..........

Keystroke Differences Between TI

83 and TI

.........

Getting Started: Roots of a Function

.....................

Setting Up the Table

.....................................

Defining the Dependent Variables

........................

Displaying the Table

.....................................

Getting Started: Drawing a Tangent Line

.................

Using the

DRAW

...................................

Clearing Drawings

.......................................

Drawing Line Segments

..................................

Drawing Horizontal and Vertical Lines

...................

Drawing Tangent Lines

..................................

Drawing Functions and Inverses

.........................

Shading Areas on a Graph

...............................

Drawing Circles

..........................................

Placing Text on a Graph

.................................

Using Pen to Draw on a Graph

...........................

Drawing Points on a Graph

..............................

Drawing Pixels

..........................................

Storing Graph Pictures (

Pic

)

.............................

Recalling Graph Pictures (

Pic

)

...........................

Storing Graph Databases (

GDB

)

.........................

Recalling Graph Databases (

GDB

)

.......................

Getting Started: Exploring the Unit Circle

................

Using Split Screen

.......................................

Horiz

(Horizontal) Split Screen

...........................

(Graph-Table) Split Screen

..........................

83 Pixels in

Horiz

and

Modes

.....................

Chapter 6:

Sequence

Graphing

Chapter 7:

Tables

Chapter 8:

DRAW

Operations

Chapter 9:

Split Screen

vi Introduction

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Getting Started: Systems of Linear Equations

............

Defining a Matrix

........................................

Viewing and Editing Matrix Elements

....................

Using Matrices with Expressions

........................

Displaying and Copying Matrices

........................

Using Math Functions with Matrices

.....................

Using the

MATRX MATH

Operations

.....................

Getting Started: Generating a Sequence

..................

Naming Lists

.............................................

Storing and Displaying Lists

.............................

Entering List Names

.....................................

Attaching Formulas to List Names

.......................

Using Lists in Expressions

...............................

LIST OPS

..........................................

LIST MATH

........................................

Getting Started: Pendulum Lengths and Periods

.........

Setting up Statistical Analyses

...........................

Using the Stat List Editor

................................

Attaching Formulas to List Names

.......................

Detaching Formulas from List Names

....................

Switching Stat List Editor Contexts

......................

Stat List Editor Contexts

.................................

STAT EDIT

........................................

Regression Model Features

..............................

STAT CALC

........................................

Statistical Variables

......................................

Statistical Analysis in a Program

.........................

Statistical Plotting

.......................................

Statistical Plotting in a Program

.........................

Getting Started: Mean Height of a Population

............

Inferential Stat Editors

...................................

STAT TESTS

......................................

Inferential Statistics Input Descriptions

..................

Test and Interval Output Variables

.......................

Distribution Functions

...................................

Distribution Shading

.....................................

Chapter 10:

Matrices

Chapter 11:

Lists

Chapter 12:

Statistics

Chapter 13:

Inferential

Statistics and

Distributions

Introduction vii

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Getting Started: Financing a Car

.........................

Getting Started: Computing Compound Interest

..........

Using the

TVM Solver

....................................

Using the Financial Functions

...........................

Calculating Time Value of Money (

TVM

)

.................

Calculating Cash Flows

..................................

Calculating Amortization

................................

Calculating Interest Conversion

..........................

Finding Days between Dates/Defining Payment Method

.....

Using the

TVM

Variables

.................................

Browsing the TI

CATALOG

...........................

Entering and Using Strings

...............................

Storing Strings to String Variables

.......................

String Functions and Instructions in the

CATALOG

......

Hyperbolic Functions in the

CATALOG

..................

Getting Started: Volume of a Cylinder

....................

Creating and Deleting Programs

.........................

Entering Command Lines and Executing Programs

......

Editing Programs

........................................

Copying and Renaming Programs

........................

PRGM CTL

(Control) Instructions

.......................

PRGM I/O

(Input/Output) Instructions

...................

Calling Other Programs as Subroutines

..................

Comparing Test Results Using Box Plots

................

Graphing Piecewise Functions

...........................

Graphing Inequalities

....................................

Solving a System of Nonlinear Equations

................

Using a Program to Create the Sierpinski Triangle

.......

Graphing Cobweb Attractors

............................

Using a Program to Guess the Coefficients

...............

Graphing the Unit Circle and Trigonometric Curves

......

Finding the Area between Curves

........................

Using Parametric Equations: Ferris Wheel Problem

......

Demonstrating the Fundamental Theorem of Calculus

...

Computing Areas of Regular N-Sided Polygons

..........

Computing and Graphing Mortgage Payments

...........

Chapter 14:

Financial

Functions

Chapter 15:

CATALOG,

Strings,

Hyperbolic

Functions

Chapter 16:

Programming

Chapter 17:

Applications

viii Introduction

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Checking Available Memory

.............................

Deleting Items from Memory

............................

Clearing Entries and List Elements

......................

Resetting the TI

......................................

Getting Started: Sending Variables

.......................

LINK

...............................................

Selecting Items to Send

..................................

Receiving Items

..........................................

Transmitting Items

.......................................

Transmitting Lists to a TI

.............................

Transmitting from a TI

82 to a TI

.....................

Backing Up Memory

.....................................

Table of Functions and Instructions

.....................

Menu Map

...............................................

Variables

................................................

Statistical Formulas

.....................................

Financial Formulas

......................................

Battery Information

......................................

In Case of Difficulty

.....................................

Error Conditions

.........................................

Accuracy Information

....................................

Support and Service Information

.........................

Warranty Information

....................................

Chapter 18:

Memory

Management

Chapter 19:

Communication

Link

Appendix A:

Tables and

Reference

Information

Appendix B:

General

Information

Index

Getting Started 1

8300GETM.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 11:06 AM Printed: 02/19/01 11:06

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Gettin

Started:

Do This First!

83 Keyboard

..........................................

83 Menus

.............................................

First Steps

...............................................

Entering a Calculation: The Quadratic Formula

..........

Converting to a Fraction: The Quadratic Formula

........

Displaying Complex Results: The Quadratic Formula

....

Defining a Function: Box with Lid

.......................

Defining a Table of Values: Box with Lid

.................

Zooming In on the Table: Box with Lid

...................

Setting the Viewing Window: Box with Lid

...............

Displaying and Tracing the Graph: Box with Lid

.........

Zooming In on the Graph: Box with Lid

..................

Finding the Calculated Maximum: Box with Lid

..........

Other TI

83 Features

.....................................

Contents

2 Getting Started

8300GETM.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 11:11 AM Printed: 02/19/01 11:14

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Generally, the keyboard is divided into these zones: graphing keys, editing

keys, advanced function keys, and scientific calculator keys.

Graphing keys access the interactive graphing features.

Editing keys allow you to edit expressions and values.

Advanced function keys display menus that access the

advanced functions.

Scientific calculator keys access the capabilities of a

standard scientific calculator.

TI-83 Keyboard

Keyboard Zones

Editing Keys

Advanced

Function Keys

Scientific

Calculator Keys

Graphing Keys

Getting Started 3

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The keys on the TI

83 are color-coded to help you easily

locate the key you need.

The gray keys are the number keys. The blue keys along the

right side of the keyboard are the common math functions.

The blue keys across the top set up and display graphs.

The primary function of each key is printed in white on the

key. For example, when you press



, the

MATH

menu is

displayed.

The secondary function of each key is printed in yellow

above the key. When you press the yellow

key, the

character, abbreviation, or word printed in yellow above

the other keys becomes active for the next keystroke. For

example, when you press

and then



, the

TEST

menu is displayed. This guidebook describes this keystroke

combination as

[

TEST

The alpha function of each key is printed in green above

the key. When you press the green

key, the alpha

character printed in green above the other keys becomes

active for the next keystroke. For example, when you press

and then



, the letter

A is entered. This

guidebook describes this keystroke combination as

[

Using the

Color-Coded

Keyboard

Using the

and

Keys

The

key accesses

the second function

printed in yellow above

each key.

The

key

accesses the alpha

function printed in

green above each key.

4 Getting Started

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Displaying a Menu

While using your TI

83, you often will need

to access items from its menus.

When you press a key that displays a menu,

that menu temporarily replaces the screen

where you are working. For example, when

you press



, the

MATH

menu is displayed

as a full screen.

fter you select an item from a menu, the

screen where you are working usually is

displayed again.

Moving from One Menu to Another

Some keys access more than one menu. When

you press such a key, the names of all

accessible menus are displayed on the top

line. When you highlight a menu name, the

items in that menu are displayed. Press

and

to highlight each menu name.

Selecting an Item from a Menu

The number or letter next to the current menu

item is highlighted. If the menu continues

beyond the screen, a down arrow (

)

replaces the colon (

) in the last displayed

item. If you scroll beyond the last displayed

item, an up arrow (

) replaces the colon in

the first item displayed.You can select an item

in either of two ways.

Press

†

}

to move the cursor to the

number or letter of the item; press

Press the key or key combination for the

number or letter next to the item.

Leaving a Menu without Making a Selection

You can leave a menu without making a

selection in any of three ways.

Press

‘

to return to the screen

where you were.

Press

[

QUIT

] to return to the home

screen.

Press a key for another menu or screen.

TI-83 Menus

Getting Started 5

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Before starting the sample problems in this chapter, follow the steps on this

page to reset the TI

83 to its factory settings and clear all memory. This

ensures that the keystrokes in this chapter will produce the illustrated results.

To reset the TI

83, follow these steps.

1. Press

to turn on the calculator.

2. Press and release

, and then press

[

MEM

] (above

When you press

, you access the

operation printed in yellow above the next

key that you press. [

MEM

] is the

operation of the

key.

The

MEMORY

menu is displayed.

3. Press 5 to select 5:Reset.

The

RESET

menu is displayed.

4. Press 1 to select 1:All Memory.

The

RESET MEMORY

menu is displayed.

5. Press 2 to select 2:Reset.

All memory is cleared, and the calculator

is reset to the factory default settings.

When you reset the TI

83, the display

contrast is reset.

If the screen is very light or blank, press

and release

, and then press and

hold

}

to darken the screen.

If the screen is very dark, press and

release

, and then press and hold

†

to lighten the screen.

First Steps

6 Getting Started

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Use the quadratic formula to solve the quadratic equations 3X

+ 5X + 2 = 0

and 2X

X + 3 = 0. Begin with the equation 3X

+ 5X + 2 = 0.

1. Press

[

] (above



) to

store the coefficient of the X

term.

2. Press

[

] (above

). The colon

allows you to enter more than one

instruction on a line.

3. Press

[

] (above



) to

store the coefficient of the X

term. Press

[

] to enter a new instruction on

the same line. Press

[

]

(above



) to store the constant.

4. Press

to store the values to the

variables A, B, and C.

The last value you stored is shown on the

right side of the display. The cursor moves

to the next line, ready for your next entry.

5. Press

[

]

[

‡

]

[

]

[

]

[

]

[

]

to enter the expression for

one of the solutions for the quadratic

formula,

−

+−

bb ac

6. Press

to find one solution for the

equation 3X

+ 5X + 2 = 0.

The answer is shown on the right side of

the display. The cursor moves to the next

line, ready for you to enter the next

expression.

Entering a Calculation: The Quadratic Formula

Getting Started 7

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You can show the solution as a fraction.

1. Press



to display the

MATH

menu.

2. Press 1 to select 1:

Frac from the

MATH

menu.

When you press

1, Ans

Frac is displayed on

the home screen.

Ans is a variable that

contains the last calculated answer.

3. Press

to convert the result to a

fraction.

To save keystrokes, you can recall the last expression you entered, and then

edit it for a new calculation.

4. Press

[

ENTRY

] (above

) to recall

the fraction conversion entry, and then

press

[

ENTRY

] again to recall the

quadratic-formula expression,

−

+−

bb ac

5. Press

}

to move the cursor onto the + sign

in the formula. Press

to edit the

quadratic-formula expression to become:

−

−−

bb ac

6. Press

to find the other solution for

the quadratic equation 3X

+ 5X + 2 = 0.

Converting to a Fraction: The Quadratic Formula

8 Getting Started

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Now solve the equation 2X

X + 3 = 0. When you set a+b

complex number

mode, the TI

83 displays complex results.

1. Press

†

(6 times), and

then press

to position the cursor over

a+b

. Press

to select

a+b

complex-

number mode.

2. Press

[

QUIT

] (above

) to return to

the home screen, and then press

‘

clear it.

3. Press 2

[

]

[

]

[

]

[

] 3

[

]

The coefficient of the X

term, the

coefficient of the X term, and the constant

for the new equation are stored to A, B,

and C, respectively.

4. Press

[

ENTRY

] to recall the store

instruction, and then press

[

ENTRY

]

again to recall the quadratic-formula

expression,

−

−−

bb ac

5. Press

to find one solution for the

equation 2X

X + 3 = 0.

6. Press

[

ENTRY

] repeatedly until this

quadratic-formula expression is displayed:

−

+−

bb ac

7. Press

to find the other solution for

the quadratic equation: 2X

X + 3 = 0.

Note:

An alternative for solving equations for real numbers is to use the built-in Equation

Solver (Chapter 2).

Displaying Complex Results: The Quadratic Formula

Getting Started 9

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Take a 20 cm. × 25 cm. sheet of paper and cut X × X squares from two corners.

Cut X × 12.5 cm. rectangles from the other two corners as shown in the

diagram below. Fold the paper into a box with a lid. What value of X would

give your box the maximum volume V? Use the table and graphs to determine

the solution.

Begin by defining a function that describes the

olume of the box.

From the diagram: 2X + A = 20

2X + 2B = 25

V = A B X

Substituting: V = (20

2X) (25

X) X

1. Press

to display the

editor, which is

where you define functions for tables and

graphing.

2. Press

„

to define the

volume function as

in terms of X.

„

lets you enter

X quickly, without

having to press

. The highlighted

sign indicates that Y

is selected.

Defining a Function: Box with Lid

X B X B

10 Getting Started

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The table feature of the TI

83 displays numeric information about a function.

You can use a table of values from the function defined on page 9 to estimate

an answer to the problem.

1. Press

[

TBLSET

] (above

) to

display the

TABLE SETUP

menu.

2. Press

to accept

TblStart=0.

3. Press

to define the table increment

Tbl=1

. Leave Indpnt: Auto and

Depend: Auto so that the table will be

generated automatically.

4. Press

[

TABLE

] (above

) to display

the table.

Notice that the maximum value for

(box’s volume) occurs when X is about 4,

between

3 and 5.

5. Press and hold

†

to scroll the table until a

negative result for

is displayed.

Notice that the maximum length of

X for

this problem occurs where the sign of

(box’s volume) changes from positive to

negative, between

10 and 11.

6. Press

[

TBLSET

Notice that

TblStart has changed to 6 to

reflect the first line of the table as it was

last displayed. (In step 5, the first value of

X displayed in the table is 6.)

Defining a Table of Values: Box with Lid

Getting Started 11

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You can adjust the way a table is displayed to get more information about a

defined function. With smaller values for

Tbl

, you can zoom in on the table.

1. Press

to set TblStart. Press

to set

Tbl

This adjusts the table setup to get a more

accurate estimate of

X for maximum

volume

2. Press

[

TABLE

3. Press

†

and

}

to scroll the table.

Notice that the maximum value for

410.26, which occurs at X=3.7. Therefore,

the maximum occurs where

3.6<X<3.8.

4. Press

[

TBLSET

]. Press 3

set

TblStart. Press

to set

Tbl

5. Press

[

TABLE

], and then press

†

and

}

to scroll the table.

Four equivalent maximum values are

shown,

410.60 at X=3.67, 3.68, 3.69, and

3.70.

6. Press

†

and

}

to move the cursor to 3.67.

Press

to move the cursor into the

column.

The value of

at X=3.67 is displayed on

the bottom line in full precision as

410.261226.

7. Press

†

to display the other maximums.

The value of

at X=3.68 in full precision is

410.264064, at X=3.69 is 410.262318, and at

X=3.7 is 410.256.

The maximum volume of the box would

occur at

3.68 if you could measure and cut

the paper at .01-cm. increments.

Zooming In on the Table: Box with Lid

12 Getting Started

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You also can use the graphing features of the TI

83 to find the maximum value

of a previously defined function. When the graph is activated, the viewing

window defines the displayed portion of the coordinate plane. The values of

the window variables determine the size of the viewing window.

1. Press

to display the window

editor, where you can view and edit the

values of the window variables.

The standard window variables define the

viewing window as shown.

Xmin, Xmax,

Ymin, and Ymax define the boundaries of

the display.

Xscl and Yscl define the

distance between tick marks on the

X and

Y axes. Xres controls resolution.

Xmax

Ymin

Ymax

Xscl

Yscl

Xmin

2. Press 0

to define Xmin.

3. Press

2 to define Xmax using an

expression.

4. Press

. The expression is evaluated,

and

10 is stored in Xmax. Press

Xscl as 1.

5. Press

500

100

to define the remaining window variables.

Setting the Viewing Window: Box with Lid

Getting Started 13

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Now that you have defined the function to be graphed and the window in

which to graph it, you can display and explore the graph. You can trace along a

function using the

TRACE

feature.

1. Press

to graph the selected function

in the viewing window.

The graph of

=(20

2X)(25

X)X is

displayed.

2. Press

to activate the free-moving graph

cursor.

The

X and Y coordinate values for the

position of the graph cursor are displayed

on the bottom line.

3. Press

}

, and

†

to move the free-

moving cursor to the apparent maximum

of the function.

As you move the cursor, the

X and Y

coordinate values are updated continually.

Displaying and Tracing the Graph: Box with Lid

14 Getting Started

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4. Press

. The trace cursor is displayed

on the

function.

The function that you are tracing is

displayed in the top-left corner.

5. Press

and

to trace along

, one X dot

at a time, evaluating

at each X.

You also can enter your estimate for the

maximum value of

6. Press

8. When you press a number key

while in

TRACE

, the X= prompt is displayed

in the bottom-left corner.

7. Press

The trace cursor jumps to the point on the

function evaluated at X=3.8.

8. Press

and

until you are on the

maximum

Y value.

This is the maximum of

(X) for the X

pixel values. The actual, precise maximum

may lie between pixel values.

Getting Started 15

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To help identify maximums, minimums, roots, and intersections of functions,

you can magnify the viewing window at a specific location using the

ZOOM

instructions.

1. Press

to display the

ZOOM

menu.

This menu is a typical TI

83 menu. To

select an item, you can either press the

number or letter next to the item, or you

can press

†

until the item number or letter

is highlighted, and then press

2. Press 2 to select 2:Zoom In.

The graph is displayed again. The cursor

has changed to indicate that you are using

ZOOM

instruction.

3. With the cursor near the maximum value

of the function (as in step 8 on page 14),

press

The new viewing window is displayed.

Both

Xmax

Xmin and Ymax

Ymin have

been adjusted by factors of 4, the default

values for the zoom factors.

4. Press

to display the new window

settings.

Zooming In on the Graph: Box with Lid

16 Getting Started

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You can use a

CALCULATE

menu operation to calculate a local maximum of a

function.

1. Press

[

CALC

] (above

) to display

the

CALCULATE

menu. Press 4 to select

4:maximum.

The graph is displayed again with a

Left Bound? prompt.

2. Press

to trace along the curve to a point

to the left of the maximum, and then press

at the top of the screen indicates the

selected bound.

Right Bound? prompt is displayed.

3. Press

to trace along the curve to a point

to the right of the maximum, and then

press

at the top of the screen indicates the

selected bound.

Guess? prompt is displayed.

4. Press

to trace to a point near the

maximum, and then press

Or, press

8, and then press

enter a guess for the maximum.

When you press a number key in

TRACE

the

X= prompt is displayed in the bottom-

left corner.

Notice how the values for the calculated

maximum compare with the maximums

found with the free-moving cursor, the

trace cursor, and the table.

Note:

In steps 2 and 3 above, you can enter values

directly for Left Bound and Right Bound, in the same

way as described in step 4.

Finding the Calculated Maximum: Box with Lid

Getting Started 17

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Getting Started has introduced you to basic TI

83 operation. This guidebook

describes in detail the features you used in Getting Started. It also covers the

other features and capabilities of the TI

83.

You can store, graph, and analyze up to 10 functions

(Chapter 3), up to six parametric functions (Chapter 4), up

to six polar functions (Chapter 5), and up to three

sequences (Chapter 6). You can use

DRAW

operations to

annotate graphs (Chapter 8).

You can generate sequences and graph them over time. Or,

you can graph them as web plots or as phase plots

(Chapter 6).

You can create function evaluation tables to analyze many

functions simultaneously (Chapter 7).

You can split the screen horizontally to display both a

graph and a related editor (such as the

editor), the

table, the stat list editor, or the home screen. Also, you can

split the screen vertically to display a graph and its table

simultaneously (Chapter 9).

You can enter and save up to 10 matrices and perform

standard matrix operations on them (Chapter 10).

You can enter and save as many lists as memory allows for

use in statistical analyses. You can attach formulas to lists

for automatic computation. You can use lists to evaluate

expressions at multiple values simultaneously and to graph

a family of curves (Chapter 11).

You can perform one- and two-variable, list-based

statistical analyses, including logistic and sine regression

analysis. You can plot the data as a histogram, xyLine,

scatter plot, modified or regular box-and-whisker plot, or

normal probability plot. You can define and store up to

three stat plot definitions (Chapter 12).

Other TI-83 Features

Graphing

Sequences

Tables

Split Screen

Matrices

Lists

Statistics

18 Getting Started

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You can perform 16 hypothesis tests and confidence

intervals and 15 distribution functions. You can display

hypothesis test results graphically or numerically

(Chapter 13).

You can use time-value-of-money (

TVM

) functions to

analyze financial instruments such as annuities, loans,

mortgages, leases, and savings. You can analyze the value

of money over equal time periods using cash flow

functions. You can amortize loans with the amortization

functions (Chapter 14).

The

CATALOG

is a convenient, alphabetical list of all

functions and instructions on the TI

83. You can paste any

function or instruction from the

CATALOG

to the current

cursor location (Chapter 15).

You can enter and store programs that include extensive

control and input/output instructions (Chapter 16).

The TI

83 has a port to connect and communicate with

another TI

83, a TI

82, the Calculator-Based Laboratory

(CBL 2

, CBL

) System, a Calculator-Based Ranger

(CBR

), or a personal computer. The unit-to-unit link

cable is included with the TI

83 (Chapter 19).

Inferential

Statistics

Financial

Functions

CATALOG

Programming

Communication

Link

Operating the TI

83 1-1

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Operatin

the TI-83

Turning On and Turning Off the TI

....................

1-2

Setting the Display Contrast

.............................

1-3

The Display

..............................................

1-4

Entering Expressions and Instructions

...................

1-6

83 Edit Keys

..........................................

1-8

Setting Modes

...........................................

1-9

Using TI

83 Variable Names

.............................

1-13

Storing Variable Values

..................................

1-14

Recalling Variable Values

................................

1-15

ENTRY

(Last Entry) Storage Area

........................

1-16

Ans

(Last Answer) Storage Area

.........................

1-18

83 Menus

.............................................

1-19

VARS

and

VARS Y

VARS

Menus

.........................

1-21

Equation Operating System (EOS

)

.....................

1-22

Error Conditions

.........................................

1-24

Contents

1-2 Operating the TI

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To turn on the TI

83, press

•

If you previously had turned off the calculator by

pressing

[

OFF

], the TI

83 displays the home screen

as it was when you last used it and clears any error.

•

If Automatic Power Down™ (APD

) had previously

turned off the calculator, the TI

83 will return exactly as

you left it, including the display, cursor, and any error.

To prolong the life of the batteries, APD turns off the TI

automatically after about five minutes without any activity.

To turn off the TI

83 manually, press

[

OFF

•

All settings and memory contents are retained by

Constant Memory

•

Any error condition is cleared.

The TI

83 uses four AAA alkaline batteries and has a user-

replaceable backup lithium battery (CR1616 or CR1620).

To replace batteries without losing any information stored

in memory, follow the steps in Appendix B.

Turning On and Turning Off the TI-83

Turning On the

Calculator

Turning Off the

Calculator

Batteries

Operating the TI

83 1-3

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You can adjust the display contrast to suit your viewing

angle and lighting conditions. As you change the contrast

setting, a number from

0 (lightest) to 9 (darkest) in the

top-right corner indicates the current level. You may not be

able to see the number if contrast is too light or too dark.

Note:

The TI

83 has 40 contrast settings, so each number

through

represents four settings.

The TI

83 retains the contrast setting in memory when it is

turned off.

To adjust the contrast, follow these steps.

1. Press and release the

key.

2. Press and hold

†

}

, which are below and above the

contrast symbol (yellow, half-shaded circle).

•

†

lightens the screen.

•

}

darkens the screen.

Note:

If you adjust the contrast setting to

, the display may become

completely blank. To restore the screen, press and release

, and

then press and hold

}

until the display reappears.

When the batteries are low, a low-battery message is

displayed when you turn on the calculator.

To replace the batteries without losing any information in

memory, follow the steps in Appendix B.

Generally, the calculator will continue to operate for one

or two weeks after the low-battery message is first

displayed. After this period, the TI

83 will turn off

automatically and the unit will not operate. Batteries must

be replaced. All memory is retained.

Note:

The operating period following the first low-battery message

could be longer than two weeks if you use the calculator infrequently.

Setting the Display Contrast

Adjusting the

Display Contrast

When to Replace

Batteries

1-4 Operating the TI

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The TI

83 displays both text and graphs. Chapter 3

describes graphs. Chapter 9 describes how the TI

83 can

display a horizontally or vertically split screen to show

graphs and text simultaneously.

The home screen is the primary screen of the TI

83. On

this screen, enter instructions to execute and expressions

to evaluate. The answers are displayed on the same screen.

When text is displayed, the TI

83 screen can display a

maximum of eight lines with a maximum of 16 characters

per line. If all lines of the display are full, text scrolls off

the top of the display. If an expression on the home screen,

the

editor (Chapter 3), or the program editor

(Chapter 16) is longer than one line, it wraps to the

beginning of the next line. In numeric editors such as the

window screen (Chapter 3), a long expression scrolls to

the right and left.

When an entry is executed on the home screen, the answer

is displayed on the right side of the next line.

Entry

Answer

The mode settings control the way the TI

83 interprets

expressions and displays answers (page 1

9).

If an answer, such as a list or matrix, is too long to display

entirely on one line, an ellipsis (

...) is displayed to the right

or left. Press

and

to scroll the answer.

Entry

Answer

To return to the home screen from any other screen, press

[

QUIT

When the TI

83 is calculating or graphing, a vertical

moving line is displayed as a busy indicator in the top-right

corner of the screen. When you pause a graph or a

program, the busy indicator becomes a vertical moving

dotted line.

The Display

Types of

Displays

Home Screen

Displaying

Entries and

Answers

Returning to the

Home Screen

Busy Indicator

Operating the TI

83 1-5

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In most cases, the appearance of the cursor indicates what

will happen when you press the next key or select the next

menu item to be pasted as a character.

Cursor Appearance Effect of Next Keystroke

Entry Solid rectan

A character is entered at the

cursor; any existin

character is

overwritten

Insert Underline

A character is inserted in front of

the cursor location

Second Reverse arrow

A 2nd character

(

yellow on the

keyboard

)

is entered or a 2nd

operation is executed

lpha Reverse A

An alpha character

reen on the

keyboard

)

is entered or

SOLVE

executed

Full Checkerboard

rectan

No entry; the maximum characters

are entered at a prompt or memory

is full

If you press

during an insertion, the cursor becomes

an underlined

(

) If you press

during an insertion, the

underline cursor becomes an underlined

(

Graphs and editors sometimes display additional cursors,

which are described in other chapters.

Display Cursors

1-6 Operating the TI

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An expression is a group of numbers, variables, functions

and their arguments, or a combination of these elements.

An expression evaluates to a single answer. On the TI

83,

you enter an expression in the same order as you would

write it on paper. For example,

is an expression.

You can use an expression on the home screen to calculate

an answer. In most places where a value is required, you

can use an expression to enter a value.

To create an expression, you enter numbers, variables, and

functions from the keyboard and menus. An expression is

completed when you press

, regardless of the cursor

location. The entire expression is evaluated according to

Equation Operating System (EOS

) rules (page 1

22), and

the answer is displayed.

Most TI

83 functions and operations are symbols

comprising several characters. You must enter the symbol

from the keyboard or a menu; do not spell it out. For

example, to calculate the log of 45, you must press

45.

Do not enter the letters

L, O, and G. If you enter LOG, the

83 interprets the entry as implied multiplication of the

variables

L, O, and G.

Calculate 3.76 ÷ (

7.9 +

‡

5) + 2 log 45.

[

‡

] 5

To enter two or more expressions or instructions on a line,

separate them with colons (

[

]). All instructions are

stored together in last entry (

ENTRY

; page 1

16).

Entering Expressions and Instructions

What Is an

Expression?

Entering an

Expression

Multiple Entries

on a Line

Operating the TI

83 1-7

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To enter a number in scientific notation, follow these

steps.

1. Enter the part of the number that precedes the

exponent. This value can be an expression.

2. Press

[

is pasted to the cursor location.

3. If the exponent is negative, press

, and then enter the

exponent, which can be one or two digits.

When you enter a number in scientific notation, the TI

does not automatically display answers in scientific or

engineering notation. The mode settings (page 1

9) and the

size of the number determine the display format.

A function returns a value. For example,

÷,

, +,

‡

(

, and log(

are the functions in the example on page 1

6. In general, the

first letter of each function is lowercase on the TI

83. Most

functions take at least one argument, as indicated by an open

parenthesis (

( ) following the name. For example, sin(

requires one argument, sin(

value

An instruction initiates an action. For example,

ClrDraw is

an instruction that clears any drawn elements from a

graph. Instructions cannot be used in expressions. In

general, the first letter of each instruction name is

uppercase. Some instructions take more than one

argument, as indicated by an open parenthesis (

( ) at the

end of the name. For example,

Circle( requires three

arguments,

Circle(

radius

To interrupt a calculation or graph in progress, which

would be indicated by the busy indicator, press

When you interrupt a calculation, the menu is displayed.

•

To return to the home screen, select

1:Quit.

•

To go to the location of the interruption, select

2:Goto.

When you interrupt a graph, a partial graph is displayed.

•

To return to the home screen, press

‘

or any

nongraphing key.

•

To restart graphing, press a graphing key or select a

graphing instruction.

Entering a

Number in

Scientific

Notation

Functions

Instructions

Interrupting a

Calculation

1-8 Operating the TI

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Keystrokes Result

Moves the cursor within an expression; these keys repeat.

}

†

Moves the cursor from line to line within an expression that

occupies more than one line; these keys repeat.

On the top line of an expression on the home screen,

}

moves

the cursor to the beginning of the expression.

On the bottom line of an expression on the home screen,

†

moves the cursor to the end of the expression.

Moves the cursor to the beginning of an expression.

Moves the cursor to the end of an expression.

Evaluates an expression or executes an instruction.

‘

On a line with text on the home screen, clears the current line.

On a blank line on the home screen, clears everythin

on the

home screen.

In an editor, clears the expression or value where the cursor is

located; it does not store a zero.

{

Deletes a character at the cursor; this key repeats.

[

INS

] Chan

es the cursor to

; inserts characters in front of the

underline cursor; to end insertion, press

[

INS

] or press

}

, or

†

Chan

es the cursor to

; the next keystroke performs a

2nd

operation

(

an operation in yellow above a key and to the left

)

; to

cancel

2nd

, press

again.

Chan

es the cursor to

; the next keystroke pastes an alpha

character

(

a character in

reen above a key and to the ri

)

executes

SOLVE

(

Chapters 10 and 11

)

; to cancel

, press

or press

}

, or

†

[

LOCK

] Chan

es the cursor to

; sets alpha-lock; subsequent keystrokes

(

on an alpha key

)

paste alpha characters; to cancel alpha-lock,

press

; name prompts set alpha-lock automatically.

„

Pastes an

Func

mode, a

Par

mode, a

Pol

mode, or an

Seq

mode with one keystroke.

TI-83 Edit Keys

Operating the TI

83 1-9

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Mode settings control how the TI

83 displays and

interprets numbers and graphs. Mode settings are retained

by the Constant Memory feature when the TI

83 is turned

off. All numbers, including elements of matrices and lists,

are displayed according to the current mode settings.

To display the mode settings, press

. The current

settings are highlighted. Defaults are highlighted below.

The following pages describe the mode settings in detail.

Normal Sci Eng

Numeric notation

Float 0123456789

Number of decimal places

Radian Degree

Unit of angle measure

Func Par Pol Seq

Type of graphing

Connected Dot

Whether to connect graph points

Sequential Simul

Whether to plot simultaneously

Real a+bi re^

Real, rectangular cplx, or polar cplx

Full Horiz G-T

Full screen, two split-screen modes

To change mode settings, follow these steps.

1. Press

†

}

to move the cursor to the line of the

setting that you want to change.

2. Press

to move the cursor to the setting you

want.

3. Press

You can set a mode from a program by entering the name

of the mode as an instruction; for example,

Func or Float.

From a blank command line, select the mode setting from

the mode screen; the instruction is pasted to the cursor

location.

Setting Modes

Checking Mode

Settings

Changing Mode

Settings

Setting a Mode

from a Program

1-10 Operating the TI

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Notation modes only affect the way an answer is displayed

on the home screen. Numeric answers can be displayed

with up to 10 digits and a two-digit exponent. You can

enter a number in any format.

Normal notation mode is the usual way we express

numbers, with digits to the left and right of the decimal, as

12345.67.

Sci (scientific) notation mode expresses numbers in two

parts. The significant digits display with one digit to the left

of the decimal. The appropriate power of 10 displays to the

right of

, as in 1.234567

Eng (engineering) notation mode is similar to scientific

notation. However, the number can have one, two, or three

digits before the decimal; and the power-of-10 exponent is

a multiple of three, as in

12.34567

Note

: If you select

Normal

notation, but the answer cannot display in

10 digits (or the absolute value is less than .001), the TI

83 expresses

the answer in scientific notation.

Float (floating) decimal mode displays up to 10 digits, plus

the sign and decimal.

0123456789 (fixed) decimal mode specifies the number of

digits (

0 through 9) to display to the right of the decimal.

Place the cursor on the desired number of decimal digits,

and then press

The decimal setting applies to

Normal, Sci, and Eng

notation modes.

The decimal setting applies to these numbers:

•

An answer displayed on the home screen

•

Coordinates on a graph (Chapters 3, 4, 5, and 6)

•

The

Tangent(

DRAW

instruction equation of the line, x,

and dy/dx values (Chapter 8)

•

Results of

CALCULATE

operations (Chapters 3, 4, 5,

and 6)

•

The regression equation stored after the execution of a

regression model (Chapter 12)

Normal, Sci, Eng

Float,

0123456789

Operating the TI

83 1-11

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Angle modes control how the TI

83 interprets angle values

in trigonometric functions and polar/rectangular

conversions.

Radian mode interprets angle values as radians. Answers

display in radians.

Degree mode interprets angle values as degrees. Answers

display in degrees.

Graphing modes define the graphing parameters. Chapters

3, 4, 5, and 6 describe these modes in detail.

Func (function) graphing mode plots functions, where Y is

a function of

X (Chapter 3).

Par (parametric) graphing mode plots relations, where X

and Y are functions of T (Chapter 4).

Pol (polar) graphing mode plots functions, where r is a

function of

(Chapter 5).

Seq (sequence) graphing mode plots sequences (Chapter 6).

Connected plotting mode draws a line connecting each

point calculated for the selected functions.

Dot plotting mode plots only the calculated points of the

selected functions.

Radian, Degree

Func, Par, Pol,

Seq

Connected, Dot

1-12 Operating the TI

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Sequential graphing-order mode evaluates and plots one

function completely before the next function is evaluated

and plotted.

Simul (simultaneous) graphing-order mode evaluates and

plots all selected functions for a single value of

X and then

evaluates and plots them for the next value of

Note:

Regardless of which graphing mode is selected, the TI

83 will

sequentially graph all stat plots before it graphs any functions.

Real mode does not display complex results unless

complex numbers are entered as input.

Two complex modes display complex results.

•

a+b

(rectangular complex mode) displays complex

numbers in the form a+b

•

re^

(polar complex mode) displays complex numbers

in the form re^

Full screen mode uses the entire screen to display a graph

or edit screen.

Each split-screen mode displays two screens

simultaneously.

•

Horiz (horizontal) mode displays the current graph on

the top half of the screen; it displays the home screen or

an editor on the bottom half (Chapter 9).

•

T (graph-table) mode displays the current graph on

the left half of the screen; it displays the table screen on

the right half (Chapter 9).

Sequential, Simul

Real, a+b

, re^

Full, Horiz, G

Operating the TI

83 1-13

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On the TI

83 you can enter and use several types of data,

including real and complex numbers, matrices, lists,

functions, stat plots, graph databases, graph pictures, and

strings.

The TI

83 uses assigned names for variables and other

items saved in memory. For lists, you also can create your

own five-character names.

Variable Type Names

Real numbers

, . . . ,

Complex numbers

, . . . ,

Matrices

, . . . ,

Lists

, and user-

defined names

Functions

, . . . ,

Parametric equations

and

, . . . ,

and

Polar functions

Sequence functions

Stat plots

Plot1, Plot2, Plot3

Graph databases

GDB1

GDB2

, . . . ,

GDB9

GDB0

Graph pictures

Pic1

Pic2

, . . . ,

Pic9

Pic0

Strings

Str1

Str2

, . . . ,

Str9

Str0

System variables

Xmin

Xmax

, and others

•

You can create as many list names as memory will allow

(Chapter 11).

•

Programs have user-defined names and share memory

with variables (Chapter 16).

•

From the home screen or from a program, you can store

to matrices (Chapter 10), lists (Chapter 11), strings

(Chapter 15), system variables such as

Xmax

(Chapter

1),

TblStart

(Chapter 7), and all

functions (Chapters

3, 4, 5, and 6).

•

From an editor, you can store to matrices, lists, and

functions (Chapter 3).

•

From the home screen, a program, or an editor, you can

store a value to a matrix element or a list element.

•

You can use

DRAW STO

menu items to store and recall

graph databases and pictures (Chapter 8).

Using TI-83 Variable Names

Variables and

Defined Items

Notes about

Variables

1-14 Operating the TI

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Values are stored to and recalled from memory using

variable names. When an expression containing the name

of a variable is evaluated, the value of the variable at that

time is used.

To store a value to a variable from the home screen or a

program using the

key, begin on a blank line and

follow these steps.

1. Enter the value you want to store. The value can be an

expression.

2. Press

is copied to the cursor location.

3. Press

and then the letter of the variable to which

you want to store the value.

4. Press

. If you entered an expression, it is

evaluated. The value is stored to the variable.

To display the value of a variable, enter the name on a

blank line on the home screen, and then press

Storing Variable Values

Storing Values in

a Variable

Displaying a

Variable Value

Operating the TI

83 1-15

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To recall and copy variable contents to the current cursor

location, follow these steps. To leave

RCL

, press

‘

1. Press

RCLä

Rcl and the edit cursor are displayed on

the bottom line of the screen.

2. Enter the name of the variable in any of five ways.

•

Press

and then the letter of the variable.

•

Press

LISTä

, and then select the name of the list,

or press

[

•

Press



, and then select the name of the matrix.

•

Press



to display the

VARS

menu or



display the

VARS Y

VARS

menu; then select the type

and then the name of the variable or function.

•

Press



, and then select the name of the

program (in the program editor only).

The variable name you selected is displayed on the

bottom line and the cursor disappears.

3. Press

. The variable contents are inserted where

the cursor was located before you began these steps.

Note:

You can edit the characters pasted to the expression without

affecting the value in memory.

Recalling Variable Values

Using Recall

(RCL)

1-16 Operating the TI

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When you press

on the home screen to evaluate an

expression or execute an instruction, the expression or

instruction is placed in a storage area called

ENTRY

(last

entry). When you turn off the TI

83,

ENTRY

is retained in

memory.

To recall

ENTRY

, press

[

ENTRY

]. The last entry is

pasted to the current cursor location, where you can edit

and execute it. On the home screen or in an editor, the

current line is cleared and the last entry is pasted to the

line.

Because the TI

83 updates

ENTRY

only when you press

, you can recall the previous entry even if you have

begun to enter the next expression.

[

ENTRY

]

The TI

83 retains as many previous entries as possible in

ENTRY

, up to a capacity of 128 bytes. To scroll those

entries, press

[

ENTRY

] repeatedly. If a single entry is

more than 128 bytes, it is retained for

ENTRY

, but it cannot

be placed in the

ENTRY

storage area.

[

ENTRY

]

If you press

[

ENTRY

] after displaying the oldest stored

entry, the newest stored entry is displayed again, then the

next-newest entry, and so on.

[

ENTRY

]

ENTRY (Last Entry) Storage Area

Using ENTRY

(Last Entry)

Accessing a

Operating the TI

83 1-17

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After you have pasted the last entry to the home screen

and edited it (if you chose to edit it), you can execute the

entry. To execute the last entry, press

To reexecute the displayed entry, press

again. Each

reexecution displays an answer on the right side of the

next line; the entry itself is not redisplayed.

To store to

ENTRY

two or more expressions or

instructions, separate each expression or instruction with

a colon, then press

. All expressions and instructions

separated by colons are stored in

ENTRY

When you press

[

ENTRY

], all the expressions and

instructions separated by colons are pasted to the current

cursor location. You can edit any of the entries, and then

execute all of them when you press

For the equation A=

, use trial and error to find the radius of a

circle that covers 200 square centimeters. Use 8 as your first

guess.

[

]

[

]

[

ENTRY

]

[

INS

]

Continue until the answer is as accurate as you want.

Clear Entries (Chapter 18) clears all data that the TI

83 is

holding in the

ENTRY

storage area.

Reexecuting the

Multiple Entry

Values on a Line

Clearing ENTRY

1-18 Operating the TI

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When an expression is evaluated successfully from the

home screen or from a program, the TI

83 stores the

answer to a storage area called

Ans (last answer). Ans may

be a real or complex number, a list, a matrix, or a string.

When you turn off the TI

83, the value in

Ans is retained in

memory.

You can use the variable

Ans to represent the last answer in

most places. Press

[

ANS

] to copy the variable name Ans

to the cursor location. When the expression is evaluated, the

83 uses the value of

Ans in the calculation.

Calculate the area of a garden plot 1.7 meters by 4.2 meters.

Then calculate the yield per square meter if the plot produces a

total of 147 tomatoes.

147

[

ANS

]

You can use Ans as the first entry in the next expression

without entering the value again or pressing

[

ANS

]. On

a blank line on the home screen, enter the function. The

83 pastes the variable name

Ans to the screen, then the

function.

To store an answer, store Ans to a variable before you

evaluate another expression.

Calculate the area of a circle of radius 5 meters. Next, calculate

the volume of a cylinder of radius 5 meters and height 3.3 meters,

and then store the result in the variable V.

[

] 5

Ans (Last Answer) Storage Area

Using Ans in an

Expression

Continuing an

Expression

Storing Answers

Operating the TI

83 1-19

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You can access most TI

83 operations using menus. When

you press a key or key combination to display a menu, one

or more menu names appear on the top line of the screen.

•

The menu name on the left side of the top line is

highlighted. Up to seven items in that menu are

displayed, beginning with item

1, which also is

highlighted.

•

A number or letter identifies each menu item’s place in

the menu. The order is

1 through 9, then 0, then A, B, C,

and so on. The

LIST NAMES

PRGM EXEC

, and

PRGM

EDIT

menus only label items 1 through 9 and 0.

•

When the menu continues beyond the displayed items, a

down arrow (

) replaces the colon next to the last

displayed item.

•

When a menu item ends in an ellipsis, the item displays

a secondary menu or editor when you select it.

To display any other menu listed on the top line, press

until that menu name is highlighted. The cursor

location within the initial menu is irrelevant. The menu is

displayed with the cursor on the first item.

Note:

The Menu Map in Appendix A shows each menu, each

operation under each menu, and the key or key combination you press

to display each menu.

To scroll down the menu items, press

†

. To scroll up the

menu items, press

}

To page down six menu items at a time, press

†

. To

page up six menu items at a time, press

}

. The

green arrows on the calculator, between

†

and

}

, are the

page-down and page-up symbols.

To wrap to the last menu item directly from the first menu

item, press

}

. To wrap to the first menu item directly from

the last menu item, press

†

TI-83 Menus

Using a TI-83

Scrolling a Menu

1-20 Operating the TI

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You can select an item from a menu in either of two ways.

•

Press the number or letter of the item you want to

select. The cursor can be anywhere on the menu, and

the item you select need not be displayed on the screen.

•

Press

†

}

to move the cursor to the item you want,

and then press

After you select an item from a menu, the TI

83 typically

displays the previous screen.

Note:

On the

LIST NAMES

PRGM EXEC

, and

PRGM EDIT

menus, only items

through

and

are labeled in such a way that

you can select them by pressing the appropriate number key. To move

the cursor to the first item beginning with any alpha character or

press the key combination for that alpha character or

. If no items

begin with that character, then the cursor moves beyond it to the next

item.

Calculate

‡

27.



†

You can leave a menu without making a selection in any of

four ways.

•

Press

[

QUIT

] to return to the home screen.

•

Press

‘

to return to the previous screen.

•

Press a key or key combination for a different menu,

such as



[

LIST

•

Press a key or key combination for a different screen,

such as

[

TABLE

Selecting an Item

from a Menu

Leaving a Menu

without Making a

Selection

Operating the TI

83 1-21

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You can enter the names of functions and system variables

in an expression or store to them directly.

To display the

VARS

menu, press



. All

VARS

items display secondary menus, which show the names of

the system variables.

1:Window, 2:Zoom, and 5:Statistics

each access more than one secondary menu.

VARS Y-VARS

1: Window

...

X/Y

, and

U/V/W

variables

2: Zoom

...

ZX/ZY

ZT/Z

, and

variables

3: GDB

...

Graph database

variables

4: Picture

...

Picture

variables

5: Statistics

...

TEST

, and

PTS

variables

6: Table

...

TABLE

variables

7: String

...

String

variables

To display the

VARS Y

VARS

menu, press



1:Function, 2:Parametric, and 3:Polar display secondary

menus of the

function variables.

VARS Y-VARS

1: Function

...

functions

2: Parametric

...

, Y

functions

3: Polar

...

functions

4: On/Off

...

Lets you select/deselect functions

Note:

The sequence variables (

) are located on the keyboard

as the second functions of

−

, and

To select a variable from the

VARS

VARS Y

VARS

menu,

follow these steps.

1. Display the

VARS

VARS Y

VARS

menu.

•

Press



to display the

VARS

menu.

•

Press



to display the

VARS Y

VARS

menu.

2. Select the type of variable, such as

2:Zoom from the

VARS

menu or 3:Polar from the

VARS Y

VARS

menu. A

secondary menu is displayed.

3. If you selected

1:Window, 2:Zoom, or 5:Statistics from

the

VARS

menu, you can press

to display other

secondary menus.

4. Select a variable name from the menu. It is pasted to the

cursor location.

VARS and VARS Y-VARS Menus

VARS Menu

Selecting a

Variable from the

VARS Menu or

VARS Y-VARS

1-22 Operating the TI

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The Equation Operating System (EOS

) defines the order

in which functions in expressions are entered and

evaluated on the TI

83. EOS lets you enter numbers and

functions in a simple, straightforward sequence.

EOS evaluates the functions in an expression in this order:

1 Single-argument functions that precede the

argument, such as

‡

(

, sin(, or log(

2 Functions that are entered after the argument,

such as

, !,

, and conversions

3 Powers and roots, such as 2^5 or 5

‡

4 Permutations (nPr) and combinations (nCr)

5 Multiplication, implied multiplication, and

division

6 Addition and subtraction

7 Relational functions, such as > or



8 Logic operator and

9 Logic operators or and xor

Within a priority level, EOS evaluates functions from left to

right.

Calculations within parentheses are evaluated first.

Multiargument functions, such as

nDeriv(A

,A,6), are

evaluated as they are encountered.

Equation Operating System (EOS™)

Order of

Evaluation

Operating the TI

83 1-23

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The TI

83 recognizes implied multiplication, so you need

not press

to express multiplication in all cases. For

example, the TI

83 interprets

, 4sin(46), 5(1+2), and (2

5)7

as implied multiplication.

Note:

83 implied multiplication rules differ from those of the TI

82.

For example, the TI

83 evaluates

, while the TI

evaluates

1/(2

(Chapter 2).

All calculations inside a pair of parentheses are completed

first. For example, in the expression

4(1+2), EOS first

evaluates the portion inside the parentheses,

1+2, and then

multiplies the answer,

3, by 4.

You can omit the close parenthesis ( ) ) at the end of an

expression. All open parenthetical elements are closed

automatically at the end of an expression. This is also true

for open parenthetical elements that precede the store or

display-conversion instructions.

Note:

An open parenthesis following a list name, matrix name, or

function name does not indicate implied multiplication. It specifies

elements in the list (Chapter 11) or matrix (Chapter 10) and specifies a

value for which to solve the

function.

To enter a negative number, use the negation key. Press

and then enter the number. On the TI

83, negation is in the

third level in the EOS hierarchy. Functions in the first

level, such as squaring, are evaluated before negation.

For example,

, evaluates to a negative number (or 0).

Use parentheses to square a negative number.

Note:

Use the

key for subtraction and the

key for negation. If

you press

to enter a negative number, as in

, or if you

press

to indicate subtraction, as in

, an error occurs. If you

press

, it is interpreted as implied multiplication

(

Implied

Multiplication

Parentheses

Negation

1-24 Operating the TI

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The TI

83 detects errors while performing these tasks.

•

Evaluating an expression

•

Executing an instruction

•

Plotting a graph

•

Storing a value

When the TI

83 detects an error, it returns an error

message as a menu title, such as

ERR:SYNTAX

ERR:DOMAIN

. Appendix B describes each error type and

possible reasons for the error.

•

If you select

1:Quit (or press

[

QUIT

] or

‘

), then

the home screen is displayed.

•

If you select

2:Goto, then the previous screen is

displayed with the cursor at or near the error location.

Note

: If a syntax error occurs in the contents of a Y= function during

program execution, then the

Goto

option returns to the Y= editor, not

to the program.

To correct an error, follow these steps.

1. Note the error type (

ERR:

error type

2. Select

2:Goto, if it is available. The previous screen is

displayed with the cursor at or near the error location.

3. Determine the error. If you cannot recognize the error,

refer to Appendix B.

4. Correct the expression.

Error Conditions

Diagnosing an

Error

Correcting an

Error

Math, Angle, and Test Operations 2-1

Math, An

le, and Test

Operations

Getting Started: Coin Flip

................................

2-2

Keyboard Math Operations

..............................

2-3

MATH

Operations

........................................

2-5

Using the Equation Solver

...............................

2-8

MATH NUM

(Number) Operations

........................

2-13

Entering and Using Complex Numbers

...................

2-16

MATH CPX

(Complex) Operations

.......................

2-18

MATH PRB

(Probability) Operations

.....................

2-20

ANGLE

Operations

.......................................

2-23

TEST

(Relational) Operations

............................

2-24

TEST LOGIC

(Boolean) Operations

......................

2-26

Contents

2-2 Math, Angle, and Test Operations

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Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to model flipping a fair coin 10 times. You want to track

how many of those 10 coin flips result in heads. You want to perform this

simulation 40 times. With a fair coin, the probability of a coin flip resulting in

heads is 0.5 and the probability of a coin flip resulting in tails is 0.5.

1. Begin on the home screen. Press



display the

MATH PRB

menu. Press 7 to

select

7:randBin( (random Binomial).

randBin( is pasted to the home screen. Press

10 to enter the number of coin flips. Press

. Press

5 to enter the probability of

heads. Press

. Press

40 to enter the

number of simulations. Press

2. Press

to evaluate the expression. A

list of 40 elements is displayed. The list

contains the count of heads resulting from

each set of 10 coin flips. The list has 40

elements because this simulation was

performed 40 times. In this example, the

coin came up heads five times in the first

set of 10 coin flips, five times in the second

set of 10 coin flips, and so on.

3. Press

L1ä

to store the data

to the list name

. You then can use the

data for another activity, such as plotting a

histogram (Chapter 12).

4. Press

to view the additional counts

in the list. Ellipses (

...) indicate that the list

continues beyond the screen.

Note:

Since

randBin(

generates random

numbers, your list elements may differ from those

in the example.

Getting Started: Coin Flip

Math, Angle, and Test Operations 2-3

Math operations that are valid for lists return a list

calculated element by element. If you use two lists in the

same expression, they must be the same length.

You can use + (addition,

(subtraction,

(multiplication,

), and

(division,

) with real and

complex numbers, expressions, lists, and matrices. You

cannot use

with matrices.

valueA

valueB valueA

valueB

valueA

valueB valueA

valueB

You can use the trigonometric (trig) functions (sine,

;

cosine,

™

; and tangent,

) with real numbers,

expressions, and lists. The current angle mode setting

affects interpretation. For example,

sin(30) in Radian mode

returns

.9880316241

; in Degree mode it returns .5.

sin(

value

) cos(

value

) tan(

value

)

You can use the inverse trig functions (arcsine,

[

SIN

];

arccosine,

[

COS

]; and arctangent,

[

TAN

]) with

real numbers, expressions, and lists. The current angle

mode setting affects interpretation.

sin

(

value

) cos

(

value

) tan

(

value

)

Note:

The trig functions do not operate on complex numbers.

You can use ^ (power,

›

(square,

), and

‡

(

(square

root,

[

‡

]) with real and complex numbers, expressions,

lists, and matrices. You cannot use

‡

(

with matrices.

value

power value

‡

(

value

)

You can use

(inverse,

—

) with real and complex

numbers, expressions, lists, and matrices. The

multiplicative inverse is equivalent to the reciprocal, 1

value

Keyboard Math Operations

Using Lists with

Math Operations

+ (Addition),

(Subtraction),

(Multiplication),

(Division)

Trigonometric

Functions

^ (Power),

(Square),

‡

( (Square Root)

(Inverse)

2-4 Math, Angle, and Test Operations

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You can use log( (logarithm,

), 10^( (power of 10,

[

]), and ln( (natural log,

) with real or complex

numbers, expressions, and lists.

log(

value

) 10^(

power

)ln(

value

)

e^(

(exponential,

]) returns the constant e raised to

a power. You can use

e^( with real or complex numbers,

expressions, and lists.

e^(

power

)

e (constant,

[

]) is stored as a constant on the TI

83.

Press

[

] to copy e to the cursor location. In

calculations, the TI

83 uses 2.718281828459 for

(negation,

) returns the negative of

value

. You can use

with real or complex numbers, expressions, lists, and

matrices.

value

EOS rules (Chapter 1) determine when negation is

evaluated. For example,

returns a negative number,

because squaring is evaluated before negation. Use

parentheses to square a negated number, as in

(

Note:

On the TI

83, the negation symbol (

) is shorter and higher than

the subtraction sign (

), which is displayed when you press

(Pi,

[

]) is stored as a constant in the TI

83. In

calculations, the TI

83 uses 3.1415926535898 for

log(,

10^(,

ln(

e^( (Exponential)

e (Constant)

(Negation)

(Pi)

Math, Angle, and Test Operations 2-5

To display the

MATH

menu, press



MATH NUM CPX PRB

Frac

Displays the answer as a fraction.

Dec

Displays the answer as a decimal.

Calculates the cube.

‡

(

Calculates the cube root.

‡

Calculates the

root.

6: fMin(

Finds the minimum of a function.

7: fMax(

Finds the maximum of a function.

8: nDeriv(

Computes the numerical derivative.

9: fnInt(

Computes the function integral.

0: Solver

...

Displays the equation solver.

Frac

(display as a fraction) displays an answer as its

rational equivalent. You can use

Frac

with real or complex

numbers, expressions, lists, and matrices. If the answer

cannot be simplified or the resulting denominator is more

than three digits, the decimal equivalent is returned. You

can only use

Frac

following

value

Frac

Dec

(display as a decimal) displays an answer in decimal

form. You can use

Dec

with real or complex numbers,

expressions, lists, and matrices. You can only use

Dec

following

value

Dec

MATH Operations

MATH Menu

Frac,

Dec

2-6 Math, Angle, and Test Operations

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(cube) returns the cube of

value

. You can use

with real

or complex numbers, expressions, lists, and square

matrices.

value

‡

(

(cube root) returns the cube root of

value

. You can use

‡

(

with real or complex numbers, expressions, and lists.

‡

(

value

)

‡

(

root) returns the

root

value

. You can use

‡

with real or complex numbers, expressions, and lists.

root

‡

value

fMin( (function minimum) and fMax( (function maximum)

return the value at which the local minimum or local

maximum value of

expression

with respect to

variable

occurs, between

lower

and

upper

values for

variable

fMin(

and fMax( are not valid in

expression

. The accuracy is

controlled by

tolerance

(if not specified, the default is

5).

fMin(

expression

variable

lower

upper

[

tolerance

]

)

fMax(

expression

variable

lower

upper

[

tolerance

]

)

Note:

In this guidebook, optional arguments and the commas that

accompany them are enclosed in brackets ([ ]).

(Cube),

‡

( (Cube Root)

‡

(Root)

fMin(,

fMax(

Math, Angle, and Test Operations 2-7

nDeriv( (numerical derivative) returns an approximate

derivative of

expression

with respect to

variable

, given the

value

at which to calculate the derivative and

(if not

specified, the default is 1

3). nDeriv( is valid only for real

numbers.

nDeriv(

expression

variable

value

[

]

)

nDeriv( uses the symmetric difference quotient method,

which approximates the numerical derivative value as the

slope of the secant line through these points.

(

)

(

) =

becomes smaller, the approximation usually becomes

more accurate.

You can use nDeriv( once in

expression

. Because of the

method used to calculate

nDeriv(, the TI

83 can return a

false derivative value at a nondifferentiable point.

fnInt( (function integral) returns the numerical integral

(Gauss-Kronrod method) of

expression

with respect to

variable

, given

lower

limit,

upper

limit, and a

tolerance

(if

not specified, the default is 1

5). fnInt( is valid only for real

numbers.

fnInt(

expression

variable

lower

upper

[

tolerance

]

)

Tip:

To speed the drawing of integration graphs (when

fnInt(

is used

in a Y= equation), increase the value of the

Xres

window variable

before you press

nDeriv(

fnInt(

2-8 Math, Angle, and Test Operations

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Solver displays the equation solver, in which you can solve

for any variable in an equation. The equation is assumed to

be equal to zero.

Solver is valid only for real numbers.

When you select

Solver, one of two screens is displayed.

•

The equation editor (see step 1 picture below) is

displayed when the equation variable

eqn is empty.

•

The interactive solver editor (see step 3 picture on page

9) is displayed when an equation is stored in

eqn.

To enter an expression in the equation solver, assuming

that the variable

eqn is empty, follow these steps.

1. Select

0:Solver from the

MATH

menu to display the

equation editor.

2. Enter the expression in any of three ways.

•

Enter the expression directly into the equation

solver.

•

Paste a

variable name from the

VARS Y

VARS

menu to the equation solver.

•

Press

[

RCL

], paste a

variable name from the

VARS Y

VARS

menu, and press

. The

expression is pasted to the equation solver.

The expression is stored to the variable

eqn as you

enter it.

Using the Equation Solver

Solver

Entering an

Expression in the

Equation Solver

Math, Angle, and Test Operations 2-9

3. Press

†

. The interactive solver editor is

displayed.

•

The equation stored in

eqn is set equal to zero and

displayed on the top line.

•

Variables in the equation are listed in the order in

which they appear in the equation. Any values stored

to the listed variables also are displayed.

•

The default lower and upper bounds appear in the

last line of the editor (

bound={

99,1

99}).

•

is displayed in the first column of the bottom line

if the editor continues beyond the screen.

Tip:

To use the solver to solve an equation such as

K=.5MV

, enter

eqn:0=K

.5MV

in the equation editor.

When you enter or edit a value for a variable in the

interactive solver editor, the new value is stored in

memory to that variable.

You can enter an expression for a variable value. It is

evaluated when you move to the next variable.

Expressions must resolve to real numbers at each step

during the iteration.

You can store equations to any

VARS Y

VARS

variables,

such as

or r

, and then reference the variables in the

equation. The interactive solver editor displays all

variables of all

functions referenced in the equation.

Entering and

Editing Variable

Values

2-10 Math, Angle, and Test Operations

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To solve for a variable using the equation solver after an

equation has been stored to

eqn, follow these steps.

1. Select

0:Solver from the

MATH

menu to display the

interactive solver editor, if not already displayed.

2. Enter or edit the value of each known variable. All

variables, except the unknown variable, must contain a

value. To move the cursor to the next variable, press

†

3. Enter an initial guess for the variable for which you are

solving. This is optional, but it may help find the

solution more quickly. Also, for equations with multiple

roots, the TI

83 will attempt to display the solution that

is closest to your guess.

The default guess is calculated as

(

upper +lower

)

Solving for a

Variable in the

Equation Solver

Math, Angle, and Test Operations 2-11

4. Edit

bound={

lower

upper

lower

and

upper

are the

bounds between which the TI

83 searches for a solution.

This is optional, but it may help find the solution more

quickly. The default is

bound={

99,1

99}.

5. Move the cursor to the variable for which you want to

solve and press

[

SOLVE

] (above the

key).

•

The solution is displayed next to the variable for

which you solved. A solid square in the first column

marks the variable for which you solved and

indicates that the equation is balanced. An ellipsis

shows that the value continues beyond the screen.

Note:

When a number continues beyond the screen, be sure to

press

to scroll to the end of the number to see whether it

ends with a negative or positive exponent. A very small number

may appear to be a large number until you scroll right to see

the exponent.

•

The values of the variables are updated in memory.

•

left

rt=

diff

is displayed in the last line of the editor.

diff

is the difference between the left and right sides

of the equation. A solid square in the first column

next to

left

rt= indicates that the equation has been

evaluated at the new value of the variable for which

you solved.

2-12 Math, Angle, and Test Operations

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To edit or replace an equation stored to eqn when the

interactive equation solver is displayed, press

}

until the

equation editor is displayed. Then edit the equation.

Some equations have more than one solution. You can

enter a new initial guess (page 2

10) or new bounds

(page 2

11) to look for additional solutions.

After you solve for a variable, you can continue to explore

solutions from the interactive solver editor. Edit the values

of one or more variables. When you edit any variable value,

the solid squares next to the previous solution and

left

rt=

diff

disappear. Move the cursor to the variable for

which you now want to solve and press

[

SOLVE

The TI

83 solves equations through an iterative process. To

control that process, enter bounds that are relatively close

to the solution and enter an initial guess within those

bounds. This will help to find a solution more quickly. Also,

it will define which solution you want for equations with

multiple solutions.

The function

solve( is available only from

CATALOG

from within a program. It returns a solution (root) of

expression

for

variable

, given an initial

guess

, and

lower

and

upper

bounds within which the solution is sought. The

default for

lower

99. The default for

upper

is 1

99.

solve( is valid only for real numbers.

solve(

expression

variable

guess

[

lower

upper

}])

expression

is assumed equal to zero. The value of

variable

will not be updated in memory.

guess

may be a value or a

list of two values. Values must be stored for every variable

expression

, except

variable

, before

expression

evaluated.

lower

and

upper

must be entered in list format.

Editing an

Equation Stored

to eqn

Equations with

Multiple Roots

Further Solutions

Controlling the

Solution for

Solver or solve(

Using solve( on

the Home Screen

or from a

Program

Math, Angle, and Test Operations 2-13

To display the

MATH NUM

menu, press



MATH NUM CPX PRB

1: abs(

Absolute value

2: round(

Round

3: iPart(

Integer part

4: fPart(

Fractional part

5: int(

Greatest integer

6: min(

Minimum value

7: max(

Maximum value

8: lcm(

Least common multiple

9: gcd(

Greatest common divisor

abs( (absolute value) returns the absolute value of real or

complex (modulus) numbers, expressions, lists, and

matrices.

abs(

value

)

Note:

abs(

is also available on the

MATH CPX

menu.

round( returns a number, expression, list, or matrix

rounded to

#decimals

(



9). If

#decimals

is omitted,

value

is rounded to the digits that are displayed, up to 10 digits.

round(

value

[

#decimals

]

)

MATH NUM (Number) Operations

MATH NUM Menu

abs(

round(

2-14 Math, Angle, and Test Operations

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iPart( (integer part) returns the integer part or parts of real

or complex numbers, expressions, lists, and matrices.

iPart(

value

)

fPart( (fractional part) returns the fractional part or parts of

real or complex numbers, expressions, lists, and matrices.

fPart(

value

)

int( (greatest integer) returns the largest integer



real or

complex numbers, expressions, lists, and matrices.

int(

value

)

Note:

For a given

value

, the result of

int(

is the same as the result of

iPart(

for nonnegative numbers and negative integers, but one integer

less than the result of

iPart(

for negative noninteger numbers.

iPart(,

fPart(

int(

Math, Angle, and Test Operations 2-15

min( (minimum value) returns the smaller of

valueA

and

valueB

or the smallest element in

list

. If

listA

and

listB

are

compared,

min( returns a list of the smaller of each pair of

elements. If

list

and

value

are compared,

min( compares

each element in

list

with

value

max( (maximum value) returns the larger of

valueA

and

valueB

or the largest element in

list

. If

listA

and

listB

are

compared,

max( returns a list of the larger of each pair of

elements. If

list

and

value

are compared,

max( compares

each element in

list

with

value

min(

valueA

valueB

) max(

valueA

valueB

)

min(

list

) max(

list

)

min(

listA

listB

) max(

listA

listB

)

min(

list

value

) max(

list

value

)

Note:

min(

and

max(

also are available on the

LIST MATH

menu.

lcm( returns the least common multiple of

valueA

and

valueB

, both of which must be nonnegative integers. When

listA

and

listB

are specified,

lcm( returns a list of the lcm

of each pair of elements. If

list

and

value

are specified,

lcm( finds the lcm of each element in

list

and

value

gcd( returns the greatest common divisor of

valueA

and

valueB

, both of which must be nonnegative integers. When

listA

and

listB

are specified,

gcd( returns a list of the gcd

of each pair of elements. If

list

and

value

are specified,

gcd( finds the gcd of each element in

list

and

value

lcm(

valueA

valueB

) gcd(

valueA

valueB

)

lcm(

listA

listB

) gcd(

listA

listB

)

lcm(

list

value

) gcd(

list

value

)

min(,

max(

lcm(,

gcd(

2-16 Math, Angle, and Test Operations

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The TI

83 displays complex numbers in rectangular form

and polar form. To select a complex-number mode, press

, and then select either of the two modes.

•

a+b

(rectangular-complex mode)

•

re^

(polar-complex mode)

On the TI

83, complex numbers can be stored to variables.

Also, complex numbers are valid list elements.

Real mode, complex-number results return an error,

unless you entered a complex number as input. For

example, in

Real mode ln(

1) returns an error; in a+b

mode

ln(

1) returns an answer.

Real mode a+b

mode

Complex numbers are stored in rectangular form, but you

can enter a complex number in rectangular form or polar

form, regardless of the mode setting. The components of

complex numbers can be real numbers or expressions that

evaluate to real numbers; expressions are evaluated when

the command is executed.

Radian mode is recommended for complex number

calculations. Internally, the TI

83 converts all entered trig

values to radians, but it does not convert values for

exponential, logarithmic, or hyperbolic functions.

In degree mode, complex identities such as

) = cos(

) +

sin(

) are not generally true because

the values for cos and sin are converted to radians, while

those for e^() are not. For example,

45) = cos(45) +

sin(45) is treated internally as

45) = cos(

/4) +

sin(

/4). Complex identities are

always true in radian mode.

Entering and Using Complex Numbers

Complex-Number

Modes

Entering

Complex

Numbers

Note about

Radian versus

Degree Mode

Math, Angle, and Test Operations 2-17

Complex numbers in results, including list elements, are

displayed in either rectangular or polar form, as specified

by the mode setting or by a display conversion instruction

(page 2

19). In the example below,

re^

and

Radian modes

are set.

Rectangular-complex mode recognizes and displays a

complex number in the form

a+b

, where

is the real

component,

is the imaginary component, and

is a constant

equal to

-1

To enter a complex number in rectangular form, enter the

value of

(

real component

), press

, enter the value

(

imaginary component

), and press

[

] (constant).

real component

(

+ or

)

imaginary componenti

Polar-complex mode recognizes and displays a complex

number in the form

re^

, where

is the magnitude,

is the

base of the natural log,

is the angle, and

is a constant equal

-1

To enter a complex number in polar form, enter the value

(

magnitude

), press

[

] (exponential function),

enter the value of

(

angle

), press

[

] (constant), and

then press

magnitude

e^(

angle

)

Interpreting

Complex Results

Rectangular-

Complex Mode

Polar-Complex

Mode

2-18 Math, Angle, and Test Operations

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To display the

MATH CPX

menu, press



MATH NUM CPX PRB

1: conj(

Returns the complex conjugate.

2: real(

Returns the real part.

3: imag(

Returns the imaginary part.

4: angle(

Returns the polar angle.

5: abs(

Returns the magnitude (modulus).

Rect

Displays the result in rectangular form.

Polar

Displays the result in polar form.

conj( (conjugate) returns the complex conjugate of a

complex number or list of complex numbers.

conj(

) returns

aNb

in a+b

mode.

conj(

e^(

)) returns

e^(

) in re^

mode.

real( (real part) returns the real part of a complex number

or list of complex numbers.

real(

) returns

real(

e^(

)) returns

cos

(

imag( (imaginary part) returns the imaginary (nonreal) part

of a complex number or list of complex numbers.

imag(

) returns

imag(

e^(

)) returns

sin(

)

MATH CPX (Complex) Operations

MATH CPX Menu

conj(

real(

imag(

Math, Angle, and Test Operations 2-19

angle( returns the polar angle of a complex number or list

of complex numbers, calculated as tan

(b/a), where b is

the imaginary part and a is the real part. The calculation is

adjusted by +

in the second quadrant or

in the third

quadrant.

angle(

) returns

tan

(b/a)

angle(

e^(

)) returns

, where

abs( (absolute value) returns the magnitude (modulus),

(real2+imag2)

, of a complex number or list of complex

numbers.

abs(

) returns

(a2+b2)

abs(

e^(

)) returns

(magnitude).

Rect

(display as rectangular) displays a complex result in

rectangular form. It is valid only at the end of an

expression. It is not valid if the result is real.

complex result

Rect

returns

Polar

(display as polar) displays a complex result in polar

form. It is valid only at the end of an expression. It is not

valid if the result is real.

complex result

Polar

returns

e^(

angle(

abs(

Rect

Polar

2-20 Math, Angle, and Test Operations

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To display the

MATH PRB

menu, press



MATH NUM CPX PRB

1: rand

Random-number generator

2: nPr

Number of permutations

3: nCr

Number of combinations

4: !

Factorial

5: randInt(

Random-integer generator

6: randNorm(

Random # from Normal distribution

7: randBin(

Random # from Binomial distribution

rand (random number) generates and returns one or more

random numbers > 0 and < 1. To generate a list of random-

numbers, specify an integer > 1 for

numtrials

(number of

trials). The default for

numtrials

is 1.

rand[(

numtrials

)]

Tip:

To generate random numbers beyond the range of 0 to 1, you

can include

rand

in an expression. For example,

rand

generates a

random number > 0 and < 5.

With each rand execution, the TI

83 generates the same

random-number sequence for a given seed value. The TI

factory-set seed value for

rand is 0. To generate a different

random-number sequence, store any nonzero seed value to

rand. To restore the factory-set seed value, store 0 to rand

or reset the defaults (Chapter 18).

Note:

The seed value also affects

randInt(

randNorm(

, and

randBin(

instructions (page 2

22).

MATH PRB (Probability) Operations

MATH PRB Menu

rand

Math, Angle, and Test Operations 2-21

nPr (number of permutations) returns the number of

permutations of

items

taken

number

at a time.

items

and

number

must be nonnegative integers. Both

items

and

number

can be lists.

items

nPr

number

nCr (number of combinations) returns the number of

combinations of

items

taken

number

at a time.

items

and

number

must be nonnegative integers. Both

items

and

number

can be lists.

items

nCr

number

! (factorial) returns the factorial of either an integer or a

multiple of .5. For a list, it returns factorials for each

integer or multiple of .5.

value

must be

‚L

.5 and



69.

value

Note:

The factorial is computed recursively using the relationship

(n+1)! = n

n!, until n is reduced to either 0 or

1/2. At that point, the

definition 0!=1 or the definition (

2)!=

‡p

is used to complete the

calculation. Hence:

n!=n

...

1, if n is an integer

‚

n!= n

...

‡p

, if n+1

2 is an integer

‚

n! is an error, if neither n nor n+1

2 is an integer

‚

(The variable n equals

value

in the syntax description above.)

nPr,

nCr

! (Factorial)

2-22 Math, Angle, and Test Operations

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randInt( (random integer) generates and displays a random

integer within a range specified by

lower

and

upper

integer

bounds. To generate a list of random numbers, specify an

integer >1 for

numtrials

(number of trials); if not

specified, the default is 1.

randInt(

lower

upper

[

numtrials

]

)

randNorm( (random Normal) generates and displays a

random real number from a specified Normal distribution.

Each generated value could be any real number, but most

will be within the interval [

+3(

)]. To generate a

list of random numbers, specify an integer > 1 for

numtrials

(number of trials); if not specified, the default

is 1.

randNorm(

numtrials

]

)

randBin( (random Binomial) generates and displays a

random integer from a specified Binomial distribution.

numtrials

(number of trials) must be

‚

prob

(probability

of success) must be

‚

0 and



1. To generate a list of

random numbers, specify an integer > 1 for

numsimulations

(number of simulations); if not specified,

the default is 1.

randBin(

numtrials

prob

[

numsimulations

]

)

Note:

The seed value stored to

rand

also affects

randInt(

randNorm(

, and

randBin(

instructions (page 2

20).

randInt(

randNorm(

randBin(

Math, Angle, and Test Operations 2-23

To display the

ANGLE

menu, press

[

ANGLE

]. The

ANGLE

menu displays angle indicators and instructions. The

Radian/Degree mode setting affects the TI

83’s

interpretation of

ANGLE

menu entries.

ANGLE

Degree notation

2: '

DMS minute notation

Radian notation

DMS

Displays as degree/minute/second

5: R

Pr(

Returns

, given

and

6: R

(

Returns

, given

and

7: P

Rx(

Returns

, given

and

8: P

Ry(

Returns

, given

and

DMS (degrees/minutes/seconds) entry notation comprises

the degree symbol (

), the minute symbol ('), and the

second symbol (

").

degrees

must be a real number;

minutes

and

seconds

must be real numbers

‚

degrees

minutes

seconds

For example, enter for 30 degrees, 1 minute, 23 seconds. If

the angle mode is not set to

Degree, you must use

so that

the TI

83 can interpret the argument as degrees, minutes,

and seconds.

Degree mode Radian mode

(degree) designates an angle or list of angles as degrees,

regardless of the current angle mode setting. In

Radian

mode, you can use

to convert degrees to radians.

value

{

value1

value2

value3

value4

,...,

value n

}

also designates

degrees

(D) in DMS format.

' (minutes) designates

minutes

(M) in DMS format.

" (seconds) designates

seconds

(S) in DMS format.

Note:

is not on the

ANGLE

menu. To enter

, press

[

ANGLE Operations

ANGLE Menu

DMS Entry

Notation

(Degree)

2-24 Math, Angle, and Test Operations

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(radians) designates an angle or list of angles as radians,

regardless of the current angle mode setting. In

Degree

mode, you can use

to convert radians to degrees.

value

Degree mode

DMS

(degree/minute/second) displays

answer

in DMS

format (page 2

23). The mode setting must be

Degree for

answer

to be interpreted as degrees, minutes, and seconds.

DMS

is valid only at the end of a line.

answer

DMS

Pr( converts rectangular coordinates to polar

coordinates and returns

r. R

( converts rectangular

coordinates to polar coordinates and returns

and

can

be lists.

Pr(

), R

(

)

Note:

Radian

mode is set.

Rx(

converts polar coordinates to rectangular

coordinates and returns

x. P

Ry( converts polar

coordinates to rectangular coordinates and returns

and

can be lists.

Rx(

), P

Ry(

)

Note:

Radian

mode is set.

(Radians)

DMS

Pr(,

Rx(,

Ry(

Math, Angle, and Test Operations 2-25

To display the

TEST

menu, press

[

TEST

This operator... Returns 1 (true) if...

TEST LOGIC

Equal

Not equal to

Greater than

‚

Greater than or equal to

Less than



Less than or equal to

Relational operators compare

valueA

and

valueB

and

return

if the test is true or

if the test is false.

valueA

and

valueB

can be real numbers, expressions, or lists. For

and

only,

valueA

and

valueB

also can be matrices or

complex numbers. If

valueA

and

valueB

are matrices, both

must have the same dimensions.

Relational operators are often used in programs to control

program flow and in graphing to control the graph of a

function over specific values.

valueA

valueB valueA

valueB

valueA

valueB valueA

‚

valueB

valueA

valueB valueA



valueB

Relational operators are evaluated after mathematical

functions according to EOS rules (Chapter 1).

•

The expression

2+2=2+3

returns

. The TI

83 performs

the addition first because of EOS rules, and then it

compares 4 to 5.

•

The expression

2+(2=2)+3

returns

. The TI

83 performs

the relational test first because it is in parentheses, and

then it adds 2, 1, and 3.

TEST (Relational) Operations

TEST Menu

‚



Using Tests

2-26 Math, Angle, and Test Operations

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To display the

TEST LOGIC

menu, press

TESTä

This operator... Returns a 1 (true) if...

TEST LOGIC

1: and

Both values are nonzero (true).

2: or

At least one value is nonzero (true).

3: xor

Only one value is zero (false).

4: not(

The value is zero (false).

Boolean operators are often used in programs to control

program flow and in graphing to control the graph of the

function over specific values. Values are interpreted as

zero (false) or nonzero (true).

and

, and

xor

(exclusive or) return a value of

if an

expression is true or

if an expression is false, according

to the table below.

valueA

and

valueB

can be real

numbers, expressions, or lists.

valueA

and

valueB

valueA

valueB

valueA

xor

valueB

valueA valueB and or xor

0 returns

110

0 0 returns

011

0 returns

011

0 0 returns

000

not(

returns

value

(which can be an expression) is

not(

value

)

Boolean logic is often used with relational tests. In the

following program, the instructions store

into

TEST LOGIC (Boolean) Operations

TEST LOGIC

Boolean

Operators

and,

or,

xor

not(

Using Boolean

Operations

Function Graphing 3-1

8303FUNC.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:16 PM Printed: 02/19/01 1:50

PM Page 1 of 28

Function

Graphin

Getting Started: Graphing a Circle

.......................

3-2

Defining Graphs

.........................................

3-3

Setting the Graph Modes

.................................

3-4

Defining Functions

......................................

3-5

Selecting and Deselecting Functions

.....................

3-7

Setting Graph Styles for Functions

.......................

3-9

Setting the Viewing Window Variables

...................

3-11

Setting the Graph Format

................................

3-13

Displaying Graphs

.......................................

3-15

Exploring Graphs with the Free-Moving Cursor

..........

3-17

Exploring Graphs with

TRACE

...........................

3-18

Exploring Graphs with the

ZOOM

Instructions

...........

3-20

Using

ZOOM MEMORY

..................................

3-23

Using the

CALC

(Calculate) Operations

..................

3-25

Contents

3-2 Function Graphing

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Getting Started is a fast-paced introduction. Read the chapter for details.

Graph a circle of radius 10, centered on the origin in the standard viewing

window. To graph this circle, you must enter separate formulas for the upper

and lower portions of the circle. Then use

ZSquare (zoom square) to adjust the

display and make the functions appear as a circle.

1. In

Func mode, press

to display the

editor. Press

‡

100

„

to enter the expression Y=

‡

(100

which defines the top half of the circle.

The expression Y=

L‡

(100

) defines the

bottom half of the circle. On the TI

83, you

can define one function in terms of another.

To define

, press

to enter the

negation sign. Press



to display the

VARS Y

VARS

menu. Then press

select

1:Function. The

FUNCTION

secondary

menu is displayed. Press

1 to select 1:Y

2. Press

6 to select 6:ZStandard. This is a

quick way to reset the window variables to

the standard values. It also graphs the

functions; you do not need to press

Notice that the functions appear as an

ellipse in the standard viewing window.

3. To adjust the display so that each pixel

represents an equal width and height, press

5 to select 5:ZSquare. The functions

are replotted and now appear as a circle on

the display.

4. To see the ZSquare window variables, press

and notice the new values for

Xmin,

Xmax, Ymin, and Ymax.

Getting Started: Graphing a Circle

Function Graphing 3-3

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Chapter 3 specifically describes function graphing, but the

steps shown here are similar for each TI

83 graphing

mode. Chapters 4, 5, and 6 describe aspects that are unique

to parametric graphing, polar graphing, and sequence

graphing.

To define a graph in any graphing mode, follow these

steps. Some steps are not always necessary.

1. Press

and set the appropriate graph mode

(page 3

4).

2. Press

and enter, edit, or select one or more functions

in the

editor (page 3

5 and 3

7).

3. Deselect stat plots, if necessary (page 3

7).

4. Set the graph style for each function (page 3

9).

5. Press

and define the viewing window variables

(page 3

11).

6. Press

[

FORMAT

] and select the graph format settings

(page 3

13).

After you have defined a graph, press

to display it.

Explore the behavior of the function or functions using the

83 tools described in this chapter.

You can store the elements that define the current graph to

any of 10 graph database variables (

GDB1 through GDB9,

and

GDB0; Chapter 8). To recreate the current graph later,

simply recall the graph database to which you stored the

original graph.

These types of information are stored in a

GDB.

•

functions

•

Graph style settings

•

Window settings

•

Format settings

You can store a picture of the current graph display to any

of 10 graph picture variables (

Pic1 through Pic9, and Pic0;

Chapter 8). Then you can superimpose one or more stored

pictures onto the current graph.

Defining Graphs

TI-83—Graphing

Mode Similarities

Defining a Graph

Displaying and

Exploring a

Graph

Saving a Graph

for Later Use

3-4 Function Graphing

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To display the mode screen, press

. The default

settings are highlighted below. To graph functions, you

must select

Func mode before you enter values for the

window variables and before you enter the functions.

The TI

83 has four graphing modes.

•

Func (function graphing)

•

Par (parametric graphing; Chapter 4)

•

Pol (polar graphing; Chapter 5)

•

Seq (sequence graphing; Chapter 6)

Other mode settings affect graphing results. Chapter 1

describes each mode setting.

•

Float or 0123456789 (fixed) decimal mode affects

displayed graph coordinates.

•

Radian or Degree angle mode affects interpretation of

some functions.

•

Connected or Dot plotting mode affects plotting of

selected functions.

•

Sequential or Simul graphing-order mode affects

function plotting when more than one function is

selected.

To set the graphing mode and other modes from a

program, begin on a blank line in the program editor and

follow these steps.

1. Press

to display the mode settings.

2. Press

†

, and

}

to place the cursor on the mode

that you want to select.

3. Press

to paste the mode name to the cursor

location.

The mode is changed when the program is executed.

Setting the Graph Modes

Checking and

Changing the

Graphing Mode

Setting Modes

from a Program

Function Graphing 3-5

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To display the

editor, press

. You can store up to 10

functions to the function variables

through Y

, and Y

You can graph one or more defined functions at once. In

this example, functions

and Y

are defined and selected.

To define or edit a function, follow these steps.

1. Press

to display the

editor.

2. Press

†

to move the cursor to the function you want to

define or edit. To erase a function, press

‘

3. Enter or edit the expression to define the function.

•

You may use functions and variables (including

matrices and lists) in the expression. When the

expression evaluates to a nonreal number, the value

is not plotted; no error is returned.

•

The independent variable in the function is

X. Func

mode defines

„

as X. To enter X, press

„

or press

[

•

When you enter the first character, the

= is

highlighted, indicating that the function is selected.

As you enter the expression, it is stored to the variable

as a user-defined function in the

editor.

4. Press

†

to move the cursor to the next

function.

Defining Functions

Displaying

Functions in the

Y= Editor

Defining or

Editing a

Function

3-6 Function Graphing

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To define a function from the home screen or a program,

begin on a blank line and follow these steps.

1. Press

[

], enter the expression, and then press

[

] again.

2. Press

3. Press



1 to select 1:Function from the

VARS Y

VARS

menu.

4. Select the function name, which pastes the name to the

cursor location on the home screen or program editor.

5. Press

to complete the instruction.

expression

When the instruction is executed, the TI

83 stores the

expression to the designated variable

, selects the

function, and displays the message

Done.

You can calculate the value of a

function Y

at a

specified

value

X. A list of

values

returns a list.

(

value

)

({

value1

value2

value3

. . .

value n

})

Defining a

Function from

the Home Screen

or a Program

Evaluating Y=

Functions in

Expressions

Function Graphing 3-7

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You can select and deselect (turn on and turn off) a

function in the

editor. A function is selected when the =

sign is highlighted. The TI

83 graphs only the selected

functions. You can select any or all functions

through

, and Y

To select or deselect a function in the

editor, follow

these steps.

1. Press

to display the

editor.

2. Move the cursor to the function you want to select or

deselect.

3. Press

to place the cursor on the function’s

= sign.

4. Press

to change the selection status.

When you enter or edit a function, it is selected

automatically. When you clear a function, it is deselected.

To view and change the on/off status of a stat plot in the

editor, use Plot1 Plot2 Plot3 (the top line of the

editor). When a plot is on, its name is highlighted on this

line.

To change the on/off status of a stat plot from the

editor, press

}

and

to place the cursor on Plot1,

Plot2, or Plot3, and then press

Selecting and Deselecting Functions

Selecting and

Deselecting a

Function

Turning On or

Turning Off a Stat

Plot in the Y=

Editor

Plot1

is turned on.

Plot2

and

Plot3

are turned off.

3-8 Function Graphing

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To select or deselect a function from the home screen or a

program, begin on a blank line and follow these steps.

1. Press



to display the

VARS Y

VARS

menu.

2. Select

4:On/Off to display the

ON/OFF

secondary menu.

3. Select

1:FnOn to turn on one or more functions or

2:FnOff to turn off one or more functions. The

instruction you select is copied to the cursor location.

4. Enter the number (

1 through 9, or 0; not the variable

) of each function you want to turn on or turn off.

•

If you enter two or more numbers, separate them

with commas.

•

To turn on or turn off all functions, do not enter a

number after

FnOn or FnOff.

FnOn[

function#

, . . .,

function n

]

FnOff[

function#

, . . .,

function n

]

5. Press

. When the instruction is executed, the

status of each function in the current mode is set and

Done is displayed.

For example, in

Func mode, FnOff :FnOn 1,3 turns off all

functions in the

editor, and then turns on Y

and Y

Selecting and

Deselecting

Functions from

the Home Screen

or a Program

Function Graphing 3-9

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This table describes the graph styles available for function

graphing. Use the styles to visually differentiate functions

to be graphed together. For example, you can set

as a

solid line,

as a dotted line, and Y

as a thick line.

Icon Style Description

Line A solid line connects plotted points; this is

the default in

Connected mode

Thick A thick solid line connects plotted points

Above Shading covers the area a*bove the graph

Below Shading covers the area below the graph

Path A circular cursor traces the leadin

e of

the graph and draws a path

Animate A circular cursor traces the leadin

e of

the graph without drawing a path

Dot A small dot represents each plotted point;

this is the default in

Dot mode

Note:

Some graph styles are not available in all graphing modes.

Chapters 4, 5, and 6 list the styles for

Par

Pol

, and

Seq

modes.

To set the graph style for a function, follow these steps.

1. Press

to display the

editor.

2. Press

†

and

}

to move the cursor to the function.

3. Press

to move the cursor left, past the

= sign, to

the graph style icon in the first column. The insert

cursor is displayed. (Steps 2 and 3 are interchangeable.)

4. Press

repeatedly to rotate through the graph

styles. The seven styles rotate in the same order in

which they are listed in the table above.

5. Press

}

, or

†

when you have selected a style.

Setting Graph Styles for Functions

Graph Style

Icons in the Y=

Editor

Setting the Graph

Style

3-10 Function Graphing

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When you select

for two or more functions, the

83 rotates through four shading patterns.

•

Vertical lines shade the first function with a

graph style.

•

Horizontal lines shade the second.

•

Negatively sloping diagonal lines shade the third.

•

Positively sloping diagonal lines shade the fourth.

•

The rotation returns to vertical lines for the fifth

function, repeating the order described above.

When shaded areas intersect, the patterns overlap.

Note:

When

is selected for a Y= function that graphs a family of

curves, such as

Y1={1,2,3}X

, the four shading patterns rotate for

each member of the family of curves.

To set the graph style from a program, select

H:GraphStyle(

from the

PRGM CTL

menu. To display this menu, press



while in the program editor.

function#

is the number

of the

function name in the current graphing mode.

graphstyle#

is an integer from

that corresponds to

the graph style, as shown below.

(line)

(thick)

(above)

(below)

(path)

(animate)

(dot)

GraphStyle(

function#

graphstyle#

)

For example, when this program is executed in

Func

mode,

GraphStyle(1,3)

sets

(above).

Shading Above

and Below

Setting a Graph

Style from a

Program

Function Graphing 3-11

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The viewing window is the portion of the coordinate plane

defined by

Xmin, Xmax, Ymin, and Ymax. Xscl (X scale)

defines the distance between tick marks on the x-axis.

Yscl

(Y scale) defines the distance between tick marks on the

y-axis. To turn off tick marks, set

Xscl=0 and Yscl=0.

Xmax

Ymin

Ymax

Xscl

Yscl

Xmin

To display the current window variable values, press

. The window editor above and to the right shows

the default values in

Func graphing mode and Radian angle

mode. The window variables differ from one graphing

mode to another.

Xres sets pixel resolution (1 through 8) for function graphs

only. The default is

•

Xres=1, functions are evaluated and graphed at each

pixel on the x-axis.

•

Xres=8, functions are evaluated and graphed at every

eighth pixel along the x-axis.

Tip:

Small

Xres

values improve graph resolution but may cause the

83 to draw graphs more slowly.

To change a window variable value from the window

editor, follow these steps.

1. Press

†

}

to move the cursor to the window

variable you want to change.

2. Edit the value, which can be an expression.

•

Enter a new value, which clears the original value.

•

Move the cursor to a specific digit, and then edit it.

3. Press

†

, or

}

. If you entered an expression, the

83 evaluates it. The new value is stored.

Note:

Xmin

Xmax

and

Ymin

Ymax

must be true in order to graph.

Setting the Viewing Window Variables

The TI-83 Viewing

Window

Displaying the

Window

Variables

Changing a

Window Variable

Value

3-12 Function Graphing

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To store a value, which can be an expression, to a window

variable, begin on a blank line and follow these steps.

1. Enter the value you want to store.

2. Press

3. Press



to display the

VARS

menu.

4. Select

1:Window to display the Func window variables

(

X/Y

secondary menu).

•

Press

to display the

Par and Pol window variables

(

secondary menu).

•

Press

to display the

Seq window variables

(

U/V/W

secondary menu).

5. Select the window variable to which you want to store a

value. The name of the variable is pasted to the current

cursor location.

6. Press

to complete the instruction.

When the instruction is executed, the TI

83 stores the

value to the window variable and displays the value.

The variables

and

(items 8 and 9 on the

VARS

(1:Window)

X/Y

secondary menu) define the distance from

the center of one pixel to the center of any adjacent pixel

on a graph (graphing accuracy).

X and

Y are calculated

from

Xmin, Xmax, Ymin, and Ymax when you display a

graph.

(Xmax

Xmin)

Y =

(Ymax

Ymin)

You can store values to

and

. If you do, Xmax and

Ymax are calculated from

, Xmin,

, and Ymin.

Storing to a

Window Variable

from the Home

Screen or a

Program

X and

Function Graphing 3-13

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To display the format settings, press

[

FORMAT

]. The

default settings are highlighted below.

RectGC PolarGC

Sets cursor coordinates.

CoordOn CoordOff

Sets coordinates display on or off.

GridOff GridOn

Sets grid off or on.

AxesOn AxesOff

Sets axes on or off.

LabelOff LabelOn

Sets axes label off or on.

ExprOn ExprOff

Sets expression display on or off.

Format settings define a graph’s appearance on the display.

Format settings apply to all graphing modes.

Seq graphing

mode has an additional mode setting (Chapter 6).

To change a format setting, follow these steps.

1. Press

†

}

, and

as necessary to move the cursor

to the setting you want to select.

2. Press

to select the highlighted setting.

RectGC (rectangular graphing coordinates) displays the

cursor location as rectangular coordinates

X and Y.

PolarGC (polar graphing coordinates) displays the cursor

location as polar coordinates

R and

The

RectGC/PolarGC setting determines which variables

are updated when you plot the graph, move the free-

moving cursor, or trace.

•

RectGC updates X and Y; if CoordOn format is selected,

X and Y are displayed.

•

PolarGC updates X, Y, R, and

; if CoordOn format is

selected, R and

are displayed.

Setting the Graph Format

Displaying the

Format Settings

Changing a

Format Setting

RectGC, PolarGC

3-14 Function Graphing

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CoordOn (coordinates on) displays the cursor coordinates

at the bottom of the graph. If

ExprOff format is selected,

the function number is displayed in the top-right corner.

CoordOff (coordinates off) does not display the function

number or coordinates.

Grid points cover the viewing window in rows that

correspond to the tick marks (page 3

11) on each axis.

GridOff does not display grid points.

GridOn displays grid points.

AxesOn displays the axes.

AxesOff does not display the axes.

This overrides the

LabelOff/LabelOn format setting.

LabelOff and LabelOn determine whether to display labels

for the axes (

X and Y), if AxesOn format is also selected.

ExprOn and ExprOff determine whether to display the

expression when the trace cursor is active. This format

setting also applies to stat plots.

When

ExprOn is selected, the expression is displayed in the

top-left corner of the graph screen.

When

ExprOff and CoordOn both are selected, the number

in the top-right corner specifies which function is being

traced.

CoordOn,

CoordOff

GridOff, GridOn

AxesOn, AxesOff

LabelOff,

LabelOn

ExprOn, ExprOff

Function Graphing 3-15

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To display the graph of the selected function or functions,

press

TRACE

ZOOM

instructions, and

CALC

operations display the graph automatically. As the TI

plots the graph, the busy indicator is on. As the graph is

plotted,

X and Y are updated.

While plotting a graph, you can pause or stop graphing.

•

Press

to pause; then press

to resume.

•

Press

to stop; then press

to redraw.

Smart Graph is a TI

83 feature that redisplays the last

graph immediately when you press

, but only if all

graphing factors that would cause replotting have

remained the same since the graph was last displayed.

If you performed any of these actions since the graph was

last displayed, the TI

83 will replot the graph based on new

values when you press

•

Changed a mode setting that affects graphs

•

Changed a function in the current picture

•

Selected or deselected a function or stat plot

•

Changed the value of a variable in a selected function

•

Changed a window variable or graph format setting

•

Cleared drawings by selecting

ClrDraw

•

Changed a stat plot definition

Displaying Graphs

Displaying a New

Graph

Pausing or

Stopping a Graph

Smart Graph

3-16 Function Graphing

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On the TI

83, you can graph one or more new functions

without replotting existing functions. For example, store

sin(X) to Y

in the

editor and press

. Then store

cos(X) to Y

and press

again. The function Y

graphed on top of

, the original function.

If you enter a list (Chapter 11) as an element in an

expression, the TI

83 plots the function for each value in

the list, thereby graphing a family of curves. In

Simul

graphing-order mode, it graphs all functions sequentially

for the first element in each list, and then for the second,

and so on.

{2,4,6}sin(X) graphs three functions: 2 sin(X), 4 sin(X), and

6 sin(X).

{2,4,6}sin({1,2,3}X) graphs 2 sin(X), 4 sin(2X), and 6 sin(3X).

Note:

When using more than one list, the lists must have the same

dimensions.

Overlaying

Functions on a

Graph

Graphing a

Family of Curves

Function Graphing 3-17

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When a graph is displayed, press

}

, or

†

to move

the cursor around the graph. When you first display the

graph, no cursor is visible. When you press

}

, or

†

the cursor moves from the center of the viewing window.

As you move the cursor around the graph, the coordinate

values of the cursor location are displayed at the bottom of

the screen if

CoordOn format is selected. The Float/Fix

decimal mode setting determines the number of decimal

digits displayed for the coordinate values.

To display the graph with no cursor and no coordinate

values, press

‘

. When you press

}

, or

†

, the cursor moves from the same position.

The free-moving cursor moves from pixel to pixel on the

screen. When you move the cursor to a pixel that appears

to be on the function, the cursor may be near, but not

actually on, the function. The coordinate value displayed at

the bottom of the screen actually may not be a point on the

function. To move the cursor along a function, use

(page 3

18).

The coordinate values displayed as you move the cursor

approximate actual math coordinates, *accurate to within

the width and height of the pixel. As

Xmin, Xmax, Ymin, and

Ymax get closer together (as in a ZoomIn) graphing

accuracy increases, and the coordinate values more closely

approximate the math coordinates.

Exploring Graphs with the Free-Moving Cursor

Free-Moving

Cursor

Graphing

Accuracy

Free-moving cursor “on” the curve

3-18 Function Graphing

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Use

TRACE

to move the cursor from one plotted point to

the next along a function. To begin a trace, press

. If

the graph is not displayed already, press

to display

it. The trace cursor is on the first selected function in the

editor, at the middle X value on the screen. The cursor

coordinates are displayed at the bottom of the screen if

CoordOn format is selected. The

expression is displayed

in the top-left corner of the screen, if

ExprOn format is

selected.

To move the TRACE cursor . . . do this:

. . . to the previous or next plotted

point,

press

. . . five plotted points on a function

(Xres affects this),

press

. . . to any valid X value on a function, enter a value, and

then press

. . . from one function to another, press

}

†

When the trace cursor moves along a function, the

Y value

is calculated from the

X value; that is, Y=Y

(X). If the

function is undefined at an

X value, the Y value is blank.

If you move the trace cursor beyond the top or bottom of

the screen, the coordinate values at the bottom of the

screen continue to change appropriately.

To move the trace cursor from function to function, press

†

and

}

. The cursor follows the order of the selected

functions in the

editor. The trace cursor moves to each

function at the same

X value. If ExprOn format is selected,

the expression is updated.

Exploring Graphs with TRACE

Beginning a

Trace

Moving the Trace

Cursor

Moving the Trace

Cursor from

Function to

Function

Trace cursor on the curve

Function Graphing 3-19

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To move the trace cursor to any valid X value on the

current function, enter the value. When you enter the first

digit, an

X= prompt and the number you entered are

displayed in the bottom-left corner of the screen. You can

enter an expression at the

X= prompt. The value must be

valid for the current viewing window. When you have

completed the entry, press

to move the cursor.

Note:

This feature does not apply to stat plots.

If you trace a function beyond the left or right side of the

screen, the viewing window automatically pans to the left

or right.

Xmin and Xmax are updated to correspond to the

new viewing window.

While tracing, you can press

to adjust the viewing

window so that the cursor location becomes the center of

the new viewing window, even if the cursor is above or

below the display. This allows panning up and down. After

Quick Zoom, the cursor remains in

TRACE

When you leave and return to

TRACE

, the trace cursor is

displayed in the same location it was in when you left

TRACE

, unless Smart Graph has replotted the graph

(page 3

15).

On a blank line in the program editor, press

. The

instruction

Trace is pasted to the cursor location. When the

instruction is encountered during program execution, the

graph is displayed with the trace cursor on the first

selected function. As you trace, the cursor coordinate

values are updated. When you finish tracing the functions,

press

to resume program execution.

Moving the Trace

Cursor to Any

Valid X Value

Panning to the

Left or Right

Quick Zoom

Leaving and

Returning to

TRACE

Using TRACE in

a Program

3-20 Function Graphing

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To display the

ZOOM

menu, press

. You can adjust the

viewing window of the graph quickly in several ways. All

ZOOM

instructions are accessible from programs.

ZOOM MEMORY

1: ZBox

Draws a box to define the viewing window.

2: Zoom In

Magnifies the graph around the cursor.

3: Zoom Out

Views more of a graph around the cursor.

4: ZDecimal

Sets

X and

Y to 0.1.

5: ZSquare

Sets equal-size pixels on the X and Y axes.

6: ZStandard

Sets the standard window variables.

7: ZTrig

Sets the built-in trig window variables.

8: ZInteger

Sets integer values on the X and Y axes.

9: ZoomStat

Sets the values for current stat lists.

0: ZoomFit

Fits YMin and YMax between XMin and XMax.

When you select

1:ZBox, 2:Zoom In, or 3:Zoom Out, the

cursor on the graph becomes the zoom cursor (

), a

smaller version of the free-moving cursor (

+).

To define a new viewing window using

ZBox, follow these

steps.

1. Select

1:ZBox from the

ZOOM

menu. The zoom cursor is

displayed at the center of the screen.

2. Move the zoom cursor to any spot you want to define as

a corner of the box, and then press

. When you

move the cursor away from the first defined corner, a

small, square dot indicates the spot.

3. Press

}

, or

†

. As you move the cursor, the sides

of the box lengthen or shorten proportionately on the

screen.

Note:

To cancel

ZBox

before you press

, press

‘

4. When you have defined the box, press

to replot

the graph.

To use ZBox to define another box within the new graph,

repeat steps 2 through 4. To cancel

ZBox, press

‘

Exploring Graphs with the ZOOM Instructions

ZOOM Menu

Zoom Cursor

ZBox

Function Graphing 3-21

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Zoom In magnifies the part of the graph that surrounds the

cursor location.

Zoom Out displays a greater portion of the

graph, centered on the cursor location. The

XFact and

YFact settings determine the extent of the zoom.

To zoom in on a graph, follow these steps.

1. Check

XFact and YFact (page 3

24); change as needed.

2. Select

2:Zoom In from the

ZOOM

menu. The zoom

cursor is displayed.

3. Move the zoom cursor to the point that is to be the

center of the new viewing window.

4. Press

. The TI

83 adjusts the viewing window by

XFact and YFact; updates the window variables; and

replots the selected functions, centered on the cursor

location.

5. Zoom in on the graph again in either of two ways.

•

To zoom in at the same point, press

•

To zoom in at a new point, move the cursor to the

point that you want as the center of the new viewing

window, and then press

To zoom out on a graph, select

3:Zoom Out and repeat

steps 3 through 5.

To cancel

Zoom In or Zoom Out, press

‘

ZDecimal replots the functions immediately. It updates the

window variables to preset values, as shown below. These

values set

X and

Y equal to 0.1 and set the X and Y value

of each pixel to one decimal place.

Xmin=

4.7 Ymin=

3.1

Xmax=4.7 Ymax=3.1

Xscl=1 Yscl=1

ZSquare

replots the functions immediately. It redefines the

viewing window based on the current values of the

window variables. It adjusts in only one direction so that

, which makes the graph of a circle look like a circle.

Xscl and Yscl remain unchanged. The midpoint of the

current graph (not the intersection of the axes) becomes

the midpoint of the new graph.

Zoom In,

Zoom Out

ZDecimal

ZSquare

3-22 Function Graphing

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ZStandard replots the functions immediately. It updates the

window variables to the standard values shown below.

Xmin=

10 Ymin=

10 Xres=1

Xmax=10 Ymax=10

Xscl=1 Yscl=1

ZTrig

replots the functions immediately. It updates the

window variables to preset values that are appropriate for

plotting trig functions. Those preset values in

Radian mode

are shown below.

Xmin=

(47

24)

Ymin=

Xmax=(47

24)

Ymax=4

Xscl=

/2 Yscl=1

ZInteger

redefines the viewing window to the dimensions

shown below. To use

ZInteger, move the cursor to the point

that you want to be the center of the new window, and

then press

;

ZInteger replots the functions.

X=1 Xscl=10

Y=1 Yscl=10

ZoomStat

redefines the viewing window so that all

statistical data points are displayed. For regular and

modified box plots, only

Xmin and Xmax are adjusted.

ZoomFit replots the functions immediately. ZoomFit

recalculates YMin and YMax to include the minimum and

maximum

Y values of the selected functions between the

current

XMin and XMax. XMin and XMax are not changed.

ZStandard

ZTrig

ZInteger

ZoomStat

ZoomFit

Function Graphing 3-23

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To display the

ZOOM MEMORY

menu, press

ZOOM MEMORY

1:ZPrevious

Uses the previous viewing window.

2:ZoomSto

Stores the user-defined window.

3:ZoomRcl

Recalls the user-defined window.

4:SetFactors

...

Changes

Zoom In

and

Zoom Out

factors.

ZPrevious

replots the graph using the window variables of

the graph that was displayed before you executed the last

ZOOM

instruction.

ZoomSto

immediately stores the current viewing window.

The graph is displayed, and the values of the current

window variables are stored in the user-defined

ZOOM

variables

ZXmin

ZXmax

ZXscl

ZYmin

ZYmax

ZYscl

, and

ZXres

These variables apply to all graphing modes. For example,

changing the value of

ZXmin

Func

mode also changes it

Par

mode.

ZoomRcl

graphs the selected functions in a user-defined

viewing window. The user-defined viewing window is

determined by the values stored with the

ZoomSto

instruction. The window variables are updated with the

user-defined values, and the graph is plotted.

Using ZOOM MEMORY

ZOOM MEMORY

ZPrevious

ZoomSto

ZoomRcl

3-24 Function Graphing

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The zoom factors, XFact and YFact, are positive numbers

(not necessarily integers) greater than or equal to 1. They

define the magnification or reduction factor used to

Zoom

or Zoom Out around a point.

To display the

ZOOM FACTORS

screen, where you can

review the current values for

XFact and YFact, select

4:SetFactors from the

ZOOM MEMORY

menu. The values

shown are the defaults.

You can change XFact and YFact in either of two ways.

•

Enter a new value. The original value is cleared

automatically when you enter the first digit.

•

Place the cursor on the digit you want to change, and

then enter a value or press

{

to delete it.

From the home screen or a program, you can store directly

to any of the user-defined

ZOOM

variables.

From a program, you can select the ZoomSto and ZoomRcl

instructions from the

ZOOM MEMORY

menu.

ZOOM FACTORS

Checking XFact

and YFact

Changing XFact

and YFact

Using ZOOM

MEMORY Menu

Items from the

Home Screen or

a Program

Function Graphing 3-25

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To display the

CALCULATE

menu, press

CALCä

. Use the

items on this menu to analyze the current graph functions.

CALCULATE

1: value

Calculates a function Y value for a given X.

2: zero

Finds a zero (x-intercept) of a function.

3: minimum

Finds a minimum of a function.

4: maximum

Finds a maximum of a function.

5: intersect

Finds an intersection of two functions.

6: dy/dx

Finds a numeric derivative of a function.

‰

f(x)dx

Finds a numeric integral of a function.

value evaluates one or more currently selected functions

for a specified value of

Note:

When a value is displayed for

, press

‘

to clear the value.

When no value is displayed, press

‘

to cancel the

value

operation.

To evaluate a selected function at X, follow these steps.

1. Select

1:value from the

CALCULATE

menu. The graph is

displayed with

X= in the bottom-left corner.

2. Enter a real value, which can be an expression, for

between Xmin and Xmax.

3. Press

The cursor is on the first selected function in the

editor

at the

X value you entered, and the coordinates are

displayed, even if

CoordOff format is selected.

To move the cursor from function to function at the

entered

X value, press

}

†

. To restore the free-moving

cursor, press

Using the CALC (Calculate) Operations

CALCULATE

value

3-26 Function Graphing

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zero finds a zero (x-intercept or root) of a function using

solve(. Functions can have more than one x-intercept

value;

zero finds the zero closest to your guess.

The time

zero spends to find the correct zero value

depends on the accuracy of the values you specify for the

left and right bounds and the accuracy of your guess.

To find a zero of a function, follow these steps.

1. Select

2:zero from the

CALCULATE

menu. The current

graph is displayed with

Left Bound?

in the bottom-left

corner.

2. Press

}

†

to move the cursor onto the function for

which you want to find a zero.

3. Press

(or enter a value) to select the x-value for

the left bound of the interval, and then press

. A

indicator on the graph screen shows the left bound.

Right Bound? is displayed in the bottom-left corner.

Press

(or enter a value) to select the x-value for

the right bound, and then press

. A

indicator on

the graph screen shows the right bound.

Guess? is then

displayed in the bottom-left corner.

4. Press

(or enter a value) to select a point near

the zero of the function, between the bounds, and then

press

The cursor is on the solution and the coordinates are

displayed, even if

CoordOff format is selected. To move to

the same x-value for other selected functions, press

}

†

. To restore the free-moving cursor, press

zero

Function Graphing 3-27

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minimum and maximum find a minimum or maximum of a

function within a specified interval to a tolerance of 1

âL

To find a minimum or maximum, follow these steps.

1. Select

3:minimum or 4:maximum from the

CALCULATE

menu. The current graph is displayed.

2. Select the function and set left bound, right bound, and

guess as described for

zero (steps 2 through 4; page 3

26).

The cursor is on the solution, and the coordinates are

displayed, even if you have selected

CoordOff format;

Minimum or Maximum is displayed in the bottom-left

corner.

To move to the same x-value for other selected functions,

press

}

†

. To restore the free-moving cursor, press

intersect finds the coordinates of a point at which two or

more functions intersect using

solve(. The intersection

must appear on the display to use

intersect.

To find an intersection, follow these steps.

1. Select

5:intersect from the

CALCULATE

menu. The

current graph is displayed with

First curve?

in the

bottom-left corner.

2. Press

†

}

, if necessary, to move the cursor to the

first function, and then press

Second curve? is

displayed in the bottom-left corner.

3. Press

†

}

, if necessary, to move the cursor to the

second function, and then press

4. Press

to move the cursor to the point that is

your guess as to location of the intersection, and then

press

The cursor is on the solution and the coordinates are

displayed, even if

CoordOff format is selected. Intersection

is displayed in the bottom-left corner. To restore the free-

moving cursor, press

}

, or

†

minimum,

maximum

intersect

3-28 Function Graphing

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dy/dx (numerical derivative) finds the numerical derivative

(slope) of a function at a point, with

âL

To find a function’s slope at a point, follow these steps.

1. Select

6:dy/dx from the

CALCULATE

menu. The current

graph is displayed.

2. Press

}

†

to select the function for which you want

to find the numerical derivative.

3. Press

(or enter a value) to select the

X value at

which to calculate the derivative, and then press

The cursor is on the solution and the numerical derivative

is displayed.

To move to the same x-value for other selected functions,

press

}

†

. To restore the free-moving cursor, press

‰

f(x)dx

(numerical integral) finds the numerical integral of a

function in a specified interval. It uses the

fnInt( function,

with a tolerance of

âL

To find the numerical derivative of a function, follow these

steps.

1. Select

‰

f(x)dx from the

CALCULATE

menu. The current

graph is displayed with

Lower Limit? in the bottom-left

corner.

2. Press

}

†

to move the cursor to the function for

which you want to calculate the integral.

3. Set lower and upper limits as you would set left and

right bounds for

zero (step 3; page 3

26). The integral

value is displayed, and the integrated area is shaded.

Note:

The shaded area is a drawing. Use

ClrDraw

(Chapter 8) or

any action that invokes Smart Graph to clear the shaded area.

dy/dx

‰

f(x)dx

Parametric Graphing 4-1

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Parametric

Graphin

Getting Started: Path of a Ball

...........................

4-2

Defining and Displaying Parametric Graphs

..............

4-4

Exploring Parametric Graphs

............................

4-7

Contents

4-2 Parametric Graphing

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Getting Started is a fast-paced introduction. Read the chapter for details.

Graph the parametric equation that describes the path of a ball hit at an initial

speed of 30 meters per second, at an initial angle of 25 degrees with the

horizontal from ground level. How far does the ball travel? When does it hit the

ground? How high does it go? Ignore all forces except gravity.

For initial velocity v

and angle

, the position of the ball as a function of time

has horizontal and vertical components.

Horizontal: X1(t)=tv

cos(

)

Vertical: Y1(t)=tv

sin(

)

The vertical and horizontal vectors of the ball’s motion also will be graphed.

Vertical vector: X2(t)=0 Y2(t)=Y1(t)

Horizontal vector: X3(t)=X1(t) Y3(t)=0

Gravity constant: g=9.8 m/sec

1. Press

. Press

†

select

Par mode. Press

†

select

Simul for simultaneous graphing of

all three parametric equations in this

example.

2. Press

. Press 30

„

™

[

ANGLE

] 1 (to select

)

to define

in terms of T.

3. Press

„

[

ANGLE

] 1

9.8

„

to define Y

The vertical component vector is defined

and Y

4. Press

to define X

5. Press



to display the

VARS Y

VARS

menu. Press 2 to display the

PARAMETRIC

secondary menu. Press 2

to define

Getting Started: Path of a Ball

Parametric Graphing 4-3

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The horizontal component vector is

defined by

and Y

6. Press



2, and then press 1

define

. Press 0

to define Y

7. Press

}

to change the graph

style to

for

and Y

. Press

}

to change the graph style to

for

and Y

. Press

}

change the graph style to

for

and Y

(These keystrokes assume that all graph

styles were set to

originally.)

8. Press

. Enter these values for the

window variables.

Tmin=0 Xmin=

10 Ymin=

Tmax=5 Xmax=100 Ymax=15

Tstep=.1 Xscl=50 Yscl=10

9. Press

[

FORMAT

]

†

to set

AxesOff, which turns off the axes.

10. Press

. The plotting action

simultaneously shows the ball in flight and

the vertical and horizontal component

vectors of the motion.

Tip:

To simulate the ball flying through the air, set

graph style to

(animate) for

and

11. Press

to obtain numerical results

and answer the questions at the beginning

of this section.

Tracing begins at

Tmin on the first

parametric equation (

and Y

). As you

press

to trace the curve, the cursor

follows the path of the ball over time. The

values for

X (distance), Y (height), and T

(time) are displayed at the bottom of the

screen.

4-4 Parametric Graphing

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The steps for defining a parametric graph are similar to the

steps for defining a function graph. Chapter 4 assumes that

you are familiar with Chapter 3: Function Graphing.

Chapter 4 details aspects of parametric graphing that differ

from function graphing.

To display the mode screen, press

. To graph

parametric equations, you must select

Par graphing mode

before you enter window variables and before you enter

the components of parametric equations.

After selecting

Par graphing mode, press

to display the

parametric

editor.

In this editor, you can display and enter both the X and Y

components of up to six equations, X

and Y

through X

and Y

. Each is defined in terms of the independent

variable

T. A common application of parametric graphs is

graphing equations over time.

The icons to the left of

through X

represent the graph

style of each parametric equation (Chapter 3). The default

Par mode is

(line), which connects plotted points. Line,

(thick),

(path),

(animate), and

(dot) styles are

available for parametric graphing.

Defining and Displaying Parametric Graphs

TI-83 Graphing

Mode Similarities

Setting

Parametric

Graphing Mode

Displaying the

Parametric Y=

Editor

Selecting a

Graph Style

Parametric Graphing 4-5

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To define or edit a parametric equation, follow the steps in

Chapter 3 for defining a function or editing a function. The

independent variable in a parametric equation is

T. In Par

graphing mode, you can enter the parametric variable T in

either of two ways.

•

Press

„

•

Press

Tä

Two components,

X and Y, define a single parametric

equation. You must define both of them.

The TI

83 graphs only the selected parametric equations.

In the

editor, a parametric equation is selected when the

= signs of both the X and Y components are highlighted.

You may select any or all of the equations

and Y

through X

and Y

To change the selection status, move the cursor onto the =

sign of either the

X or Y component and press

. The

status of both the

X and Y components is changed.

To display the window variable values, press

These variables define the viewing window. The values

below are defaults for

Par graphing in Radian angle mode.

Tmin=0

Smallest T value to evaluate

Tmax=6.2831853

...

Largest T value to evaluate (2

)

Tstep=.1308996

...

T value increment (

pà

24)

Xmin=

Smallest X value to be displayed

Xmax=10

Largest X value to be displayed

Xscl=1

Spacing between the X tick marks

Ymin=

Smallest Y value to be displayed

Ymax=10

Largest Y value to be displayed

Yscl=1

Spacing between the Y tick marks

Note:

To ensure that sufficient points are plotted, you may want to

change the

window variables.

Defining and

Editing

Parametric

Equations

Selecting and

Deselecting

Parametric

Equations

Setting Window

Variables

4-6 Parametric Graphing

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To display the current graph format settings, press

[

FORMAT

]. Chapter 3 describes the format settings in detail.

The other graphing modes share these format settings;

Seq

graphing mode has an additional axes format setting.

When you press

, the TI

83 plots the selected

parametric equations. It evaluates the

X and Y components

for each value of

T (from Tmin to Tmax in intervals of

Tstep), and then plots each point defined by X and Y. The

window variables define the viewing window.

As the graph is plotted,

X, Y, and T are updated.

Smart Graph applies to parametric graphs (Chapter 3).

You can perform these actions from the home screen or a

program.

•

Access functions by using the name of the

X or Y

component of the equation as a variable.

•

Store parametric equations.

•

Select or deselect parametric equations.

•

Store values directly to window variables.

Setting the Graph

Format

Displaying a

Graph

Window

Variables and

Y-VARS Menus

Parametric Graphing 4-7

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The free-moving cursor in Par graphing works the same as

Func graphing.

RectGC format, moving the cursor updates the values of

X and Y; if CoordOn format is selected, X and Y are

displayed.

PolarGC format, X, Y, R, and

are updated; if CoordOn

format is selected, R and

are displayed.

To activate

TRACE

, press

. When

TRACE

is active,

you can move the trace cursor along the graph of the

equation one

Tstep at a time. When you begin a trace, the

trace cursor is on the first selected function at

Tmin. If

ExprOn is selected, then the function is displayed.

RectGC format,

TRACE

updates and displays the values

X, Y, and T if CoordOn format is on.

PolarGC format, X, Y, R,

and T are updated; if CoordOn

format is selected, R,

, and T are displayed. The X and Y

(or R and

) values are calculated from T.

To move five plotted points at a time on a function, press

. If you move the cursor beyond the top or

bottom of the screen, the coordinate values at the bottom

of the screen continue to change appropriately.

Quick Zoom is available in

Par graphing; panning is not

(Chapter 3).

Exploring Parametric Graphs

Free-Moving

Cursor

TRACE

4-8 Parametric Graphing

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To move the trace cursor to any valid T value on the

current function, enter the number. When you enter the

first digit, a

T= prompt and the number you entered are

displayed in the bottom-left corner of the screen. You can

enter an expression at the

T= prompt. The value must be

valid for the current viewing window. When you have

completed the entry, press

to move the cursor.

ZOOM

operations in Par graphing work the same as in Func

graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin,

Ymax, and Yscl) window variables are affected.

The

T window variables (Tmin, Tmax, and Tstep) are only

affected when you select

ZStandard. The

VARS ZOOM

secondary menu

ZT/Z

items 1:ZTmin, 2:ZTmax, and

3:ZTstep are the zoom memory variables for Par graphing.

CALC

operations in Par graphing work the same as in Func

graphing. The

CALCULATE

menu items available in Par

graphing are 1:value, 2:dy/dx, 3:dy/dt, and 4:dx/dt.

Moving the Trace

Cursor to Any

Valid T Value

ZOOM

CALC

Polar Graphing 5-1

8305POLR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:19 PM Printed: 02/19/01 1:36

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Polar

Graphin

Getting Started: Polar Rose

..............................

5-2

Defining and Displaying Polar Graphs

...................

5-3

Exploring Polar Graphs

..................................

5-6

Contents

5-2 Polar Graphing

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Getting Started is a fast-paced introduction. Read the chapter for details.

The polar equation R=Asin(B

) graphs a rose. Graph the rose for A=8 and

B=2.5, and then explore the appearance of the rose for other values of A and B.

1. Press

to display the mode screen.

Press

†

to select

Pol

graphing mode. Select the defaults (the

options on the left) for the other mode

settings.

2. Press

to display the polar

editor.

Press

2.5

„

to define

3. Press

6 to select 6:ZStandard and

graph the equation in the standard viewing

window. The graph shows only five petals

of the rose, and the rose does not appear

to be symmetrical. This is because the

standard window sets

max=2

and defines

the window, rather than the pixels, as

square.

4. Press

to display the window

variables. Press

†

[

] to increase the

value of

max

to 4

5. Press

5 to select 5:ZSquare and plot

the graph.

6. Repeat steps 2 through 5 with new values

for the variables

A and B in the polar

equation

=Asin(B

). Observe how the new

values affect the graph.

Getting Started: Polar Rose

Polar Graphing 5-3

8305POLR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:19 PM Printed: 02/19/01 1:36

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The steps for defining a polar graph are similar to the steps

for defining a function graph. Chapter 5 assumes that you

are familiar with Chapter 3: Function Graphing. Chapter 5

details aspects of polar graphing that differ from function

graphing.

To display the mode screen, press

. To graph polar

equations, you must select

Pol graphing mode before you

enter values for the window variables and before you enter

polar equations.

After selecting

Pol graphing mode, press

to display the

polar

editor.

In this editor, you can enter and display up to six polar

equations,

through r

. Each is defined in terms of the

independent variable

(page 5

4).

The icons to the left of

through r

represent the graph

style of each polar equation (Chapter 3). The default in

Pol

graphing mode is

(line), which connects plotted points.

Line,

(thick),

(path),

(animate), and

(dot) styles are

available for polar graphing.

Defining and Displaying Polar Graphs

TI-83 Graphing

Mode Similarities

Setting Polar

Graphing Mode

Displaying the

Polar Y= Editor

Selecting Graph

Styles

5-4 Polar Graphing

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To define or edit a polar equation, follow the steps in

Chapter 3 for defining a function or editing a function. The

independent variable in a polar equation is

. In Pol

graphing mode, you can enter the polar variable

in either

of two ways.

•

Press

„

•

Press

ãqä

The TI

83 graphs only the selected polar equations. In the

editor, a polar equation is selected when the = sign is

highlighted. You may select any or all of the equations.

To change the selection status, move the cursor onto the

= sign, and then press

To display the window variable values, press

These variables define the viewing window. The values

below are defaults for

Pol graphing in Radian angle mode.

min=0

Smallest

value to evaluate

max=6.2831853

...

Largest

value to evaluate (2

)

step=.1308996

...

Increment between

values (

pà

24)

Xmin=

Smallest X value to be displayed

Xmax=10

Largest X value to be displayed

Xscl=1

Spacing between the X tick marks

Ymin=

Smallest Y value to be displayed

Ymax=10

Largest Y value to be displayed

Yscl=1

Spacing between the Y tick marks

Note:

To ensure that sufficient points are plotted, you may want to

change the

window variables.

Defining and

Editing Polar

Equations

Selecting and

Deselecting Polar

Equations

Setting Window

Variables

Polar Graphing 5-5

8305POLR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:19 PM Printed: 02/19/01 1:36

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To display the current graph format settings, press

[

FORMAT

]. Chapter 3 describes the format settings in detail.

The other graphing modes share these format settings.

When you press

, the TI

83 plots the selected polar

equations. It evaluates

R for each value of

(from

min

max

in intervals of

step

) and then plots each point. The

window variables define the viewing window.

As the graph is plotted,

X, Y, R, and

are updated.

Smart Graph applies to polar graphs (Chapter 3).

You can perform these actions from the home screen or a

program.

•

Access functions by using the name of the equation as a

variable.

•

Store polar equations.

•

Select or deselect polar equations.

•

Store values directly to window variables.

Setting the Graph

Format

Displaying a

Graph

Window

Variables and

VARS Menus

5-6 Polar Graphing

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The free-moving cursor in Pol graphing works the same as

Func graphing. In RectGC format, moving the cursor

updates the values of

X and Y; if CoordOn format is

selected,

X and Y are displayed. In PolarGC format, X, Y, R,

and

are updated; if CoordOn format is selected, R and

are displayed.

To activate

TRACE

, press

. When

TRACE

is active,

you can move the trace cursor along the graph of the

equation one

step

at a time. When you begin a trace, the

trace cursor is on the first selected function at

min

. If

ExprOn format is selected, then the equation is displayed.

RectGC format,

TRACE

updates the values of X, Y, and

;

CoordOn format is selected, X, Y, and

are displayed. In

PolarGC format,

TRACE

updates X, Y, R, and

; if CoordOn

format is selected, R and

are displayed.

To move five plotted points at a time on a function, press

. If you move the trace cursor beyond the

top or bottom of the screen, the coordinate values at the

bottom of the screen continue to change appropriately.

Quick Zoom is available in

Pol graphing mode; panning is

not (Chapter 3).

To move the trace cursor to any valid

value on the

current function, enter the number. When you enter the

first digit, a

prompt and the number you entered are

displayed in the bottom-left corner of the screen. You can

enter an expression at the

prompt. The value must be

valid for the current viewing window. When you complete

the entry, press

to move the cursor.

ZOOM

operations in Pol graphing work the same as in Func

graphing. Only the X (Xmin, Xmax, and Xscl) and Y (Ymin,

Ymax, and Yscl) window variables are affected.

The

window variables (

min

max

, and

step) are not

affected, except when you select

ZStandard. The

VARS

ZOOM

secondary menu

ZT/Z

items 4:Z

min, 5:Z

max, and

6:Z

step are zoom memory variables for Pol graphing.

CALC

operations in Pol graphing work the same as in Func

graphing. The

CALCULATE

menu items available in Pol

graphing are 1:value, 2:dy/dx, and 3:dr/d

Exploring Polar Graphs

Free-Moving

Cursor

TRACE

Moving the Trace

Cursor to Any

Valid

Value

ZOOM

CALC

Sequence Graphing 6-1

8306SEQN.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:22 PM Printed: 02/19/01 1:36

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Sequence

Graphin

Getting Started: Forest and Trees

........................

6-2

Defining and Displaying Sequence Graphs

...............

6-3

Selecting Axes Combinations

............................

6-8

Exploring Sequence Graphs

..............................

6-9

Graphing Web Plots

......................................

6-11

Using Web Plots to Illustrate Convergence

...............

6-12

Graphing Phase Plots

....................................

6-13

Comparing TI

83 and TI

82 Sequence Variables

..........

6-15

Keystroke Differences Between TI

83 and TI

.........

6-16

Contents

6-2 Sequence Graphing

8306SEQN.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:22 PM Printed: 02/19/01 1:36

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Getting Started is a fast-paced introduction. Read the chapter for details.

A small forest of 4,000 trees is under a new forestry plan. Each year 20 percent

of the trees will be harvested and 1,000 new trees will be planted. Will the

forest eventually disappear? Will the forest size stabilize? If so, in how many

years and with how many trees?

1. Press

. Press

†

to select

Seq graphing mode.

2. Press

[

FORMAT

] and select Time axes

format and

ExprOn format if necessary.

3. Press

. If the graph-style icon is not

(dot), press

, press

until

displayed, and then press

4. Press



3 to select iPart( (integer

part) because only whole trees are

harvested. After each annual harvest, 80

percent (.80) of the trees remain. Press

[

]

„

to define the

number of trees after each harvest. Press

1000

to define the new trees. Press

†

4000 to define the number of trees at the

beginning of the program.

5. Press

0 to set

Min=0. Press

†

to set

Max=50.

Min and

Max evaluate

forest size over 50 years. Set the other

window variables.

PlotStart=1 Xmin=0 Ymin=0

PlotStep=1 Xmax=50 Ymax=6000

Xscl=10 Yscl=1000

6. Press

. Tracing begins at

Min (the

start of the forestry plan). Press

to trace

the sequence year by year. The sequence is

displayed at the top of the screen. The

values for

(number of years), X (X=

because

is plotted on the x-axis), and Y

(tree count) are displayed at the bottom.

When will the forest stabilize? With how

many trees?

Getting Started: Forest and Trees

Sequence Graphing 6-3

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The steps for defining a sequence graph are similar to the

steps for defining a function graph. Chapter 6 assumes that

you are familiar with Chapter 3: Function Graphing.

Chapter 6 details aspects of sequence graphing that differ

from function graphing.

To display the mode screen, press

. To graph

sequence functions, you must select

Seq graphing mode

before you enter window variables and before you enter

sequence functions.

Sequence graphs automatically plot in

Simul mode,

regardless of the current plotting-order mode setting.

The TI

83 has three sequence functions that you can enter

from the keyboard:

u, v, and w. They are above the

−

and

keys.

You can define sequence functions in terms of:

•

The independent variable

•

The previous term in the sequence function, such as

•

The term that precedes the previous term in the

sequence function, such as

•

The previous term or the term that precedes the

previous term in another sequence function, such as

or u(

referenced in the sequence v(

Note:

Statements in this chapter about

)

are also true for

)

and

)

; statements about

are also true for

and

;

statements about

are also true for

and

Defining and Displaying Sequence Graphs

TI-83 Graphing

Mode Similarities

Setting Sequence

Graphing Mode

TI-83 Sequence

Functions u, v,

and w

6-4 Sequence Graphing

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After selecting Seq mode, press

to display the sequence

editor.

In this editor, you can display and enter sequences for u(

), and w(

). Also, you can edit the value for

Min, which

is the sequence window variable that defines the minimum

value to evaluate.

The sequence

editor displays the

Min value because of

its relevance to

Min), v(

Min), and w(

Min), which are the

initial values for the sequence equations

), v(

), and

), respectively.

Min in the

editor is the same as

Min in the window

editor. If you enter a new value for

Min in one editor, the

new value for

Min is updated in both editors.

Note:

Use

Min)

, or

Min)

only with a recursive

sequence, which requires an initial value.

The icons to the left of u(

), v(

), and w(

) represent the

graph style of each sequence (Chapter 3). The default in

Seq mode is

(dot), which shows discrete values. Dot,

(line), and

(thick) styles are available for sequence

graphing. Graph styles are ignored in

Web format.

The TI

83 graphs only the selected sequence functions. In

the

editor, a sequence function is selected when the =

signs of both u(

)= and u(

Min)= are highlighted.

To change the selection status of a sequence function,

move the cursor onto the

= sign of the function name, and

then press

. The status is changed for both the

sequence function

) and its initial value u(

Min).

Displaying the

Sequence Y=

Editor

Selecting Graph

Styles

Selecting and

Deselecting

Sequence

Functions

Sequence Graphing 6-5

8306SEQN.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:22 PM Printed: 02/19/01 1:36

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To define or edit a sequence function, follow the steps in

Chapter 3 for defining a function. The independent variable

in a sequence is

Seq graphing mode, you can enter the sequence variable

in either of two ways.

•

Press

„

•

Press

[

CATALOG

] [

You can enter the function name from the keyboard.

•

To enter the function name

u, press

[

] (above

•

To enter the function name

v, press

[

] (above

−

•

To enter the function name

w, press

[

] (above

Generally, sequences are either nonrecursive or recursive.

Sequences are evaluated only at consecutive integer

values.

is always a series of consecutive integers, starting

at zero or any positive integer.

In a nonrecursive sequence, the

th term is a function of

the independent variable

. Each term is independent of all

other terms.

For example, in the nonrecursive sequence below, you can

calculate

u(5) directly, without first calculating u(1) or any

previous term.

The sequence equation above returns the sequence

2, 4, 6, 8, 10, . . . for

= 1, 2,

3, 4, 5,

. . . .

Note:

You may leave blank the initial value

u(nMin)

when calculating

nonrecursive sequences.

Defining and

Editing a

Sequence

Function

Nonrecursive

Sequences

6-6 Sequence Graphing

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In a recursive sequence, the

th term in the sequence is

defined in relation to the previous term or the term that

precedes the previous term, represented by

and

. A recursive sequence may also be defined in

relation to

, as in u(

)=u(

1)+

For example, in the sequence below you cannot calculate

u(5) without first calculating u(1), u(2), u(3), and u(4).

Using an initial value u(

Min) = 1, the sequence above

returns

1, 2, 4, 8, 16, . . .

Tip:

On the TI

83, you must type each character of the terms. For

example, to enter

, press

[

]

„

Recursive sequences require an initial value or values,

since they reference undefined terms.

•

If each term in the sequence is defined in relation to the

previous term, as in

, you must specify an initial

value for the first term.

•

If each term in the sequence is defined in relation to the

term that precedes the previous term, as in

, you

must specify initial values for the first two terms. Enter

the initial values as a list enclosed in braces ({ }) with

commas separating the values.

The value of the first term is 0 and the value of the second

term is 1 for the sequence

Recursive

Sequences

Sequence Graphing 6-7

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To display the window variables, press

. These

variables define the viewing window. The values below are

defaults for

Seq graphing in both Radian and Degree angle

modes.

nMin=1

Smallest

value to evaluate

nMax

Largest

value to evaluate

PlotStart

First term number to be plotted

PlotStep

Incremental

value (for graphing only)

Xmin

Smallest X value to be displayed

Xmax

Largest X value to be displayed

Xscl

Spacing between the X tick marks

Ymin

Smallest Y value to be displayed

Ymax

Largest Y value to be displayed

Yscl

Spacing between the Y tick marks

Min must be an integer

‚

Max, PlotStart, and PlotStep

must be integers

‚

Min is the smallest

value to evaluate.

Min also is

displayed in the sequence

editor.

Max is the largest

value to evaluate. Sequences are evaluated at u(

Min),

Min+1), u(

Min+2) , . . . , u(

Max).

PlotStart is the first term to be plotted. PlotStart=1 begins

plotting on the first term in the sequence. If you want

plotting to begin with the fifth term in a sequence, for

example, set

PlotStart=5. The first four terms are evaluated

but are not plotted on the graph.

PlotStep is the incremental

value for graphing only.

PlotStep does not affect sequence evaluation; it only

designates which points are plotted on the graph. If you

specify

PlotStep=2, the sequence is evaluated at each

consecutive integer, but it is plotted on the graph only at

every other integer.

Setting Window

Variables

6-8 Sequence Graphing

8306SEQN.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:22 PM Printed: 02/19/01 1:36

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To display the current graph format settings, press

[

FORMAT

]. Chapter 3 describes the format settings in detail.

The other graphing modes share these format settings. The

axes setting on the top line of the screen is available only

Seq mode.

Time Web uv vw uw

Type of sequence plot (axes)

RectGC PolarGC

Rectangular or polar output

CoordOn CoordOff

Cursor coordinate display on/off

GridOff GridOn

Grid display off or on

AxesOn AxesOff

Axes display on or off

LabelOff LabelOn

Axes label display off or on

ExprOn ExprOff

Expression display on or off

For sequence graphing, you can select from five axes

formats. The table below shows the values that are plotted

on the x-axis and y-axis for each axes setting.

Axes Setting x-axis y-axis

Time

), v(

), w(

)

Web u(

, v(

, w(

1) u(

), v(

), w(

)

uv u(

)v(

)

vw v(

)w(

)

uw u(

)w(

)

See pages 6

11 and 6

12 for more information on Web

plots. See page 6

13 for more information on phase plots

(

uv, vw, and uw axes settings).

To plot the selected sequence functions, press

. As a

graph is plotted, the TI

83 updates

X, Y, and

Smart Graph applies to sequence graphs (Chapter 3).

Selecting Axes Combinations

Setting the Graph

Format

Setting Axes

Format

Displaying a

Sequence Graph

Sequence Graphing 6-9

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The free-moving cursor in Seq graphing works the same as

Func graphing. In RectGC format, moving the cursor

updates the values of

X and Y; if CoordOn format is

selected,

X and Y are displayed. In PolarGC format, X, Y, R,

and

are updated; if CoordOn format is selected, R and

are displayed.

The axes format setting affects

TRACE

When

Time, uv, vw, or uw axes format is selected,

TRACE

moves the cursor along the sequence one PlotStep

increment at a time. To move five plotted points at once,

press

•

When you begin a trace, the trace cursor is on the first

selected sequence at the term number specified by

PlotStart, even if it is outside the viewing window.

•

Quick Zoom applies to all directions. To center the

viewing window on the current cursor location after

you have moved the trace cursor, press

. The

trace cursor returns to

Min.

Web format, the trail of the cursor helps identify points

with attracting and repelling behavior in the sequence.

When you begin a trace, the cursor is on the x-axis at the

initial value of the first selected function.

Tip:

To move the cursor to a specified

during a trace, enter a value

for

, and press

. For example, to quickly return the cursor to the

beginning of the sequence, paste

Min

to the

prompt and press

To move the trace cursor to any valid

value on the

current function, enter the number. When you enter the

first digit, an

= prompt and the number you entered are

displayed in the bottom-left corner of the screen. You can

enter an expression at the

= prompt. The value must be

valid for the current viewing window. When you have

completed the entry, press

to move the cursor.

Exploring Sequence Graphs

Free-Moving

Cursor

TRACE

Moving the Trace

Cursor to Any

Valid

Value

6-10 Sequence Graphing

8306SEQN.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:22 PM Printed: 02/19/01 1:36

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ZOOM

operations in Seq graphing work the same as in

Func graphing. Only the X (Xmin, Xmax, and Xscl) and Y

(Ymin, Ymax, and Yscl) window variables are affected.

PlotStart, PlotStep,

Min, and

Max are only affected when

you select

ZStandard. The

VARS Zoom

secondary menu

items 1 through 7 are the

ZOOM MEMORY

variables for Seq

graphing.

The only

CALC

operation available in Seq graphing is value.

•

When

Time axes format is selected, value displays Y (the

) value) for a specified

value.

•

When

Web axes format is selected, value draws the web

and displays Y (the u(

) value) for a specified

value.

•

When

uv, vw, or uw axes format is selected, value

displays X and Y according to the axes format setting.

For example, for uv axes format, X represents u(

) and

Y represents v(

To enter the sequence names

u, v, or w, press

[

], [

], or

[

]. You can evaluate these names in any of three ways.

•

Calculate the

th value in a sequence.

•

Calculate a list of values in a sequence.

•

Generate a sequence with u(

nstart

nstop

nstep

]).

nstep

is optional; default is 1.

ZOOM

CALC

Evaluating u, v,

and w

Sequence Graphing 6-11

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To select Web axes format, press

[

FORMAT

]

. A

web plot graphs

) versus u(

, which you can use to

study long-term behavior (convergence, divergence, or

oscillation) of a recursive sequence. You can see how the

sequence may change behavior as its initial value changes.

When

Web axes format is selected, a sequence will not

graph properly or will generate an error.

•

It must be recursive with only one recursion level

(

but not u(

•

It cannot reference

directly.

•

It cannot reference any defined sequence except itself.

Web format, press

to display the graph screen.

The TI

83:

•

Draws a

y=x

reference line in AxesOn format.

•

Plots the selected sequences with

as the

independent variable.

Note:

A potential convergence point occurs whenever a sequence

intersects the y=x reference line. However, the sequence may or may

not actually converge at that point, depending on the sequence’s initial

value.

To activate the trace cursor, press

. The screen

displays the sequence and the current

, X, and Y values (X

represents u(

and Y represents u(

)). Press

repeatedly to draw the web step by step, starting at

Min.

Web format, the trace cursor follows this course.

1. It starts on the x-axis at the initial value

Min) (when

PlotStart=1).

2. It moves vertically (up or down) to the sequence.

3. It moves horizontally to the

y=x

reference line.

4. It repeats this vertical and horizontal movement as you

continue to press

Graphing Web Plots

Graphing a Web

Plot

Valid Functions

for Web Plots

Displaying the

Graph Screen

Drawing the Web

6-12 Sequence Graphing

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1. Press

in Seq mode to display the sequence

editor.

Make sure the graph style is set to

(dot), and then

define

Min, u(

) and u(

Min) as shown below.

2. Press

[

FORMAT

]

to set Time axes format.

3. Press

and set the variables as shown below.

Min=1 Xmin=0 Ymin=

Max=25 Xmax=25 Ymax=10

PlotStart=1 Xscl=1 Yscl=1

PlotStep=1

4. Press

to graph the sequence.

5. Press

[

FORMAT

] and select the Web axes setting.

6. Press

and change the variables below.

Xmin=

10 Xmax=10

7. Press

to graph the sequence.

8. Press

, and then press

to draw the web. The

displayed cursor coordinates

, X (u(

), and

Y (u(

)) change accordingly. When you press

, a new

value is displayed, and the trace cursor is on the

sequence. When you press

again, the

value remains

the same, and the cursor moves to the

y=x

reference line.

This pattern repeats as you trace the web.

Using Web Plots to Illustrate Convergence

Example:

Convergence

Sequence Graphing 6-13

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The phase-plot axes settings uv, vw, and uw show

relationships between two sequences. To select a

phase-plot axes setting, press

[

FORMAT

], press

until

the cursor is on

uv, vw, or uw, and then press

Axes Setting x-axis y-axis

uv u(

)v(

)

vw v(

)w(

)

uw u(

)w(

)

Use the predator-prey model to determine the regional

populations of a predator and its prey that would maintain

population equilibrium for the two species.

This example uses the model to determine the equilibrium

populations of wolves and rabbits, with initial populations

of 200 rabbits (

Min)) and 50 wolves (v(

Min)).

These are the variables (given values are in parentheses):

R = number of rabbits

M = rabbit population growth rate without wolves (.05)

K = rabbit population death rate with wolves (.001)

W = number of wolves

G = wolf population growth rate with rabbits (.0002)

D = wolf population death rate without rabbits (.03)

= time (in months)

(1+M

)

(1+GR

1. Press

Seq mode to display the sequence

editor.

Define the sequences and initial values for R

and W

shown below. Enter the sequence R

as u(

) and enter

the sequence W

as v(

Graphing Phase Plots

Graphing with uv,

vw, and uw

Example:

Predator-Prey

Model

6-14 Sequence Graphing

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2. Press

[

FORMAT

]

to select Time axes format.

3. Press

and set the variables as shown below.

Min=0 Xmin=0 Ymin=0

Max=400 Xmax=400 Ymax=300

PlotStart=1 Xscl=100 Yscl=100

PlotStep=1

4. Press

to graph the sequence.

5. Press

to individually trace the number of

rabbits (

)) and wolves (v(

)) over time (

Tip:

Press a number, and then press

to jump to a specific

value (month) while in

TRACE

6. Press

[

FORMAT

]

to select uv axes

format.

7. Press

and change these variables as shown

below.

Xmin=84 Ymin=25

Xmax=237 Ymax=75

Xscl=50 Yscl=10

8. Press

. Trace both the number of rabbits (X) and

the number of wolves (

Y) through 400 generations.

Note:

When you press

, the

equation for

is displayed in the

top-left corner. Press

}

†

see the equation for

Sequence Graphing 6-15

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Refer to the table if you are familiar with the TI

82. It

shows TI

83 sequences and sequence window variables, as

well as their TI

82 counterparts.

83 TI

In the

editor:

Min) U

Start

(window variable)

Min) V

Start

(window variable)

)

not available

Min)

not available

In the window editor:

Min

Start

Max

PlotStart

Min

PlotStep

not available

Comparing TI-83 and TI-82 Sequence Variables

Sequences and

Window

Variables

6-16 Sequence Graphing

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Refer to the table if you are familiar with the TI

82. It

compares TI

83 sequence-name syntax and variable syntax

with TI

82 sequence-name syntax and variable syntax.

83 / TI

82 On TI

83, press: On TI

82, press:

„y

[

]

)

[

]

„

[

VARS

]

) / V

[

]

„

[

VARS

]

)

[

]

„

not available

1) / U

[

]

„

[

]

1) / V

[

]

„

[

]

[

]

„

not available

Keystroke Differences Between TI-83 and TI-82

Sequence

Keystroke

Changes

Tables 7-1

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Tables

Getting Started: Roots of a Function

.....................

7-2

Setting Up the Table

.....................................

7-3

Defining the Dependent Variables

........................

7-4

Displaying the Table

.....................................

7-5

Contents

7-2 Tables

8307TABL.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:26 PM Printed: 02/19/01 1:36

PM Page 2 of 6

Getting Started is a fast-paced introduction. Read the chapter for details.

Evaluate the function Y = X

2X at each integer between

10 and 10. How

many sign changes occur, and at what

X values?

1. Press

†

to set

Func

graphing mode.

2. Press

. Press

„



3 to select

Then press

„

to enter the

function

3. Press

[

TBLSET

] to display the

TABLE

SETUP

screen. Press

to set

TblStart=

10. Press 1

to set

Tbl=1

Press

to select

Indpnt: Auto

(automatically generated independent

values). Press

†

to select

Depend: Auto (automatically generated

dependent values).

4. Press

[

TABLE

] to display the table

screen.

5. Press

†

until you see the sign changes in

the value of

. How many sign changes

occur, and at what

X values?

Getting Started: Roots of a Function

Tables 7-3

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To display the

TABLE SETUP

screen, press

[

TBLSET

TblStart (table start) defines the initial value for the

independent variable.

TblStart applies only when the

independent variable is generated automatically (when

Indpnt: Auto is selected).

Tbl

(table step) defines the increment for the independent

variable.

Note:

Seq

mode, both

TblStart

and

Tbl

must be integers.

Selections Table Characteristics

Indpnt: Auto

Depend: Auto

Values are displayed automatically in both

the independent-variable column and in all

dependent-variable columns.

Indpnt: Ask

Depend: Auto

The table is empty; when you enter a value

for the independent variable, all

correspondin

dependent-variable values

are calculated and displayed automatically.

Indpnt: Auto

Depend: Ask

Values are displayed automatically for the

independent variable; to

enerate a value

for a dependent variable, move the cursor

to that cell and press

Indpnt: Ask

Depend: Ask

The table is empty; enter values for the

independent variable; to

enerate a value

for a dependent variable, move the cursor

to that cell and press

To store a value to

TblStart,

Tbl

, or Tbl

nput from the

home screen or a program, select the variable name from

the

VARS TABLE

secondary menu. Tbl

nput is a list of

independent-variable values in the current table.

When you press

[

TBLSET

] in the program editor, you

can select

IndpntAuto, IndpntAsk, DependAuto, and

DependAsk.

Setting Up the Table

TABLE SETUP

Screen

TblStart,

Tbl

Indpnt: Auto,

Indpnt: Ask,

Depend: Auto,

Depend: Ask

Setting Up the

Table from the

Home Screen or

a Program

7-4 Tables

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In the

editor, enter the functions that define the

dependent variables. Only functions that are selected in the

editor are displayed in the table. The current graphing

mode is used. In

Par mode, you must define both

components of each parametric equation (Chapter 4).

To edit a selected

function from the table editor, follow

these steps.

1. Press

[

TABLE

] to display the table, then press

to move the cursor to a dependent-variable column.

2. Press

}

until the cursor is on the function name at the

top of the column. The function is displayed on the

bottom line.

3. Press

. The cursor moves to the bottom line. Edit

the function.

4. Press

†

. The new values are calculated. The

table and the

function are updated automatically.

Note:

You also can use this feature to view the function that

defines a dependent variable without having to leave the table.

Defining the Dependent Variables

Defining

Dependent

Variables from

the Y= Editor

Editing

Dependent

Variables from

the Table Editor

Tables 7-5

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PM Page 5 of 6

To display the table, press

[

TABLE

Current cell

Independent-

variable values

in the first

column

Dependent-

variable values in

the second and

third columns

Current cell’s full value

Note:

The table abbreviates the values, if necessary.

The current graphing mode determines which independent

and dependent variables are displayed in the table

(Chapter 1). In the table above, for example, the

independent variable

and the dependent variables

and

are displayed because

Func

graphing mode is set.

Graphing Mode Independent

Variable

Dependent

Variable

Func

(function)

throu

, and

Par

(parametric)

throu

Pol

(polar)

through

Seq

(sequence)

nu(

)

, and

)

From the home screen, select the

ClrTable

instruction from

the

CATALOG

. To clear the table, press

From a program, select

9:ClrTable

from the

PRGM I/O

or from the

CATALOG

. The table is cleared upon execution.

IndpntAsk

is selected, all independent and dependent

variable values on the table are cleared. If

DependAsk

selected, all dependent variable values on the table are

cleared.

Displaying the Table

The Table

Independent and

Dependent

Variables

Clearing the

Table from the

Home Screen or

a Program

7-6 Tables

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If Indpnt: Auto is selected, you can press

}

and

†

in the

independent-variable column to display more values. As

you scroll the column, the corresponding dependent-

variable values also are displayed. All dependent-variable

values may not be displayed if

Depend: Ask is selected.

Note:

You can scroll back from the value entered for

TblStart

. As you

scroll,

TblStart

is updated automatically to the value shown on the top

line of the table. In the example above,

TblStart=0

and

Tbl=1

generates and displays values of

X=0

, . . . ,

; but you can press

}

scroll back and display the table for

, . . .,

If you have defined more than two dependent variables,

the first two selected

functions are displayed initially.

Press

to display dependent variables defined by

other selected

functions. The independent variable

always remains in the left column, except during a trace

with

Par graphing mode and G

T split-screen mode set.

Tip:

To simultaneously display on the table two dependent variables

that are not defined as consecutive Y= functions, go to the Y= editor

and deselect the Y= functions between the two you want to display.

For example, to simultaneously display

and

on the table, go to

the Y= editor and deselect

and

Scrolling

Independent-

Variable Values

Displaying Other

Dependent

Variables

DRAW Instructions 8-1

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Draw

Instructions

Getting Started: Drawing a Tangent Line

.................

8-2

Using the

DRAW

...................................

8-3

Clearing Drawings

.......................................

8-4

Drawing Line Segments

..................................

8-5

Drawing Horizontal and Vertical Lines

...................

8-6

Drawing Tangent Lines

..................................

8-8

Drawing Functions and Inverses

.........................

8-9

Shading Areas on a Graph

...............................

8-10

Drawing Circles

..........................................

8-11

Placing Text on a Graph

.................................

8-12

Using Pen to Draw on a Graph

...........................

8-13

Drawing Points on a Graph

..............................

8-14

Drawing Pixels

..........................................

8-16

Storing Graph Pictures (

Pic

............................

8-17

Recalling Graph Pictures (

Pic

..........................

8-18

Storing Graph Databases (

GDB

........................

8-19

Recalling Graph Databases (

GDB

......................

8-20

Contents

8-2 DRAW Instructions

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Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to find the equation of the tangent line at X =

‡

2/2 for the

function Y = sinX.

Before you begin, select

Radian and Func

mode from the mode screen, if necessary.

1. Press

to display the

editor. Press

„

to store

sin(X) in Y

2. Press

7 to select 7:ZTrig, which

graphs the equation in the Zoom Trig

window.

3. Press

[

DRAW

] 5 to select 5:Tangent(.

The tangent instruction is initiated.

4. Press

[

‡

] 2

5. Press

. The tangent line is drawn; the

X value and the tangent-line equation are

displayed on the graph.

Getting Started: Drawing a Tangent Line

DRAW Instructions 8-3

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To display the

DRAW

menu, press

[

DRAW

]. The TI

83’s

interpretation of these instructions depends on whether

you accessed the menu from the home screen or the

program editor or directly from a graph.

DRAW POINTS STO

1: ClrDraw

Clears all drawn elements.

2: Line(

Draws a line segment between 2 points.

3: Horizontal

Draws a horizontal line.

4: Vertical

Draws a vertical line.

5: Tangent(

Draws a line segment tangent to a function.

6: DrawF

Draws a function.

7: Shade(

Shades an area between two functions.

8: DrawInv

Draws the inverse of a function.

9: Circle(

Draws a circle.

0: Text(

Draws text on a graph screen.

A: Pen

Activates the free-form drawing tool.

The

DRAW

instructions draw on top of graphs. Therefore,

before you use the

DRAW

instructions, consider whether

you want to perform one or more of the following actions.

•

Change the mode settings on the mode screen.

•

Change the format settings on the format screen.

•

Enter or edit functions in the

editor.

•

Select or deselect functions in the

editor.

•

Change the window variable values.

•

Turn stat plots on or off.

•

Clear existing drawings with

ClrDraw (page 8

4).

Note:

If you draw on a graph and then perform any of the actions

listed above, the graph is replotted without the drawings when you

display the graph again.

You can use any

DRAW

menu instructions except DrawInv

to draw on Func, Par, Pol, and Seq graphs. DrawInv is valid

only in

Func graphing. The coordinates for all

DRAW

instructions are the display’s x-coordinate and y-coordinate

values.

You can use most

DRAW

menu and

DRAW POINTS

instructions to draw directly on a graph, using the cursor

to identify the coordinates. You also can execute these

instructions from the home screen or from within a

program. If a graph is not displayed when you select a

DRAW

menu instruction, the home screen is displayed.

Using the DRAW Menu

DRAW Menu

Before Drawing

on a Graph

Drawing on a

Graph

8-4 DRAW Instructions

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All points, lines, and shading drawn on a graph with

DRAW

instructions are temporary.

To clear drawings from the currently displayed graph,

select

1:ClrDraw from the

DRAW

menu. The current graph

is replotted and displayed with no drawn elements.

To clear drawings on a graph from the home screen or a

program, begin on a blank line on the home screen or in

the program editor. Select

1:ClrDraw from the

DRAW

menu.

The instruction is copied to the cursor location. Press

When

ClrDraw is executed, it clears all drawings from the

current graph and displays the message

Done. When you

display the graph again, all drawn points, lines, circles, and

shaded areas will be gone.

Note:

Before you clear drawings, you can store them with

StorePic

(page 8

17).

Clearing Drawings

Clearing

Drawings When

a Graph Is

Displayed

Clearing

Drawings from

the Home Screen

or a Program

DRAW Instructions 8-5

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To draw a line segment when a graph is displayed, follow

these steps.

1. Select

2:Line( from the

DRAW

menu.

2. Place the cursor on the point where you want the line

segment to begin, and then press

3. Move the cursor to the point where you want the line

segment to end. The line is displayed as you move the

cursor. Press

To continue drawing line segments, repeat steps 2 and 3.

To cancel

Line(, press

‘

Line( also draws a line segment between the coordinates

(

) and (

). The values may be entered as

expressions.

Line(

)

To erase a line segment, enter Line(

,0)

Drawing Line Segments

Drawing a Line

Segment Directly

on a Graph

Drawing a Line

Segment from

the Home Screen

or a Program

8-6 DRAW Instructions

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To draw a horizontal or vertical line when a graph is

displayed, follow these steps.

1. Select

3:Horizontal or 4:Vertical from the

DRAW

menu. A

line is displayed that moves as you move the cursor.

2. Place the cursor on the y-coordinate (for horizontal

lines) or x-coordinate (for vertical lines) through which

you want the drawn line to pass.

3. Press

to draw the line on the graph.

To continue drawing lines, repeat steps 2 and 3.

To cancel

Horizontal or Vertical, press

‘

Drawing Horizontal and Vertical Lines

Drawing a Line

Directly on a

Graph

DRAW Instructions 8-7

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Horizontal (horizontal line) draws a horizontal line at Y=

can be an expression but not a list.

Horizontal

Vertical (vertical line) draws a vertical line at X=

can be

an expression but not a list.

Vertical

To instruct the TI

83 to draw more than one horizontal or

vertical line, separate each instruction with a colon (

: ).

Drawing a Line

from the Home

Screen or a

Program

8-8 DRAW Instructions

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To draw a tangent line when a graph is displayed, follow

these steps.

1. Select

5:Tangent( from the

DRAW

menu.

2. Press

†

and

}

to move the cursor to the function for

which you want to draw the tangent line. The current

graph’s

function is displayed in the top-left corner, if

ExprOn is selected.

3. Press

and

or enter a number to select the point on

the function at which you want to draw the tangent line.

4. Press

. In

Func mode, the X value at which the

tangent line was drawn is displayed on the bottom of

the screen, along with the equation of the tangent line.

In all other modes, the

dy/dx value is displayed.

Tip:

Change the fixed decimal setting on the mode screen if you want

to see fewer digits displayed for

and the equation for

Tangent( (tangent line) draws a line tangent to

expression

in terms of

X, such as Y

or X

, at point X=

value

X can be

an expression.

expression

is interpreted as being in

Func

mode.

Tangent(

expression

value

)

Drawing Tangent Lines

Drawing

a Tangent Line

Directly

on a Graph

Drawing

a Tangent Line

from the Home

Screen or

a Program

DRAW Instructions 8-9

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DrawF (draw function) draws

expression

as a function in

terms of

X on the current graph. When you select 6:DrawF

from the

DRAW

menu, the TI

83 returns to the home screen

or the program editor.

DrawF is not interactive.

DrawF

expression

Note:

You cannot use a list in

expression

to draw a family of curves.

DrawInv (draw inverse) draws the inverse of

expression

plotting

X values on the y-axis and Y values on the x-axis.

When you select

8:DrawInv from the

DRAW

menu, the TI

returns to the home screen or the program editor.

DrawInv

is not interactive. DrawInv works in Func mode only.

DrawInv

expression

Note:

You cannot use a list in

expression

to draw a family of curves.

Drawing Functions and Inverses

Drawing a

Function

Drawing an

Inverse of a

Function

8-10 DRAW Instructions

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PM Page 10 of 20

To shade an area on a graph, select 7:Shade( from the

DRAW

menu. The instruction is pasted to the home screen

or to the program editor.

Shade( draws

lowerfunc

and

upperfunc

in terms of X on

the current graph and shades the area that is specifically

above

lowerfunc

and below

upperfunc

. Only the areas

where

lowerfunc

upperfunc

are shaded.

Xleft

and

Xright

, if included, specify left and right

boundaries for the shading.

Xleft

and

Xright

must be

numbers between

Xmin and Xmax, which are the defaults.

pattern

specifies one of four shading patterns.

pattern=

1 vertical (default)

pattern=

2 horizontal

pattern=

3 negative—slope 45

pattern=

4 positive—slope 45

patres

specifies one of eight shading resolutions.

patres=

1 shades every pixel (default)

patres=

2 shades every second pixel

patres

3 shades every third pixel

patres

4 shades every fourth pixel

patres

5 shades every fifth pixel

patres

6 shades every sixth pixel

patres

7 shades every seventh pixel

patres

8 shades every eighth pixel

Shade(

lowerfunc

upperfunc

[

Xleft

Xright

pattern

patres

]

)

Shading Areas on a Graph

Shading a Graph

DRAW Instructions 8-11

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To draw a circle directly on a displayed graph using the

cursor, follow these steps.

1. Select

9:Circle( from the

DRAW

menu.

2. Place the cursor at the center of the circle you want to

draw. Press

3. Move the cursor to a point on the circumference. Press

to draw the circle on the graph.

Note:

This circle is displayed as circular, regardless of the window

variable values, because you drew it directly on the display. When

you use the

Circle(

instruction from the home screen or a

program, the current window variables may distort the shape.

To continue drawing circles, repeat steps 2 and 3. To

cancel

Circle(, press

‘

Circle( draws a circle with center (

) and

radius.

These

values can be expressions.

Circle(

radius

)

Tip:

When you use

Circle(

on the home screen or from a program,

the current window values may distort the drawn circle. Use

ZSquare

(Chapter 3) before drawing the circle to adjust the window variables

and make the circle circular.

Drawing Circles

Drawing a Circle

Directly on a

Graph

Drawing a Circle

from the Home

Screen or a

Program

8-12 DRAW Instructions

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To place text on a graph when the graph is displayed,

follow these steps.

1. Select

0:Text( from the

DRAW

menu.

2. Place the cursor where you want the text to begin.

3. Enter the characters. Press

[

LOCK

] to

enter letters and

. You may enter TI

83 functions,

variables, and instructions. The font is proportional, so

the exact number of characters you can place on the

graph varies. As you type, the characters are placed on

top of the graph.

To cancel

Text(, press

‘

Text( places on the current graph the characters

comprising

value

, which can include TI

83 functions and

instructions. The top-left corner of the first character is at

pixel (

row

column

), where

row

is an integer between

0 and 57 and

column

is an integer between 0 and 94. Both

row

and

column

can be expressions.

Text(

row

column

value

. . .

)

value

can be text enclosed in quotation marks (

" ), or it

can be an expression. The TI

83 will evaluate an

expression and display the result with up to 10 characters.

On a Horiz split screen, the maximum value for

row

is 25.

On a

T split screen, the maximum value for

row

is 45,

and the maximum value for

column

is 46.

Placing Text on a Graph

Placing Text

Directly on a

Graph

Placing Text on a

Graph from the

Home Screen or

a Program

Split Screen

DRAW Instructions 8-13

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Pen draws directly on a graph only. You cannot execute

Pen from the home screen or a program.

To draw on a displayed graph, follow these steps.

1. Select

A:Pen from the

DRAW

menu.

2. Place the cursor on the point where you want to begin

drawing. Press

to turn on the pen.

3. Move the cursor. As you move the cursor, you draw on

the graph, shading one pixel at a time.

4. Press

to turn off the pen.

For example,

Pen was used to create the arrow pointing to

the local minimum of the selected function.

To continue drawing on the graph, move the cursor to a

new position where you want to begin drawing again, and

then repeat steps 2, 3, and 4. To cancel

Pen, press

‘

Using Pen to Draw on a Graph

Using Pen to

Draw on a Graph

8-14 DRAW Instructions

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To display the

DRAW POINTS

menu, press

[

DRAW

]

The TI

83’s interpretation of these instructions depends on

whether you accessed this menu from the home screen or

the program editor or directly from a graph.

DRAW POINTS STO

1: Pt-On(

Turns on a point.

2: Pt-Off(

Turns off a point.

3: Pt-Change(

Toggles a point on or off.

4: Pxl-On(

Turns on a pixel.

5: Pxl-Off(

Turns off a pixel.

6: Pxl-Change(

Toggles a pixel on or off.

7: pxl-Test(

Returns 1 if pixel on, 0 if pixel off.

To draw a point on a graph, follow these steps.

1. Select

1:Pt

On( from the

DRAW POINTS

menu.

2. Move the cursor to the position where you want to draw

the point.

3. Press

to draw the point.

To continue drawing points, repeat steps 2 and 3. To

cancel

On(, press

‘

Drawing Points on a Graph

DRAW POINTS

Drawing Points

Directly on a

Graph with

On(

DRAW Instructions 8-15

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To erase (turn off) a drawn point on a graph, follow these

steps.

1. Select

2:Pt

Off( (point off) from the

DRAW POINTS

menu.

2. Move the cursor to the point you want to erase.

3. Press

to erase the point.

To continue erasing points, repeat steps 2 and 3. To cancel

Off(, press

‘

To change (toggle on or off) a point on a graph, follow

these steps.

1. Select

3:Pt

Change( (point change) from the

DRAW

POINTS

menu.

2. Move the cursor to the point you want to change.

3. Press

to change the point’s on/off status.

To continue changing points, repeat steps 2 and 3. To

cancel

Change(, press

‘

On( (point on) turns on the point at (X=

,Y=

). Pt

Off(

turns the point off. Pt

Change( toggles the point on or off.

mark

is optional; it determines the point’s appearance;

specify

1, 2, or 3, where:

1 =

(dot; default) 2 =

›

(box) 3 = + (cross)

On(

[

mark

]

)

Off(

[

mark

]

)

Change(

)

Note:

If you specified

mark

to turn on a point with

On(

, you must

specify

mark

when you turn off the point with

Off(

Change(

does not have the

mark

option.

Erasing Points

with Pt-Off(

Changing Points

with Pt-Change(

Drawing Points

from the Home

Screen or a

Program

8-16 DRAW Instructions

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A pixel is a square dot on the TI

83 display. The Pxl

(pixel)

instructions let you turn on, turn off, or reverse a pixel

(dot) on the graph using the cursor. When you select a

pixel instruction from the

DRAW POINTS

menu, the TI

returns to the home screen or the program editor. The

pixel instructions are not interactive.

Pxl

On( (pixel on) turns on the pixel at (

row

column

where

row

is an integer between 0 and 62 and

column

is an

integer between 0 and 94.

Pxl

Off( turns the pixel off. Pxl

Change( toggles the pixel on

and off.

Pxl

On(

row

column

)

Pxl

Off(

row

column

)

Pxl

Change(

row

column

)

pxl

Test(

(pixel test) returns 1 if the pixel at (

row

column

)

is turned on or 0 if the pixel is turned off on the current

graph.

row

must be an integer between 0 and 62.

column

must be an integer between 0 and 94.

pxl

Test(

row

column

)

On a Horiz split screen, the maximum value for

row

is 30

for

Pxl

On(, Pxl

Off(, Pxl

Change(, and pxl

Test(.

On a

T split screen, the maximum value for

row

is 50 and

the maximum value for

column

is 46 for

Pxl

On(, Pxl

Off(,

Pxl

Change(, and pxl

Test(.

Drawing Pixels

TI-83 Pixels

Turning On and

Off Pixels with

Pxl-On( and

Pxl-Off(

Using pxl-Test(

Split Screen

DRAW Instructions 8-17

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To display the

DRAW STO

menu, press

[

DRAW

]

When you select an instruction from the

DRAW STO

menu,

the TI

83 returns to the home screen or the program editor.

The picture and graph database instructions are not

interactive.

DRAW POINTS STO

1:StorePic

Stores the current picture.

2:RecallPic

Recalls a saved picture.

3:StoreGDB

Stores the current graph database.

4:RecallGDB

Recalls a saved graph database.

You can store up to 10 graph pictures, each of which is an

image of the current graph display, in picture variables

Pic1 through Pic9, or Pic0. Later, you can superimpose the

stored picture onto a displayed graph from the home

screen or a program.

A picture includes drawn elements, plotted functions, axes,

and tick marks. The picture does not include axes labels,

lower and upper bound indicators, prompts, or cursor

coordinates. Any parts of the display hidden by these items

are stored with the picture.

To store a graph picture, follow these steps.

1. Select

1:StorePic from the

DRAW STO

menu. StorePic is

pasted to the current cursor location.

2. Enter the number (from

1 to 9, or 0) of the picture

variable to which you want to store the picture. For

example, if you enter

3, the TI

83 will store the picture

Pic3.

Note:

You also can select a variable from the

PICTURE

secondary menu (



). The variable is pasted next to

StorePic

3. Press

to display the current graph and store the

picture.

Storing Graph Pictures (Pics)

DRAW STO Menu

Storing a Graph

Picture

8-18 DRAW Instructions

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To recall a graph picture, follow these steps.

1. Select

2:RecallPic from the

DRAW STO

menu. RecallPic

is pasted to the current cursor location.

2. Enter the number (from

1 to 9, or 0) of the picture

variable from which you want to recall a picture. For

example, if you enter

3, the TI

83 will recall the picture

stored to

Pic3.

Note:

You also can select a variable from the

PICTURE

secondary menu (



). The variable is pasted next to

RecallPic

3. Press

to display the current graph with the

picture superimposed on it.

Note:

Pictures are drawings. You cannot trace a curve that is part of a

picture.

To delete graph pictures from memory, use the

MEMORY DELETE FROM

menu (Chapter 18).

Recalling Graph Pictures (Pics)

Recalling a

Graph Picture

Deleting a Graph

Picture

DRAW Instructions 8-19

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A graph database (

GDB

) contains the set of elements that

defines a particular graph. You can recreate the graph from

these elements. You can store up to 10

GDB

s in variables

GDB1 through GDB9, or GDB0 and recall them to recreate

graphs.

GDB

stores five elements of a graph.

•

Graphing mode

•

Window variables

•

Format settings

•

All functions in the

editor and the selection status of

each

•

Graph style for each

function

GDB

s do not contain drawn items or stat plot definitions.

To store a graph database, follow these steps.

1. Select

3:StoreGDB from the

DRAW STO

menu. StoreGDB

is pasted to the current cursor location.

2. Enter the number (from

1 to 9, or 0) of the

GDB

variable

to which you want to store the graph database. For

example, if you enter

7, the TI

83 will store the

GDB

GDB7.

Note:

You also can select a variable from the

GDB

secondary

menu (



). The variable is pasted next to

StoreGDB

3. Press

to store the current database to the

specified

GDB

variable.

Storing Graph Databases (GDBs)

What Is a Graph

Database?

Storing a Graph

Database

8-20 DRAW Instructions

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CAUTION:

When you recall a

GDB

, it replaces all existing

functions. Consider storing the current

functions to

another database before recalling a stored

GDB

To recall a graph database, follow these steps.

1. Select

4:RecallGDB from the

DRAW STO

menu.

RecallGDB is pasted to the current cursor location.

2. Enter the number (from

1 to 9, or 0) of the

GDB

variable

from which you want to recall a

GDB

. For example, if

you enter

7, the TI

83 will recall the

GDB

stored to

GDB7.

Note:

You also can select a variable from the

GDB

secondary

menu (



). The variable is pasted next to

RecallGDB

3. Press

to replace the current

GDB

with the

recalled

GDB

. The new graph is not plotted. The TI

changes the graphing mode automatically, if necessary.

To delete a

GDB

from memory, use the

MEMORY DELETE

FROM

menu (Chapter 18).

Recalling Graph Databases (GDBs)

Recalling a

Graph Database

Deleting a Graph

Database

Split Screen 9-1

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Split

Screen

Getting Started: Exploring the Unit Circle

................

9-2

Using Split Screen

.......................................

9-3

Horiz

(Horizontal) Split Screen

..........................

9-4

(Graph-Table) Split Screen

..........................

9-5

83 Pixels in

Horiz

and

Mode

......................

9-6

Contents

9-2 Split Screen

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Getting Started is a fast-paced introduction. Read the chapter for details.

Use

T (graph-table) split-screen mode to explore the unit circle and its

relationship to the numeric values for the commonly used trigonometric angles

of 0

, 30

, 45

, 60

, 90

, and so on.

1. Press

to display the mode screen.

Press

†

to select

Degree

mode. Press

†

to select Par

(parametric) graphing mode.

Press

†

to select

(graph-table) split-screen mode.

2. Press

[

FORMAT

] to display the format

screen. Press

†

select

ExprOff.

3. Press

to display the

editor for Par

graphing mode. Press

™

„

to store

cos(T) to X

. Press

„

to store

sin(T) to Y

4. Press

to display the window

editor. Enter these values for the window

variables.

Tmin=0 Xmin=

2.3 Ymin=

2.5

Tmax=360 Xmax=2.3 Ymax=2.5

Tstep=15 Xscl=1 Yscl=1

5. Press

. On the left, the unit circle is

graphed parametrically in

Degree mode

and the trace cursor is activated. When

T=0 (from the graph trace coordinates),

you can see from the table on the right

that the value of

(cos(T)) is 1 and Y

(sin(T)) is 0. Press

to move the cursor to

the next 15

angle increment. As you trace

around the circle in steps of 15

, an

approximation of the standard value for

each angle is highlighted in the table.

Getting Started: Exploring the Unit Circle

Split Screen 9-3

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To set a split-screen mode, press

, and then move the

cursor to the bottom line of the mode screen.

•

Select

Horiz (horizontal) to display the graph screen and

another screen split horizontally.

•

Select

T (graph-table) to display the graph screen and

table screen split vertically.

The split screen is activated when you press any key that

applies to either half of the split screen.

Some screens are never displayed as split screens. For

example, if you press

Horiz or G

T mode, the mode

screen is displayed as a full screen. If you then press a key

that displays either half of a split screen, such as

the split screen returns.

When you press a key or key combination in either

Horiz or

T mode, the cursor is placed in the half of the display for

which that key applies. For example, if you press

the cursor is placed in the half in which the graph is

displayed. If you press

[

TABLE

], the cursor is placed in

the half in which the table is displayed.

The TI

83 will remain in split-screen mode until you

change back to

Full screen mode.

Using Split Screen

Setting a Split-

Screen Mode

9-4 Split Screen

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In Horiz (horizontal) split-screen mode, a horizontal line

splits the screen into top and bottom halves.

The top half displays the graph.

The bottom half displays any of these editors.

•

Home screen (four lines)

•

editor (four lines)

•

Stat list editor (two rows)

•

Window editor (three settings)

•

Table editor (two rows)

To use the top half of the split screen:

•

Press

•

Select a

ZOOM

CALC

operation.

To use the bottom half of the split screen:

•

Press any key or key combination that displays the

home screen.

•

Press

(

editor).

•

Press

…

(stat list editor).

•

Press

(window editor).

•

Press

[

TABLE

] (table editor).

All other screens are displayed as full screens in

Horiz

split-screen mode.

To return to the

Horiz split screen from a full screen when

Horiz mode, press any key or key combination that

displays the graph, home screen,

editor, stat list editor,

window editor, or table editor.

Horiz (Horizontal) Split Screen

Horiz Mode

Moving from Half

to Half in Horiz

Mode

Full Screens in

Horiz Mode

Split Screen 9-5

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In G

T (graph-table) split-screen mode, a vertical line splits

the screen into left and right halves.

The left half displays the graph.

The right half displays the table.

To use the left half of the split screen:

•

Press

•

Select a

ZOOM

CALC

operation.

To use the right half of the split screen, press

[

TABLE

As you move the trace cursor along a graph in the split

screen’s left half in

T mode, the table on the right half

automatically scrolls to match the current cursor values.

Note:

When you trace in

Par

graphing mode, both components of an

equation (

and

) are displayed in the two columns of the table.

As you trace, the current value of the independent variable

displayed on the graph.

All screens other than the graph and the table are

displayed as full screens in

T split-screen mode.

To return to the

T split screen from a full screen when in

T mode, press any key or key combination that displays

the graph or the table.

G-T (Graph-Table) Split Screen

G-T Mode

Moving from Half

to Half in G-T

Mode

Using

G-T Mode

Full Screens in

T Mode

9-6 Split Screen

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Note:

Each set of numbers in parentheses above represents the row

and column of a corner pixel, which is turned on.

For

Pxl

On(

Pxl

Off(

Pxl

Change(

, and

pxl

Test(

•

Horiz

mode,

row

must be

{

30;

column

must be

{

94.

•

mode,

row

must be

{

50;

column

must be

{

46.

Pxl

On(

row

column

)

For the

Text(

instruction:

•

Horiz

mode,

row

must be

{

25;

column

must be

{

94.

•

mode,

row

must be

{

45;

column

must be

{

46.

Text(

row

column

text

For the

Output(

instruction:

•

Horiz

mode,

row

must be

{

column

must be

{

16.

•

mode,

row

must be

{

column

must be

{

16.

Output(

row

column

text

To set

Horiz

from a program, follow these steps.

1. Press

while the cursor is on a blank line in the

program editor.

2. Select

Horiz

The instruction is pasted to the cursor location. The mode

is set when the instruction is encountered during program

execution. It remains in effect after execution.

Note:

You also can paste

Horiz

to the home screen or

program editor from the

CATALOG

(Chapter 15).

TI-83 Pixels in Horiz and G-T Modes

TI-83 Pixels in

Horiz and G-T

Modes

DRAW POINTS

Menu Pixel

Instructions

DRAW Menu

Text( Instruction

PRGM I/O Menu

Output(

Instruction

Setting a

Split-Screen

Mode from the

Home Screen or

a Program

Matrices 10-1

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Matrices

Getting Started: Systems of Linear Equations

............

10-2

Defining a Matrix

........................................

10-2

Viewing and Editing Matrix Elements

....................

10-4

Using Matrices with Expressions

........................

10-7

Displaying and Copying Matrices

........................

10-8

Using Math Functions with Matrices

.....................

10-9

Using the

MATRX MATH

Operations

.....................

10-12

Contents

10-2 Matrices

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Getting Started is a fast-paced introduction. Read the chapter for details.

Find the solution of X + 2Y + 3Z = 3 and 2X + 3Y + 4Z = 3. On the TI

83, you

can solve a system of linear equations by entering the coefficients as elements

in a matrix, and then using

rref( to obtain the reduced row-echelon form.

1. Press



. Press

to display the

MATRX EDIT

menu. Press 1 to select 1: [A]¸

2. Press

to define a 2×4

matrix. The rectangular cursor indicates

the current element. Ellipses (

...) indicate

additional columns beyond the screen.

3. Press 1

to enter the first element.

The rectangular cursor moves to the

second column of the first row.

4. Press 2

to complete

the first row for X + 2Y + 3Z = 3.

5. Press

enter the second row for 2X + 3Y + 4Z = 3.

6. Press

[

QUIT

] to return to the home

screen. If necessary, press

‘

to clear

the home screen. Press



display the

MATRX MATH

menu. Press

}

wrap to the end of the menu. Select

B:rref(

to copy rref( to the home screen.

7. Press



1 to select 1: [A] from the

MATRX NAMES

menu. Press

. The

reduced row-echelon form of the matrix is

displayed and stored in

Ans.

1Z =

3 so X =

3 + Z

1Y + 2Z = 3 so Y = 3

Getting Started: Systems of Linear Equations

Matrices 10-3

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A matrix is a two-dimensional array. You can display,

define, or edit a matrix in the matrix editor. The TI

83 has

10 matrix variables,

[A] through [J]. You can define a

matrix directly in an expression. A matrix, depending on

available memory, may have up to 99 rows or columns.

You can store only real numbers in TI

83 matrices.

Before you can define or display a matrix in the editor, you

first must select the matrix name. To do so, follow these

steps.

1. Press



to display the

MATRX EDIT

menu. The

dimensions of any previously defined matrices are

displayed.

2. Select the matrix you want to define. The

MATRX EDIT

screen is displayed.

The dimensions of the matrix (

row

column

) are

displayed on the top line. The dimensions of a new matrix

are

1 ×1. You must accept or change the dimensions each

time you edit a matrix. When you select a matrix to define,

the cursor highlights the row dimension.

•

To accept the row dimension, press

•

To change the row dimension, enter the number of rows

(up to

99), and then press

The cursor moves to the column dimension, which you

must accept or change the same way you accepted or

changed the row dimension. When you press

, the

rectangular cursor moves to the first matrix element.

Defining a Matrix

What Is a Matrix?

Selecting a

Matrix

Accepting or

Changing Matrix

Dimensions

10-4 Matrices

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After you have set the dimensions of the matrix, you can

view the matrix and enter values for the matrix elements.

In a new matrix, all values are zero.

Select the matrix from the

MATRX EDIT

menu and enter or

accept the dimensions. The center portion of the matrix

editor displays up to seven rows and three columns of a

matrix, showing the values of the elements in abbreviated

form if necessary. The full value of the current element,

which is indicated by the rectangular cursor, is displayed

on the bottom line.

This is an 8 × 4 matrix. Ellipses in the left or right column

indicate additional columns.

in the right column

indicate additional rows.

To delete matrices from memory, use the

MEMORY DELETE

FROM

secondary menu (Chapter 18).

Viewing and Editing Matrix Elements

Displaying Matrix

Elements

Deleting a Matrix

Matrices 10-5

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The matrix editor has two contexts, viewing and editing. In

viewing context, you can use the cursor keys to move

quickly from one matrix element to the next. The full value

of the highlighted element is displayed on the bottom line.

Select the matrix from the

MATRX EDIT

menu, and then

enter or accept the dimensions.

Key Function

Moves the rectan

ular cursor within the

current row.

†

}

Moves the rectan

ular cursor within the

current column; on the top row,

}

moves

the cursor to the column dimension; on the

column dimension,

}

moves the cursor to

the row dimension.

Switches to editin

context; activates the

edit cursor on the bottom line.

‘

Switches to editin

context; clears the

alue on the bottom line.

ny entry

character

Switches to editin

context; clears the

alue on the bottom line; copies the

character to the bottom line.

[

INS

] Nothing

{

Nothing

Viewing a Matrix

Viewing-Context

Keys

10-6 Matrices

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In editing context, an edit cursor is active on the bottom

line. To edit a matrix element value, follow these steps.

1. Select the matrix from the

MATRX EDIT

menu, and then

enter or accept the dimensions.

2. Press

}

, and

†

to move the cursor to the matrix

element you want to change.

3. Switch to editing context by pressing

‘

, or

an entry key.

4. Change the value of the matrix element using the

editing-context keys described below. You may enter an

expression, which is evaluated when you leave editing

context.

Note:

You can press

‘

to restore the value at the

rectangular cursor if you make a mistake.

5. Press

}

, or

†

to move to another element.

Key Function

Moves the edit cursor within the value.

†

}

Stores the value displayed on the bottom

line to the matrix element; switches to

iewin

context and moves the rectan

ular

cursor within the column.

Stores the value displayed on the bottom

line to the matrix element; switches to

iewin

context and moves the rectan

ular

cursor to the next row element.

‘

Clears the value on the bottom line.

ny entry

character

Copies the character to the location of the

edit cursor on the bottom line.

[

INS

] Activates the insert cursor.

{

Deletes the character under the edit cursor

on the bottom line.

Editing a Matrix

Element

Editing-Context

Keys

Matrices 10-7

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To use a matrix in an expression, you can do any of the

following.

•

Copy the name from the

MATRX NAMES

menu.

•

Recall the contents of the matrix into the expression

with

[

RCL

] (Chapter 1).

•

Enter the matrix directly (see below).

You can enter, edit, and store a matrix in the matrix editor.

You also can enter a matrix directly in an expression.

To enter a matrix in an expression, follow these steps.

1. Press

[

[ ] to indicate the beginning of the matrix.

2. Press

[

[ ] to indicate the beginning of a row.

3. Enter a value, which can be an expression, for each

element in the row. Separate the values with commas.

4. Press

[

] ] to indicate the end of a row.

5. Repeat steps 2 through 4 to enter all of the rows.

6. Press

[

] ] to indicate the end of the matrix.

Note:

The closing

]]

are not necessary at the end of an expression

or preceding

The resulting matrix is displayed in the form:

[[

element

1,1

,...,

element

1,n

],...,[

element

m,1

,...,

element

m,n

]]

Any expressions are evaluated when the entry is

executed.

Note:

The commas that you must enter to separate elements are

not displayed on output.

Using Matrices with Expressions

Using a Matrix in

an Expression

Entering a Matrix

in an Expression

10-8 Matrices

8310MTRX.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:35 PM Printed: 02/19/01 1:36

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To display the contents of a matrix on the home screen,

select the matrix from the

MATRX NAMES

menu, and then

press

Ellipses in the left or right column indicate additional

columns.

in the right column indicate additional

rows. Press

†

, and

}

to scroll the matrix.

To copy a matrix, follow these steps.

1. Press



to display the

MATRX NAMES

menu.

2. Select the name of the matrix you want to copy.

3. Press

4. Press



again and select the name of the new

matrix to which you want to copy the existing matrix.

5. Press

to copy the matrix to the new matrix name.

On the home screen or from within a program, you can

store a value to, or recall a value from, a matrix element.

The element must be within the currently defined matrix

dimensions. Select

matrix

from the

MATRX NAMES

menu.

[

matrix

](

row

column

)

Displaying and Copying Matrices

Displaying a

Matrix

Copying One

Matrix to Another

Accessing a

Matrix Element

Matrices 10-9

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You can use many of the math functions on the TI

keyboard, the

MATH

menu, the

MATH NUM

menu, and the

MATH TEST

menu with matrices. However, the dimensions

must be appropriate. Each of the functions below creates a

new matrix; the original matrix remains the same.

To add (

) or subtract (

) matrices, the dimensions must

be the same. The answer is a matrix in which the elements

are the sum or difference of the individual corresponding

elements.

matrixA

matrixB

matrixA

matrixB

To multiply (

) two matrices together, the column

dimension of

matrixA

must match the row dimension of

matrixB

matrixA

matrixB

Multiplying a

matrix

by a

value

or a

value

by a

matrix

returns a matrix in which each element of

matrix

multiplied by

value

matrix

value

matrix

Negating a matrix (

) returns a matrix in which the sign

of every element is changed (reversed).

matrix

Using Math Functions with Matrices

Using Math

Functions with

Matrices

+ (Add), –

(Subtract),

(Multiply)

(Negation)

10-10 Matrices

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abs( (absolute value,

MATH NUM

menu) returns a matrix

containing the absolute value of each element of

matrix

abs(

matrix

)

round( (

MATH NUM

menu) returns a matrix. It rounds every

element in

matrix

to #

decimals

(



9). If

#decimals

omitted, the elements are rounded to 10 digits.

round(

matrix

[

#decimals

]

)

Use the

function (

—

) to invert a matrix (^

1 is not

valid).

matrix

must be square. The determinant cannot

equal zero.

matrix

To raise a matrix to a power,

matrix

must be square. You

can use

(

MATH

menu), or ^

power

(

›

) for integer

power

between

0 and 255.

matrix

power

abs(

round(

(Inverse)

Powers

Matrices 10-11

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To compare two matrices using the relational operations =

and

(

TEST

menu), they must have the same dimensions. =

and

compare

matrixA

and

matrixB

on an element-by-

element basis. The other relational operations are not valid

with matrices.

matrixA

matrixB

returns

1 if every comparison is true; it

returns

0 if any comparison is false.

matrixA

matrixB

returns

1 if at least one comparison is

false; it returns

0 if no comparison is false.

iPart( (integer part), fPart( (fractional part), and int(

(greatest integer) are on the

MATH NUM

menu.

iPart( returns a matrix containing the integer part of each

element of

matrix

fPart( returns a matrix containing the fractional part of

each element of

matrix

int( returns a matrix containing the greatest integer of each

element of

matrix

iPart(

matrix

)

fPart(

matrix

)

int(

matrix

)

Relational

Operations

iPart(, fPart(, int(

10-12 Matrices

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To display the

MATRX MATH

menu, press



NAMES MATH EDIT

1: det(

Calculates the determinant.

Transposes the matrix.

3: dim(

Returns the matrix dimensions.

4: Fill(

Fills all elements with a constant.

5: identity(

Returns the identity matrix.

6: randM(

Returns a random matrix.

7: augment(

Appends two matrices.

8: Matr

list(

Stores a matrix to a list.

9: List

matr(

Stores a list to a matrix.

0: cumSum(

Returns the cumulative sums of a matrix.

A: ref(

Returns the row-echelon form of a matrix.

B: rref(

Returns the reduced row-echelon form.

C: rowSwap(

Swaps two rows of a matrix.

D: row+(

Adds two rows; stores in the second row.

row(

Multiplies the row by a number.

row+(

Multiplies the row, adds to the second row.

det( (determinant) returns the determinant (a real number)

of a square

matrix

det(

matrix

)

(transpose) returns a matrix in which each element (row,

column) is swapped with the corresponding element

(column, row) of

matrix

dim( (dimension) returns a list containing the dimensions

(

{

rows

columns

}) of

matrix

dim(

matrix

)

Note:

dim(

matrix

)

(1)

returns the number of rows.

dim(

matrix

)

(2)

returns the number of columns.

Using the MATRX MATH Operations

MATRX MATH

det(

(Transpose)

Accessing Matrix

Dimensions with

dim(

Matrices 10-13

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Use dim( with

to create a new

matrixname

dimensions

rows

columns

with

0 as each element.

{

rows

columns

}

dim(

matrixname

)

Use dim( with

to redimension an existing

matrixname

to dimensions

rows

columns

. The elements

in the old

matrixname

that are within the new dimensions

are not changed. Additional created elements are zeros.

Matrix elements that are outside the new dimensions are

deleted.

{

rows

columns

}

dim(

matrixname

)

Fill(

stores

value

to every element in

matrixname

Fill(

value

matrixname

)

identity( returns the identity matrix of

dimension

rows ×

dimension

columns.

identity(

dimension

)

randM(

(create random matrix) returns a

rows

columns

random matrix of integers

‚

9 and



9. The seed value

stored to the

rand function controls the values (Chapter 2).

randM(

rows

columns

)

Creating a Matrix

with dim(

Redimensioning a

Matrix with dim(

Fill(

identity(

randM(

10-14 Matrices

8310MTRX.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:35 PM Printed: 02/19/01 1:36

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augment( appends

matrixA

matrixB

as new columns.

matrixA

and

matrixB

both must have the same number of

rows.

augment(

matrixA

matrixB

)

Matr

list( (matrix stored to list) fills each

listname

with

elements from each column in

matrix

Matr

list( ignores

extra

listname

arguments. Likewise,

Matr

list( ignores

extra

matrix

columns.

Matr

list(

matrix

listnameA

,...,

listname n

)

Matr

list( also fills a

listname

with elements from a specified

column#

matrix

. To fill a list with a specific column from

matrix

, you must enter

column#

after

matrix

Matr

list(

matrix

column#

listname

)

List

matr( (lists stored to matrix) fills

matrixname

column by

column with the elements from each

list

. If dimensions of all

lists

are not equal,

List

matr( fills each extra

matrixname

row with

0. Complex lists are not valid.

List

matr(

listA

,...,

list n

matrixname

)

augment(

Matr

list(

List

matr(

Matrices 10-15

8310MTRX.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:35 PM Printed: 02/19/01 1:36

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cumSum( returns cumulative sums of the elements in

matrix

, starting with the first element. Each element is the

cumulative sum of the column from top to bottom.

cumSum(

matrix

)

MATRX MATH

menu items A through F are row operations.

You can use a row operation in an expression. Row

operations do not change

matrix

in memory. You can

enter all row numbers and values as expressions. You can

select the matrix from the

MATRX NAMES

menu.

ref( (row-echelon form) returns the row-echelon form of a

real

matrix

. The number of columns must be greater than

or equal to the number of rows.

ref(

matrix

)

rref( (reduced row-echelon form) returns the reduced row-

echelon form of a real

matrix

. The number of columns must

be greater than or equal to the number of rows.

rref(

matrix

)

cumSum(

Row Operations

ref(, rref(

10-16 Matrices

8310MTRX.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:35 PM Printed: 02/19/01 1:36

PM Page 16 of 16

rowSwap( returns a matrix. It swaps

rowA

and

rowB

matrix

rowSwap(

matrix

rowA

rowB

)

row+( (row addition) returns a matrix. It adds

rowA

and

rowB

matrix

and stores the results in

rowB

row+(

matrix

rowA

rowB

)

row(

(row multiplication) returns a matrix. It multiplies

row

matrix

value

and stores the results in

row

row(

value

matrix

row

)

row+(

(row multiplication and addition) returns a matrix.

It multiplies

rowA

matrix

value

, adds it to

rowB

, and

stores the results in

rowB

row+(

value

matrix

rowA

rowB

)

rowSwap(

row+(

row(

row+(

Lists 11-1

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 1 of 18

Lists

Getting Started: Generating a Sequence

..................

11-2

Naming Lists

.............................................

11-3

Storing and Displaying Lists

.............................

11-4

Entering List Names

.....................................

11-6

Attaching Formulas to List Names

.......................

11-7

Using Lists in Expressions

...............................

11-9

LIST OPS

..........................................

11-10

LIST MATH

........................................

11-17

Contents

11-2 Lists

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 2 of 18

Getting Started is a fast-paced introduction. Read the chapter for details.

Calculate the first eight terms of the sequence 1/A

. Store the results to a user-

created list. Then display the results in fraction form. Begin this example on a

blank line on the home screen.

1. Press

[

LIST

]

to display the

LIST OPS

menu.

2. Press 5 to select 5:seq(, which pastes seq( to

the current cursor location.

3. Press

[

]

[

]

to enter the sequence.

4. Press

, and then press

turn on alpha-lock. Press [

] [

], and

then press

to turn off alpha-lock.

Press

1 to complete the list name.

5. Press

to generate the list and store it

SEQ1. The list is displayed on the home

screen. An ellipsis (

...) indicates that the list

continues beyond the viewing window.

Press

repeatedly (or press and hold

)

to scroll the list and view all the list

elements.

6. Press

[

LIST

] to display the

LIST NAMES

menu. Press

to paste

SEQ1

to the

current cursor location. (If

SEQ1 is not item

1 on your

LIST NAMES

menu, move the

cursor to

SEQ1 before you press

7. Press



to display the

MATH

menu.

Press

1 to select 1:

Frac, which pastes

Frac

to the current cursor location.

8. Press

to show the sequence in

fraction form. Press

repeatedly (or press

and hold

) to scroll the list and view all

the list elements.

Getting Started: Generating a Sequence

Lists 11-3

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 3 of 18

The TI

83 has six list names in memory: L

, L

and

. The list names L

through L

are on the keyboard

above the numeric keys

through

. To paste one of

these names to a valid screen, press

, and then press

the appropriate key.

through L

are stored in stat list

editor columns

1 through 6 when you reset memory.

To create a list name on the home screen, follow these steps.

1. Press

[

{

], enter one or more list elements, and then

press

[

}

]. Separate list elements with commas. List

elements can be real numbers, complex numbers, or

expressions.

2. Press

3. Press

[

letter from A to Z or

] to enter the first

letter of the name.

4. Enter zero to four letters,

, or numbers to complete the

name.

5. Press

. The list is displayed on the next line. The

list name and its elements are stored in memory. The

list name becomes an item on the

LIST NAMES

menu.

Note:

If you want to view a user-created list in the stat list editor,

you must store it in the stat list editor (Chapter 12).

You also can create a list name in these four places.

•

At the

Name= prompt in the stat list editor

•

At an

Xlist:, Ylist:, or Data List: prompt in the stat plot

editor

•

At a

List:, List1:, List2:, Freq:, Freq1:, Freq2:, XList:, or

YList: prompt in the inferential stat editors

•

On the home screen using

SetUpEditor

You can create as many list names as your TI

83 memory

has space to store.

Naming Lists

Using TI-83 List

Names L

through L

Creating a List

Name on the

Home Screen

11-4 Lists

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 4 of 18

You can store list elements in either of two ways.

•

Use braces and

on the home screen.

•

Use the stat list editor (Chapter 12).

The maximum dimension of a list is 999 elements.

Tip:

When you store a complex number to a list, the entire list is

converted to a list of complex numbers. To convert the list to a list of

real numbers, display the home screen, and then enter

real(

listname

)

listname

To display the elements of a list on the home screen, enter

the name of the list (preceded by

if necessary; see page

16), and then press

. An ellipsis indicates that the

list continues beyond the viewing window. Press

repeatedly (or press and hold

) to scroll the list and view

all the list elements.

Storing and Displaying Lists

Storing Elements

to a List

Displaying a List

on the Home

Screen

Lists 11-5

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 5 of 18

To copy a list, store it to another list.

You can store a value to or recall a value from a specific

list

element

. You can store to any element within the

current list dimension or one element beyond.

listname

(

element

)

To delete lists from memory, including L

through L

, use the

MEMORY DELETE FROM

secondary menu (Chapter 18).

Resetting memory restores

through L

. Removing a list

from the stat list editor does not delete it from memory.

You can use lists to graph a family of curves (Chapter 3).

Copying One List

to Another

Accessing a List

Element

Deleting a List

from Memory

Using Lists in

Graphing

11-6 Lists

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 6 of 18

To display the

LIST NAMES

menu, press

[

LIST

]. Each

item is a user-created list name.

LIST NAMES

menu items are

sorted automatically in alphanumerical order. Only the first

10 items are labeled, using

1 through 9, then 0. To jump to

the first list name that begins with a particular alpha

character or

, press

[

letter from A to Z or

Tip:

From the top of a menu, press

}

to move to the bottom. From the

bottom, press

†

to move to the top.

Note:

The

LIST NAMES

menu omits list names

through

. Enter

through

directly from the keyboard (page 11

3).

When you select a list name from the

LIST NAMES

menu,

the list name is pasted to the current cursor location.

•

The list name symbol

precedes a list name when the

name is pasted where non-list name data also is valid,

such as the home screen.

•

The

symbol does not precede a list name when the

name is pasted where a list name is the only valid input,

such as the stat list editor’s Name= prompt or the stat

plot editor’s XList: and YList: prompts.

To enter an existing list name directly, follow these steps.

1. Press

[

LIST

]

to display the

LIST OPS

menu.

2. Select

, which pastes

to the current cursor location.

is not always necessary (page 11

16).

Note:

You also can paste

to the

current cursor location from the

CATALOG

(Chapter 15).

3. Enter the characters that comprise the list name.

Entering List Names

Using the

LIST NAMES

Entering a User-

Created List

Name Directly

Lists 11-7

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Page 7 of 18

You can attach a formula to a list name so that each list

element is a result of the formula. When executed, the

attached formula must resolve to a list.

When anything in the attached formula changes, the list to

which the formula is attached is updated automatically.

•

When you edit an element of a list that is referenced in

the formula, the corresponding element in the list to

which the formula is attached is updated.

•

When you edit the formula itself, all elements in the list

to which the formula is attached are updated.

For example, the first screen below shows that elements

are stored to

, and the formula L

+10 is attached to the

list name

ADD10

. The quotation marks designate the

formula to be attached to

ADD10

. Each element of

ADD10

is the sum of an element in L

and 10.

The next screen shows another list, L

. The elements of L

are the sum of the same formula that is attached to L

However, quotation marks are not entered, so the formula

is not attached to

On the next line,

(1):L

changes the first element in L

, and then redisplays L

The last screen shows that editing L

updated

ADD10

, but

did not change

. This is because the formula L

+10 is

attached to

ADD10

, but it is not attached to L

Note:

To view a formula that is attached to a list name, use the stat list

editor (Chapter 12).

Attaching Formulas to List Names

Attaching a

Formula to a List

Name

11-8 Lists

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 8 of 18

To attach a formula to a list name from a blank line on the

home screen or from a program, follow these steps.

1. Press

[

], enter the formula (which must resolve to

a list), and press

[

] again.

Note:

When you include more than one list name in a formula,

each list must have the same dimension.

2. Press

3. Enter the name of the list to which you want to attach

the formula.

•

Press

, and then enter a TI

83 list name

through

•

Press

[

LIST

] and select a user

created list name

from the

LIST NAMES

menu.

•

Enter a user

created list name directly using

(page

16).

4. Press

Note:

The stat list editor displays a formula-lock symbol next to

each list name that has an attached formula. Chapter 12 describes

how to use the stat list editor to attach formulas to lists, edit

attached formulas, and detach formulas from lists.

You can detach (clear) an attached formula from a list in

any of three ways.

•

Enter

listname

on the home screen.

•

Edit any element of a list to which a formula is

attached.

•

Use the stat list editor (Chapter 12).

Note:

You also can use

ClrList

ClrAllList

to detach a formula

from a list (Chapter 18).

Attaching a

Formula to a List

on the Home

Screen or in a

Program

Detaching a

Formula from a

List

Lists 11-9

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 9 of 18

You can use lists in an expression in any of three ways.

When you press

, any expression is evaluated for

each list element, and a list is displayed.

•

Use

–L

or any user-created list name in an expression.

•

Enter the list elements directly (step 1 on page 11

3).

•

Use

[

RCL

] to recall the contents of the list into an

expression at the cursor location (Chapter 1).

Note:

You must paste user-created list names to the

Rcl

prompt by

selecting them from the

LIST NAMES

menu. You cannot enter them

directly using

You can use a list to input several values for some math

functions. Other chapters and Appendix A specify whether

a list is valid. The function is evaluated for each list

element, and a list is displayed.

•

When you use a list with a function, the function must

be valid for every element in the list. In graphing, an

invalid element, such as

‡

({1,0,

1})

, is ignored.

This returns an error.

This graphs

‡

(1)

and

‡

(0)

but skips

‡

(

•

When you use two lists with a two-argument function,

the dimension of each list must be the same. The

function is evaluated for corresponding elements.

•

When you use a list and a value with a two-argument

function, the value is used with each element in the list.

Using Lists in Expressions

Using a List in an

Expression

Using Lists with

Math Functions

11-10 Lists

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 10 of 18

To display the

LIST OPS

menu, press

[

LIST

]

NAMES OPS MATH

1:SortA(

Sorts lists in ascending order.

2:SortD(

Sorts lists in descending order.

3:dim(

Sets the list dimension.

4:Fill(

Fills all elements with a constant.

5:seq(

Creates a sequence.

6:cumSum(

Returns a list of cumulative sums.

7:@List(

Returns difference of successive elements.

8:Select(

Selects specific data points.

9:augment(

Concatenates two lists.

0:List

matr(

Stores a list to a matrix.

A:Matr

list(

Stores a matrix to a list.

Designates the list-name data type.

SortA( (sort ascending) sorts list elements from low to high

values.

SortD( (sort descending) sorts list elements from

high to low values. Complex lists are sorted based on

magnitude (modulus).

With one list,

SortA( and SortD( sort the elements of

listname

and update the list in memory.

SortA(

listname

) SortD(

listname

)

With two or more lists, SortA( and SortD( sort

keylistname

and then sort each

dependlist

by placing its elements in the

same order as the corresponding elements in

keylistname

All lists must have the same dimension.

SortA(

keylistname

dependlist1

[

dependlist2

,...,

dependlist n

]

)

SortD(

keylistname

dependlist1

[

dependlist2

,...,

dependlist n

]

)

Note:

In the example,

is the first element in

, and

is the first

element in

. After

SortA(L

)

becomes the second element of

, and likewise,

becomes the second element of

Note:

SortA(

and

SortD(

are the same as

SortA(

and

SortD(

on the

STAT EDIT

menu (Chapter 12).

LIST OPS Menu

SortA(, SortD(

Lists 11-11

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Page 11 of 18

dim( (dimension) returns the length (number of elements)

list

dim(

list

)

You can use dim( with

to create a new

listname

with

dimension

length

from 1 to 999. The elements are zeros.

length

dim(

listname

)

You can use dim with

to redimension an existing

listname

to dimension

length

from 1 to 999.

•

The elements in the old

listname

that are within the

new dimension are not changed.

•

Extra list elements are filled by

•

Elements in the old list that are outside the new

dimension are deleted.

length

dim(

listname

)

Fill( replaces each element in

listname

with

value

Fill(

value

listname

)

Note:

dim(

and

Fill(

are the same as

dim(

and

Fill(

on the

MATRX

MATH

menu (Chapter 10).

Using dim( to

Find List

Dimensions

Using dim( to

Create a List

Using dim( to

Redimension a

List

Fill(

11-12 Lists

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Page 12 of 18

seq( (sequence) returns a list in which each element is the

result of the evaluation of

expression

with regard to

variable

for the values ranging from

begin

end

at steps

increment

variable

need not be defined in memory.

increment

can be negative; the default value for

increment

is 1.

seq( is not valid within

expression

seq(

expression

variable

begin

end

[

increment

]

)

cumSum( (cumulative sum) returns the cumulative sums of

the elements in

list

, starting with the first element.

list

elements can be real or complex numbers.

cumSum(

list

)

List(

returns a list containing the differences between

consecutive elements in

list

List

subtracts the first

element in

list

from the second element, subtracts the

second element from the third, and so on. The list of

differences is always one element shorter than the original

list

elements can be a real or complex numbers.

List(

list

)

Select( selects one or more specific data points from a

scatter plot or xyLine plot (only), and then stores the

selected data points to two new lists,

xlistname

and

ylistname

. For example, you can use

Select( to select and

then analyze a portion of plotted CBL 2/CBL or CBR data.

Select(

xlistname

ylistname

)

Note:

Before you use

Select(

, you must have selected (turned on) a

scatter plot or xyLine plot. Also, the plot must be displayed in the

current viewing window (page 11

13).

seq(

cumSum(

List(

Select(

Lists 11-13

8311LIST.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:21 PM Printed: 02/19/01 1:37 PM

Page 13 of 18

Before using Select(, follow these steps.

1. Create two list names and enter the data.

2. Turn on a stat plot, select

(scatter plot) or

(xyLine),

and enter the two list names for

Xlist: and Ylist: (Chapter

12).

3. Use

ZoomStat to plot the data (Chapter 3).

To select data points from a scatter plot or xyLine plot,

follow these steps.

1. Press

[

LIST

]

8 to select 8:Select( from the

LIST

OPS

menu. Select( is pasted to the home screen.

2. Enter

xlistname

, press

, enter

ylistname

, and then

press

to designate list names into which you want

the selected data to be stored.

3. Press

. The graph screen is displayed with

Left Bound? in the bottom-left corner.

4. Press

}

†

(if more than one stat plot is selected) to

move the cursor onto the stat plot from which you want

to select data points.

5. Press

and

to move the cursor to the stat plot data

point that you want as the left bound.

Before Using

Select(

Using Select( to

Select Data

Points from a

Plot

11-14 Lists

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Page 14 of 18

6. Press

. A

indicator on the graph screen shows

the left bound.

Right Bound? is displayed in the bottom-

left corner.

7. Press

to move the cursor to the stat plot point

that you want for the right bound, and then press

The x-values and y-values of the selected points are

stored in

xlistname

and

ylistname

. A new stat plot of

xlistname

and

ylistname

replaces the stat plot from

which you selected data points. The list names are

updated in the stat plot editor.

Note:

The two new lists (

xlistname

and

ylistname

) will include the

points you select as left bound and right bound. Also,

left-bound

x-value



right-bound x-value

must be true.

Lists 11-15

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Page 15 of 18

augment( concatenates the elements of

listA

and

listB

. The

list elements can be real or complex numbers.

augment(

listA

listB

)

List

matr( (lists stored to matrix) fills

matrixname

column

by column with the elements from each list. If the

dimensions of all lists are not equal, then

List

matr( fills

each extra

matrixname

row with

0. Complex lists are not

valid.

List

matr(

list1

list2

, . . . ,

list n

matrixname

)

augment(

List

matr(

11-16 Lists

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Page 16 of 18

Matr

list( (matrix stored to lists) fills each

listname

with

elements from each column in

matrix

. If the number of

listname

arguments exceeds the number of columns in

matrix

, then

Matr

list( ignores extra

listname

arguments.

Likewise, if the number of columns in

matrix

exceeds the

number of

listname

arguments, then

Matr

list( ignores

extra

matrix

columns.

Matr

list(

matrix

listname1

listname2

, . . . ,

listname n

)

Matr

list( also fills a

listname

with elements from a

specified

column#

matrix

. To fill a list with a specific

column from

matrix

, you must enter a

column#

after

matrix

Matr

list(

matrix

column#

listname

)

preceding one to five characters identifies those

characters as a user-created

listname

may

comprise letters,

, and numbers, but it must begin with a

letter from A to Z or

listname

Generally,

must precede a user-created list name when

you enter a user-created list name where other input is

valid, for example, on the home screen. Without the

, the

83 may misinterpret a user-created list name as implied

multiplication of two or more characters.

need not precede a user-created list name where a list

name is the only valid input, for example, at the

Name=

prompt in the stat list editor or the Xlist: and Ylist: prompts

in the stat plot editor. If you enter

where it is not

necessary, the TI

83 will ignore the entry.

Matr

list(

Lists 11-17

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Page 17 of 18

To display the

LIST MATH

menu, press

[

LIST

]

NAMES OPS MATH

1: min(

Returns minimum element of a list.

2: max(

Returns maximum element of a list.

3: mean(

Returns mean of a list.

4: median(

Returns median of a list.

5: sum(

Returns sum of elements in a list.

6: prod(

Returns product of elements in list.

7: stdDev(

Returns standard deviation of a list.

8: variance(

Returns the variance of a list.

min( (minimum) and max( (maximum) return the smallest or

largest element of

listA

. If two lists are compared, it returns

a list of the smaller or larger of each pair of elements in

listA

and

listB

. For a complex list, the element with smallest or

largest magnitude (modulus) is returned.

min(

listA

[

listB

]

)

max(

listA

[

listB

]

)

Note:

min(

and

max(

are the same as

min(

and

max(

on the

MATH

NUM

menu.

mean( returns the mean value of

list

. median( returns the

median value of

list

. The default value for

freqlist

is 1.

Each

freqlist

element counts the number of consecutive

occurrences of the corresponding element in

list

. Complex

lists are not valid.

mean(

list

[

freqlist

]

)

median(

list

[

freqlist

]

)

LIST MATH Menu

min(, max(

mean(, median(

11-18 Lists

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Page 18 of 18

sum( (summation) returns the sum of the elements in

list

start

and

end

are optional; they specify a range of

elements.

list

elements can be real or complex numbers.

prod( returns the product of all elements of

list

start

and

end

elements are optional; they specify a range of list

elements.

list

elements can be real or complex numbers.

sum(

list

[

start

end

]

) prod(

list

[

start

end

]

)

You can combine sum( or prod( with seq( to obtain:

upper upper

expression(x)

∏

expression(x)

x=lower x=lower

To evaluate

(N–1)

from N=1 to 4:

stdDev( returns the standard deviation of the elements in

list

The default value for

freqlist

is 1. Each

freqlist

element

counts the number of consecutive occurrences of the

corresponding element in

list

. Complex lists are not valid.

variance( returns the variance of the elements in

list

. The

default value for

freqlist

is 1. Each

freqlist

element counts

the number of consecutive occurrences of the corresponding

element in

list

. Complex lists are not valid.

stdDev(

list

[

freqlist

]

) variance(

list

[

freqlist

]

)

sum(, prod(

Sums and

Products of

Numeric

Sequences

stdDev(,

variance(

Statistics 12-1

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PM Page 1 of 38

Statistics

Getting Started: Pendulum Lengths and Periods

.........

12-2

Setting Up Statistical Analyses

...........................

12-10

Using the Stat List Editor

................................

12-11

Attaching Formulas to List Names

.......................

12-14

Detaching Formulas from List Names

....................

12-16

Switching Stat List Editor Contexts

......................

12-17

Stat List Editor Contexts

.................................

12-18

STAT EDIT

........................................

12-20

Regression Model Features

..............................

12-22

STAT CALC

........................................

12-24

Statistical Variables

......................................

12-29

Statistical Analysis in a Program

.........................

12-30

Statistical Plotting

.......................................

12-31

Statistical Plotting in a Program

.........................

12-37

Contents

12-2 Statistics

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PM Page 2 of 38

Getting Started is a fast-paced introduction. Read the chapter for details.

A group of students is attempting to determine the mathematical relationship

between the length of a pendulum and its period (one complete swing of a

pendulum). The group makes a simple pendulum from string and washers and

then suspends it from the ceiling. They record the pendulum’s period for each

of 12 string lengths.*

Length (cm) Time (sec)

6.5 0.51

11.0 0.68

13.2 0.73

15.0 0.79

18.0 0.88

23.1 0.99

24.4 1.01

26.6 1.08

30.5 1.13

34.3 1.26

37.6 1.28

41.5 1.32

1. Press

†

to set

Func

graphing mode.

2. Press

…

to select

5:SetUpEditor

SetUpEditor

is pasted to the home

screen.

Press

. This removes lists from stat

list editor columns

through

, and

then stores lists

through

columns

through

Note:

Removing lists from the stat list editor does not

delete them from memory.

3. Press

…

to select

1:Edit

from the

STAT EDIT

menu. The stat list editor is

displayed. If elements are stored in

and

, press

}

to move the cursor onto

, and then press

‘

}

‘

to clear both lists. Press

to move the rectangular cursor back to

the first row in

*This example is quoted and adapted from

Contemporary Precalculus Through Applications

by the North Carolina School of Science and Mathematics, by permission of Janson

Getting Started: Pendulum Lengths and Periods

Statistics 12-3

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PM Page 3 of 38

4. Press 6

to store the first

pendulum string length (6.5 cm) in

The rectangular cursor moves to the

next row. Repeat this step to enter each

of the 12 string length values in the table

on page 12

5. Press

to move the rectangular cursor

to the first row in

Press

to store the first time

measurement (.51 sec) in

. The

rectangular cursor moves to the next

row. Repeat this step to enter each of

the 12 time values in the table on

page 12

6. Press

to display the

editor.

If necessary, press

‘

to clear the

function

. As necessary, press

}

and

to turn off

Plot1, Plot2, and Plot3

from the top line of the

editor

(Chapter 3). As necessary, press

†

and

to deselect functions.

7. Press

[

STAT PLOT

] 1 to select 1:Plot1

from the

STAT PLOTS

menu. The stat

plot editor is displayed for plot 1.

8. Press

to select On, which turns on

plot 1. Press

†

to select

(scatter plot). Press

†

[

] to

specify

Xlist:L

for plot 1. Press

†

[

] to specify Ylist:L

for plot 1.

Press

†

to select

as the Mark

for each data point on the scatter plot.

9. Press

9 to select 9:ZoomStat from

the

ZOOM

menu. The window variables

are adjusted automatically, and plot 1 is

displayed. This is a scatter plot of the

time-versus-length data.

12-4 Statistics

8312STAT.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:42 PM Printed: 02/19/01 1:37

PM Page 4 of 38

Since the scatter plot of time-versus-length data appears to be approximately

linear, fit a line to the data.

10. Press

…

4 to select 4:LinReg(ax+b)

(linear regression model) from the

STAT

CALC

menu. LinReg(ax+b) is pasted to

the home screen.

11. Press

[

]

[

]

. Press



1 to display the

VARS Y

VARS

FUNCTION

secondary menu, and then

press

1 to select 1:Y

. L

, L

, and Y

are

pasted to the home screen as arguments

LinReg(ax+b).

12. Press

to execute LinReg(ax+b). The

linear regression for the data in

and L

is calculated. Values for a and b are

displayed on the home screen. The linear

regression equation is stored in

Residuals are calculated and stored

automatically in the list name

RESID,

which becomes an item on the

LIST

NAMES

menu.

13. Press

. The regression line and the

scatter plot are displayed.

Statistics 12-5

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PM Page 5 of 38

The regression line appears to fit the central portion of the scatter plot well.

However, a residual plot may provide more information about this fit.

14. Press

…

1 to select 1:Edit. The stat

list editor is displayed.

Press

and

}

to move the cursor onto

Press

[

INS

]. An unnamed column is

displayed in column

3; L

, L

, and L

shift right one column. The Name=

prompt is displayed in the entry line, and

alpha-lock is on.

15. Press

[

LIST

] to display the

LIST

NAMES

menu.

If necessary, press

†

to move the cursor

onto the list name

RESID.

16. Press

to select RESID and paste it

to the stat list editor’s

Name= prompt.

17. Press

. RESID is stored in column 3

of the stat list editor.

Press

†

repeatedly to examine the

residuals.

Notice that the first three residuals are negative. They correspond to the

shortest pendulum string lengths in

. The next five residuals are positive, and

three of the last four are negative. The latter correspond to the longer string

lengths in

. Plotting the residuals will show this pattern more clearly.

12-6 Statistics

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PM Page 6 of 38

18. Press

[

STAT PLOT

] 2 to select 2:Plot2

from the

STAT PLOTS

menu. The stat

plot editor is displayed for plot 2.

19. Press

to select On, which turns on

plot 2.

Press

†

to select

(scatter plot).

Press

†

[

] to specify Xlist:L

for

plot 2. Press

†

[

] [

]

(alpha-lock is on) to specify

Ylist:RESID

for plot 2. Press

†

to select

›

the mark for each data point on the

scatter plot.

20. Press

to display the

editor.

Press

to move the cursor onto the

= sign, and then press

to deselect

. Press

}

to turn off plot 1.

21. Press

9 to select 9:ZoomStat from

the

ZOOM

menu. The window variables

are adjusted automatically, and plot 2 is

displayed. This is a scatter plot of the

residuals.

Notice the pattern of the residuals: a group of negative residuals, then a group

of positive residuals, and then another group of negative residuals.

Statistics 12-7

8312STAT.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:42 PM Printed: 02/19/01 1:37

PM Page 7 of 38

The residual pattern indicates a curvature associated with this data set for

which the linear model did not account. The residual plot emphasizes a

downward curvature, so a model that curves down with the data would be

more accurate. Perhaps a function such as square root would fit. Try a power

regression to fit a function of the form y = a

22. Press

to display the

editor.

Press

‘

to clear the linear regression

equation from

. Press

}

to turn

on plot 1. Press

to turn off plot

23. Press

9 to select 9:ZoomStat from

the

ZOOM

menu. The window variables

are adjusted automatically, and the

original scatter plot of time-versus-

length data (plot 1) is displayed.

24. Press

…

[

] to select

A:PwrReg from the

STAT CALC

menu.

PwrReg is pasted to the home screen.

Press

[

]

[

]

. Press



1 to display the

VARS Y

VARS

FUNCTION

secondary menu, and then

press

1 to select 1:Y

. L

, L

, and Y

are

pasted to the home screen as arguments

PwrReg.

25. Press

to calculate the power

regression. Values for

a and b are

displayed on the home screen. The

power regression equation is stored in

. Residuals are calculated and stored

automatically in the list name

RESID.

26. Press

. The regression line and the

scatter plot are displayed.

12-8 Statistics

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PM Page 8 of 38

The new function y=.192x

.522

appears to fit the data well. To get more

information, examine a residual plot.

27. Press

to display the

editor.

Press

to deselect

Press

}

to turn off plot 1. Press

to turn on plot 2.

Note:

Step 19 defined plot 2 to plot residuals (

RESID

)

versus string length (

28. Press

9 to select 9:ZoomStat from

the

ZOOM

menu. The window variables

are adjusted automatically, and plot 2 is

displayed. This is a scatter plot of the

residuals.

The new residual plot shows that the residuals are random in sign, with the

residuals increasing in magnitude as the string length increases.

To see the magnitudes of the residuals, continue with these steps.

29. Press

Press

and

to trace the data.

Observe the values for

Y at each point.

With this model, the largest positive

residual is about 0.041 and the smallest

negative residual is about

0.027. All

other residuals are less than 0.02 in

magnitude.

Statistics 12-9

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PM Page 9 of 38

Now that you have a good model for the relationship between length and

period, you can use the model to predict the period for a given string length.

To predict the periods for a pendulum with string lengths of 20 cm and 50 cm,

continue with these steps.

30. Press



1 to display the

VARS

VARS FUNCTION

secondary menu, and

then press

1 to select 1:Y

. Y

is pasted

to the home screen.

31. Press

to enter a string length of

20 cm.

Press

to calculate the predicted

time of about 0.92 seconds.

Based on the residual analysis, we would

expect the prediction of about 0.92

seconds to be within about 0.02 seconds

of the actual value.

32. Press

[

ENTRY

] to recall the Last Entry.

Press

5 to change the string

length to 50 cm.

33. Press

to calculate the predicted

time of about 1.48 seconds.

Since a string length of 50 cm exceeds

the lengths in the data set, and since

residuals appear to be increasing as

string length increases, we would expect

more error with this estimate.

Note:

You also can make predictions using the table

with the

TABLE SETUP

settings

Indpnt:Ask

and

Depend:Auto

(Chapter 7).

12-10 Statistics

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PM Page 10 of 38

Data for statistical analyses is stored in lists, which you

can create and edit using the stat list editor. The TI

83 has

six list variables in memory,

through L

, to which you

can store data for statistical calculations. Also, you can

store data to list names that you create (Chapter 11).

To set up a statistical analysis, follow these steps. Read the

chapter for details.

1. Enter the statistical data into one or more lists.

2. Plot the data.

3. Calculate the statistical variables or fit a model to the data.

4. Graph the regression equation for the plotted data.

5. Graph the residuals list for the given regression model.

The stat list editor is a table where you can store, edit, and

view up to 20 lists that are in memory. Also, you can create

list names from the stat list editor.

To display the stat list editor, press

…

, and then select

1:Edit from the

STAT EDIT

menu.

The top line displays list names. L

through L

are stored in

columns

1 through 6 after a memory reset. The number of

the current column is displayed in the top-right corner.

The bottom line is the entry line. All data entry occurs on

this line. The characteristics of this line change according

to the current context (page 12

17).

The center area displays up to seven elements of up to

three lists; it abbreviates values when necessary. The entry

line displays the full value of the current element.

Setting Up Statistical Analyses

Using Lists to

Store Data

Setting Up a

Statistical

Analysis

Displaying the

Stat List Editor

Statistics 12-11

8312STAT.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:42 PM Printed: 02/19/01 1:37

PM Page 11 of 38

To enter a list name in the stat list editor, follow these steps.

1. Display the

Name= prompt in the entry line in either of

two ways.

•

Move the cursor onto the list name in the column

where you want to insert a list, and then press

[

INS

]. An unnamed column is displayed and the

remaining lists shift right one column.

•

Press

}

until the cursor is on the top line, and then

press

until you reach the unnamed column.

Note:

If list names are stored to all 20 columns, you must remove

a list name to make room for an unnamed column.

The Name= prompt is displayed and alpha-lock is on.

2. Enter a valid list name in any of four ways.

•

Select a name from the

LIST NAMES

menu (Chapter 11).

•

Enter

, L

, or L

from the keyboard.

•

Enter an existing user-created list name directly from

the keyboard.

•

Enter a new user-created list name (page 12

12).

3. Press

†

to store the list name and its

elements, if any, in the current column of the stat list

editor.

To begin entering, scrolling, or editing list elements, press

†

. The rectangular cursor is displayed.

Note:

If the list name you entered in step 2 already was stored in

another stat list editor column, then the list and its elements, if any,

move to the current column from the previous column. Remaining list

names shift accordingly.

Using the Stat List Editor

Entering a List

Name in the Stat

List Editor

12-12 Statistics

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PM Page 12 of 38

To create a name in the stat list editor, follow these steps.

1. Follow step 1 on page 12

11 to display the

Name=

prompt.

2. Press [

letter from A to Z or

] to enter the first letter of

the name. The first character cannot be a number.

3. Enter zero to four letters,

, or numbers to complete the

new user-created list name. List names can be one to

five characters long.

4. Press

†

to store the list name in the current

column of the stat list editor. The list name becomes an

item on the

LIST NAMES

menu (Chapter 11).

To remove a list from the stat list editor, move the cursor

onto the list name and then press

{

. The list is not deleted

from memory; it is only removed from the stat list editor.

Note:

To delete a list name from memory, use the

MEMORY

DELETE:List

selection screen (Chapter 18).

You can remove all user-created lists from the stat list

editor and restore list names

through L

to columns 1

through 6 in either of two ways.

•

Use

SetUpEditor with no arguments (page 12

21).

•

Reset all memory (Chapter 18).

You can clear all elements from a list in any of five ways.

•

Use

ClrList to clear specified lists (page 12

20).

•

In the stat list editor, press

}

to move the cursor onto a

list name, and then press

‘

•

In the stat list editor, move the cursor onto each

element, and then press

{

one by one.

•

On the home screen or in the program editor, enter

dim(

listname

) to set the dimension of

listname

to 0

(Chapter 11).

•

Use

ClrAllLists to clear all lists in memory (Chapter 18).

Creating a Name

in the Stat List

Editor

Removing a List

from the Stat List

Editor

Removing All

Lists and

Restoring L

through L

Clearing All

Elements from a

List

Statistics 12-13

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To edit a list element, follow these steps.

1. Move the rectangular cursor onto the element you want

to edit.

2. Press

to move the cursor to the entry line.

Note:

If you want to replace the current value, you can enter a new

value without first pressing

. When you enter the first

character, the current value is cleared automatically.

3. Edit the element in the entry line.

•

Press one or more keys to enter the new value. When

you enter the first character, the current value is

cleared automatically.

•

Press

to move the cursor to the character before

which you want to insert, press

[

INS

], and then

enter one or more characters.

•

Press

to move the cursor to a character you want to

delete, and then press

{

to delete the character.

To cancel any editing and restore the original element at

the rectangular cursor, press

‘

Note:

You can enter expressions and variables for elements.

4. Press

}

, or

†

to update the list. If you entered

an expression, it is evaluated. If you entered only a

variable, the stored value is displayed as a list element.

When you edit a list element in the stat list editor, the list is

updated in memory immediately.

Editing a List

Element

12-14 Statistics

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You can attach a formula to a list name in the stat list

editor, and then display and edit the calculated list

elements. When executed, the attached formula must

resolve to a list. Chapter 11 describes in detail the concept

of attaching formulas to list names.

To attach a formula to a list name that is stored in the stat

list editor, follow these steps.

1. Press

…

to display the stat list editor.

2. Press

}

to move the cursor to the top line.

3. Press

, if necessary, to move the cursor onto the

list name to which you want to attach the formula.

Note:

If a formula in quotation marks is displayed on the entry line,

then a formula is already attached to the list name. To edit the

formula, press

, and then edit the formula.

4. Press

[

], enter the formula, and press

[

Note:

If you do not use quotation marks, the TI

83 calculates and

displays the same initial list of answers, but does not attach the

formula for future calculations.

Note:

Any user-created list name referenced in a formula must be

preceded by an

symbol (Chapter 11).

5. Press

. The TI

83 calculates each list element and

stores it to the list name to which the formula is

attached. A lock symbol is displayed in the stat list

editor, next to the list name to which the formula is

attached.

Attaching Formulas to List Names

Attaching a

Formula to a List

Name in Stat List

Editor

lock symbol

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When you edit an element of a list referenced in an

attached formula, the TI

83 updates the corresponding

element in the list to which the formula is attached

(Chapter 11).

When a list with a formula attached is displayed in the stat

list editor and you edit or enter elements of another

displayed list, then the TI

83 takes slightly longer to accept

each edit or entry than when no lists with formulas

attached are in view.

Tip:

To speed editing time, scroll horizontally until no lists with

formulas are displayed, or rearrange the stat list editor so that no lists

with formulas are displayed.

On the home screen, you can attach to a list a formula that

references another list with dimension 0 (Chapter 11).

However, you cannot display the formula-generated list in

the stat list editor or on the home screen until you enter at

least one element to the list that the formula references.

All elements of a list referenced by an attached formula

must be valid for the attached formula. For example, if

Real

number mode is set and the attached formula is

log(L

)

, then each element of

must be greater than 0,

since the logarithm of a negative number returns a

complex result.

Tip:

If an error menu is returned when you attempt to display a

formula-generated list in the stat list editor, you can select

2:Goto

write down the formula that is attached to the list, and then press

‘

to detach (clear) the formula. You then can use the stat

list editor to find the source of the error. After making the appropriate

changes, you can reattach the formula to a list.

If you do not want to clear the formula, you can select

1:Quit

, display

the referenced list on the home screen, and find and edit the source of

the error. To edit an element of a list on the home screen, store the

new value to

listname

(

element#

)

(Chapter 11).

Using the Stat

List Editor When

Formula-

Generated Lists

Are Displayed

Handling Errors

Resulting from

Attached

Formulas

12-16 Statistics

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You can detach (clear) a formula from a list name in any of

four ways.

•

In the stat list editor, move the cursor onto the name of

the list to which a formula is attached. Press

‘

. All list elements remain, but the formula

is detached and the lock symbol disappears.

•

In the stat list editor, move the cursor onto an element

of the list to which a formula is attached. Press

edit the element, and then press

. The element

changes, the formula is detached, and the lock symbol

disappears. All other list elements remain.

•

Use

ClrList (page 12

20). All elements of one or more

specified lists are cleared, each formula is detached, and

each lock symbol disappears. All list names remain.

•

Use

ClrAllLists (Chapter 18). All elements of all lists in

memory are cleared, all formulas are detached from all

list names, and all lock symbols disappear. All list

names remain.

As described above, one way to detach a formula from a

list name is to edit an element of the list to which the

formula is attached. The TI

83 protects against

inadvertently detaching the formula from the list name by

editing an element of the formula-generated list.

Because of the protection feature, you must press

before you can edit an element of a formula-generated list.

The protection feature does not allow you to delete an

element of a list to which a formula is attached. To delete

an element of a list to which a formula is attached, you

must first detach the formula in any of the ways described

above.

Detaching Formulas from List Names

Detaching a

Formula from a

List Name

Editing an

Element of a

Formula-

Generated List

Statistics 12-17

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The stat list editor has four contexts.

•

View-elements context

•

Edit-elements context

•

View-names context

•

Enter-name context

The stat list editor is first displayed in view-elements

context. To switch through the four contexts, select

1:Edit

from the

STAT EDIT

menu and follow these steps.

1. Press

}

to move the cursor onto a list name. You are

now in view-names context. Press

and

to view list

names stored in other stat list editor columns.

2. Press

. You are now in edit-elements context. You

may edit any element in a list. All elements of the

current list are displayed in braces (

{ } )in the entry

line. Press

and

to view more list elements.

3. Press

again. You are now in view-elements

context. Press

†

, and

}

to view other list

elements. The current element’s full value is displayed

in the entry line.

4. Press

again. You are now in edit-elements

context. You may edit the current element in the entry

line.

5. Press

}

until the cursor is on a list name, then press

[

INS

]. You are now in enter-name context.

6. Press

‘

. You are now in view-names context.

7. Press

†

. You are now back in view-elements context.

Switching Stat List Editor Contexts

Stat List Editor

Contexts

12-18 Statistics

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In view-elements context, the entry line displays the list

name, the current element’s place in that list, and the full

value of the current element, up to 12 characters at a time.

An ellipsis (

...) indicates that the element continues beyond

12 characters.

To page down the list six elements, press

†

. To

page up six elements, press

}

. To delete a list

element, press

{

. Remaining elements shift up one row.

To insert a new element, press

[

INS

]. 0 is the default

value for a new element.

In edit-elements context, the data displayed in the entry

line depends on the previous context.

•

When you switch to edit-elements context from view-

elements context, the full value of the current element

is displayed. You can edit the value of this element, and

then press

†

and

}

to edit other list elements.

•

When you switch to edit-elements context from view-

names context, the full values of all elements in the list

are displayed. An ellipsis indicates that list elements

continue beyond the screen. You can press

and

edit any element in the list.

Note:

In edit-elements context, you can attach a formula to a list

name only if you switched to it from view-names context.

Stat List Editor Contexts

View-Elements

Context

Edit-Elements

Context

Statistics 12-19

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In view-names context, the entry line displays the list name

and the list elements.

To remove a list from the stat list editor, press

{

Remaining lists shift to the left one column. The list is not

deleted from memory.

To insert a name in the current column, press

[

INS

Remaining columns shift to the right one column.

In enter-name context, the

Name= prompt is displayed in

the entry line, and alpha-lock is on.

At the

Name= prompt, you can create a new list name,

paste a list name from

to L

from the keyboard, or paste

an existing list name from the

LIST NAMES

(Chapter 11). The

symbol is not required at the Name=

prompt.

To leave enter-name context without entering a list name,

press

‘

. The stat list editor switches to view-names

context.

View-Names

Context

Enter-Name

Context

12-20 Statistics

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To display the

STAT EDIT

menu, press

…

EDIT CALC TESTS

1: Edit

...

Displays the stat list editor.

2: SortA(

Sorts a list in ascending order.

3: SortD(

Sorts a list in descending order.

4: ClrList

Deletes all elements of a list.

5: SetUpEditor

Stores lists in the stat list editor.

Note:

Chapter 13: Inferential Statistics describes the

STAT TESTS

menu items.

SortA(

(sort ascending) sorts list elements from low to high

values.

SortD(

(sort descending) sorts list elements from

high to low values. Complex lists are sorted based on

magnitude (modulus).

SortA(

and

SortD(

each can sort in

either of two ways.

•

With one

listname

SortA(

and

SortD(

sort the elements

listname

and update the list in memory.

•

With two or more lists,

SortA(

and

SortD(

sort

keylistname

, and then sort each

dependlist

by placing

its elements in the same order as the corresponding

elements in

keylistname

. This lets you sort two-variable

data on

and keep the data pairs together. All lists

must have the same dimension.

The sorted lists are updated in memory.

SortA(

listname

)

SortD(

listname

)

SortA(

keylistname

dependlist1

[

dependlist2

...

dependlist n

]

)

SortD(

keylistname

dependlist1

[

dependlist2

...

dependlist n

]

)

Note:

SortA(

and

SortD(

are the same as

SortA(

and

SortD(

on the

LIST OPS

menu.

ClrList

clears (deletes) from memory the elements of one

or more

listnames

ClrList

also detaches any formula

attached to a

listname

ClrList

listname1

listname2

...

listname n

Note:

To clear from memory all elements of all list names, use

ClrAllLists

(Chapter 18).

STAT EDIT Menu

SortA(, SortD(

ClrList

Statistics 12-21

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With SetUpEditor you can set up the stat list editor to

display one or more

listnames

in the order that you

specify. You can specify zero to 20

listnames

SetUpEditor [

listname1

listname2

,...,

listname n

]

SetUpEditor with one to 20

listnames

removes all list

names from the stat list editor and then stores

listnames

the stat list editor columns in the specified order,

beginning in column

If you enter a

listname

that is not stored in memory

already, then

listname

is created and stored in memory; it

becomes an item on the

LIST NAMES

menu.

SetUpEditor with no

listnames

removes all list names from

the stat list editor and restores list names

through L

the stat list editor columns

1 through 6.

SetUpEditor

Restoring L

through L

to the

Stat List Editor

12-22 Statistics

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STAT CALC

menu items 3 through C are regression models

(page 12

24). The automatic residual list and automatic

regression equation features apply to all regression

models. Diagnostics display mode applies to some

regression models.

When you execute a regression model, the automatic

residual list feature computes and stores the residuals to

the list name

RESID. RESID becomes an item on the

LIST NAMES

menu (Chapter 11).

The TI

83 uses the formula below to compute RESID list

elements. The next section describes the variable

RegEQ.

RESID =

Ylistname

RegEQ(

Xlistname

)

Each regression model has an optional argument,

regequ

, for

which you can specify a

variable such as Y

. Upon

execution, the regression equation is stored automatically to

the specified

variable and the

function is selected.

Regardless of whether you specify a

variable for

regequ

the regression equation always is stored to the TI

variable

RegEQ, which is item 1 on the

VARS Statistics EQ

secondary menu.

Note:

For the regression equation, you can use the fixed-decimal

mode setting to control the number of digits stored after the decimal

point (Chapter 1). However, limiting the number of digits to a small

number could affect the accuracy of the fit.

Regression Model Features

Regression

Model Features

Automatic

Residual List

Automatic

Regression

Equation

Statistics 12-23

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When you execute some regression models, the TI

computes and stores diagnostics values for

r (correlation

coefficient) and

(coefficient of determination) or for R

(coefficient of determination).

r and r

are computed and stored for these regression

models.

LinReg(ax+b) LnReg PwrReg

LinReg(a+bx) ExpReg

is computed and stored for these regression models.

QuadReg CubicReg QuartReg

The r and r

that are computed for LnReg, ExpReg, and

PwrReg are based on the linearly transformed data. For

example, for

ExpReg (y=ab^x), r and r

are computed on

ln y=ln a+x(ln b).

By default, these values are not displayed with the results

of a regression model when you execute it. However, you

can set the diagnostics display mode by executing the

DiagnosticOn or DiagnosticOff instruction. Each instruction

is in the

CATALOG

(Chapter 15).

Note:

To set

DiagnosticOn

DiagnosticOff

from the home

screen, press

[

CATALOG

], and then select the instruction for the

mode you want. The instruction is pasted to the home screen. Press

to set the mode.

When DiagnosticOn is set, diagnostics are displayed with

the results when you execute a regression model.

When DiagnosticOff is set, diagnostics are not displayed

with the results when you execute a regression model.

Diagnostics

Display Mode

12-24 Statistics

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To display the

STAT CALC

menu, press

…

EDIT CALC TESTS

1: 1-Var Stats

Calculates 1-variable statistics.

2: 2-Var Stats

Calculates 2-variable statistics.

3: Med-Med

Calculates a median-median line.

4: LinReg(ax+b)

Fits a linear model to data.

5: QuadReg

Fits a quadratic model to data.

6: CubicReg

Fits a cubic model to data.

7: QuartReg

Fits a quartic model to data.

8: LinReg(a+bx)

Fits a linear model to data.

9: LnReg

Fits a logarithmic model to data.

0: ExpReg

Fits an exponential model to data.

A: PwrReg

Fits a power model to data.

B: Logistic

Fits a logistic model to data.

C: SinReg

Fits a sinusoidal model to data.

For each

STAT CALC

menu item, if neither

Xlistname

nor

Ylistname

is specified, then the default list names are

and L

. If you do not specify

freqlist

, then the default is 1

occurrence of each list element.

For most

STAT CALC

menu items, you can specify a list of

data occurrences, or frequencies (

freqlist

Each element in

freqlist

indicates how many times the

corresponding data point or data pair occurs in the data set

you are analyzing.

For example, if

={15,12,9,14} and

FREQ={1,4,1,3}

, then

the TI

83 interprets the instruction

Var Stats L

FREQ

mean that

15 occurs once, 12 occurs four times, 9 occurs

once, and

14 occurs three times.

Each element in

freqlist

must be

‚

0, and at least one

element must be > 0.

Noninteger

freqlist

elements are valid. This is useful when

entering frequencies expressed as percentages or parts

that add up to 1. However, if

freqlist

contains noninteger

frequencies,

Sx and Sy are undefined; values are not

displayed for

Sx and Sy in the statistical results.

STAT CALC Menu

STAT CALC

Frequency of

Occurrence for

Data Points

Statistics 12-25

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Var Stats (one-variable statistics) analyzes data with one

measured variable. Each element in

freqlist

is the

frequency of occurrence for each corresponding data point

Xlistname

freqlist

elements must be real numbers > 0.

Var Stats [

Xlistname

freqlist

]

Var Stats (two-variable statistics) analyzes paired data.

Xlistname

is the independent variable.

Ylistname

is the

dependent variable. Each element in

freqlist

is the

frequency of occurrence for each data pair

(

Xlistname,Ylistname

Var Stats [

Xlistname

Ylistname

freqlist

]

Med

Med (median-median) fits the model equation y=ax+b

to the data using the median-median line (resistant line)

technique, calculating the summary points

, y

, x

, y

, x

and

. Med

Med displays values for a (slope) and

b (y-intercept).

Med

Med [

Xlistname

Ylistname

freqlist

regequ

]

LinReg(ax+b) (linear regression) fits the model equation

y=ax+b to the data using a least-squares fit. It displays values

for

a (slope) and b (y-intercept); when DiagnosticOn is set, it

also displays values for

and r.

LinReg(ax+b) [

Xlistname

Ylistname

freqlist

regequ

]

QuadReg (quadratic regression) fits the second-degree

polynomial y=ax

+bx+c to the data. It displays values for a,

b, and c; when DiagnosticOn is set, it also displays a value

for

. For three data points, the equation is a polynomial

fit; for four or more, it is a polynomial regression. At least

three data points are required.

QuadReg [

Xlistname

Ylistname

freqlist

regequ

]

1-Var Stats

2-Var Stats

Med-Med

(ax+b)

LinReg

(ax+b)

QuadReg

(ax

+bx+c)

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CubicReg (cubic regression) fits the third-degree

polynomial y=ax

+bx

+cx+d to the data. It displays values

for

a, b, c, and d; when DiagnosticOn is set, it also displays

a value for

. For four points, the equation is a polynomial

fit; for five or more, it is a polynomial regression. At least

four points are required.

CubicReg [

Xlistname

Ylistname

freqlist

regequ

]

QuartReg (quartic regression) fits the fourth-degree

polynomial y=ax

+bx

+cx

+dx+e to the data. It displays

values for

a, b, c, d, and e; when DiagnosticOn is set, it also

displays a value for

. For five points, the equation is a

polynomial fit; for six or more, it is a polynomial

regression. At least five points are required.

QuartReg [

Xlistname

Ylistname

freqlist

regequ

]

LinReg(a+bx) (linear regression) fits the model equation

y=a+bx to the data using a least-squares fit. It displays values

for

a (y-intercept) and b (slope); when DiagnosticOn is set, it

also displays values for

and r.

LinReg(a+bx) [

Xlistname

Ylistname

freqlist

regequ

]

LnReg (logarithmic regression) fits the model equation

y=a+b ln(x) to the data using a least-squares fit and

transformed values ln(x) and y. It displays values for

a and

b; when DiagnosticOn is set, it also displays values for r

and r.

LnReg [

Xlistname

Ylistname

freqlist

regequ

]

ExpReg (exponential regression) fits the model equation

y=ab

to the data using a least-squares fit and transformed

values x and ln(y). It displays values for

a and b; when

DiagnosticOn is set, it also displays values for r

and r.

ExpReg [

Xlistname

Ylistname

freqlist

regequ

]

CubicReg

(ax

+bx

+cx+d)

QuartReg

(ax

+bx

+cx

dx+e)

LinReg

(a+bx)

LnReg

(a+b ln(x))

ExpReg

(ab

)

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PwrReg (power regression) fits the model equation y=ax

the data using a least-squares fit and transformed values

ln(x) and ln(y). It displays values for

a and b; when

DiagnosticOn is set, it also displays values for r

and r.

PwrReg [

Xlistname

Ylistname

freqlist

regequ

]

Logistic fits the model equation y=c / (1+a

) to the data

using an iterative least-squares fit. It displays values for

a, b,

and

Logistic [

Xlistname

Ylistname

freqlist

regequ

]

SinReg (sinusoidal regression) fits the model equation

y=a sin(bx+c)+d to the data using an iterative least-squares

fit. It displays values for

a, b, c, and d. At least four data

points are required. At least two data points per cycle are

required in order to avoid aliased frequency estimates.

SinReg [

iterations

Xlistname

Ylistname

period

regequ

]

iterations

is the maximum number of times the algorithm

will iterate to find a solution. The value for

iterations

can

be an integer

‚

1 and



16; if not specified, the default is 3.

The algorithm may find a solution before

iterations

reached. Typically, larger values for

iterations

result in

longer execution times and better accuracy for

SinReg, and

vice versa.

period

guess is optional. If you do not specify

period

, the

difference between time values in

Xlistname

must be equal

and the time values must be ordered in ascending

sequential order. If you specify

period

, the algorithm may

find a solution more quickly, or it may find a solution when

it would not have found one if you had omitted a value for

period

. If you specify

period

, the differences between time

values in

Xlistname

can be unequal.

Note:

The output of

SinReg

is always in radians, regardless of the

Radian/Degree

mode setting.

A SinReg example is shown on the next page.

PwrReg

(ax

)

Logistic

c/(1+a

)

SinReg

a sin(bx+c)+d

12-28 Statistics

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Compute the regression model for the number of hours of

daylight in Alaska during one year.

With noisy data, you will achieve better convergence

results when you specify an accurate estimate for

period

You can obtain a

period

guess in either of two ways.

•

Plot the data and trace to determine the x-distance

between the beginning and end of one complete period,

or cycle. The illustration above and to the right

graphically depicts a complete period, or cycle.

•

Plot the data and trace to determine the x-distance

between the beginning and end of N complete periods,

or cycles. Then divide the total distance by N.

After your first attempt to use

SinReg and the default value

for

iterations

to fit the data, you may find the fit to be

approximately correct, but not optimal. For an optimal fit,

execute

SinReg 16,

Xlistname

Ylistname

where

the value obtained from the previous

SinReg execution.

SinReg Example:

Daylight Hours in

Alaska for One

Year

1 period

Statistics 12-29

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The statistical variables are calculated and stored as indicated below. To

access these variables for use in expressions, press



, and select

5:Statistics. Then select the

VARS

menu shown in the column below under

VARS

menu. If you edit a list or change the type of analysis, all statistical

variables are cleared.

Variables

Var

Stats

Var

Stats

Other

VARS

mean of x values

sum of x values

sum of x

values

sample standard deviation of xSxSx

population standard deviation of x

number of data points nn

mean of y values

sum of y values

sum of y

values

sample standard deviation of ySy

population standard deviation of y

sum of x

…

minimum of x values minX minX

maximum of x values maxX maxX

minimum of y values minY

maximum of y values maxY

1st quartile Q

PTS

median Med

PTS

3rd quartile Q

PTS

regression/fit coefficients a, b

polynomial, Logistic, and SinReg

coefficients

a, b, c,

d, e

correlation coefficient r

coefficient of determination r

, R

regression equation RegEQ

summary points (Med

Med only) x1, y1, x2,

y2, x3, y3

PTS

The first quartile (Q

) is the median of points between

minX and Med (median). The third quartile (Q

) is the

median of points between

Med and maxX.

Statistical Variables

and Q

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You can enter statistical data, calculate statistical results,

and fit models to data from a program. You can enter

statistical data into lists directly within the program

(Chapter 11).

To perform a statistical calculation from a program, follow

these steps.

1. On a blank line in the program editor, select the type of

calculation from the

STAT CALC

menu.

2. Enter the names of the lists to use in the calculation.

Separate the list names with a comma.

3. Enter a comma and then the name of a

variable, if you

want to store the regression equation to a

variable.

Statistical Analysis in a Program

Entering Stat

Data

Statistical

Calculations

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You can plot statistical data that is stored in lists. The six

types of plots available are scatter plot, xyLine, histogram,

modified box plot, regular box plot, and normal probability

plot. You can define up to three plots.

To plot statistical data in lists, follow these steps.

1. Store the stat data in one or more lists.

2. Select or deselect

functions as appropriate.

3. Define the stat plot.

4. Turn on the plots you want to display.

5. Define the viewing window.

6. Display and explore the graph.

Scatter plots plot the data points from Xlist and Ylist as

coordinate pairs, showing each point as a box (

›

), cross

(

+ ), or dot (

). Xlist and Ylist must be the same length.

You can use the same list for

Xlist and Ylist.

xyLine is a scatter plot in which the data points are plotted

and connected in order of appearance in

Xlist and Ylist.

You may want to use

SortA( or SortD( to sort the lists

before you plot them (page 12

20).

Statistical Plotting

Steps for Plotting

Statistical Data in

Lists

(Scatter)

(xyLine)

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Histogram plots one-variable data. The Xscl window variable

value determines the width of each bar, beginning at

Xmin.

ZoomStat adjusts Xmin, Xmax, Ymin, and Ymax to include all

values, and also adjusts

Xscl. The inequality

(

Xmax

Xmin)

Xscl



47 must be true. A value that occurs

on the edge of a bar is counted in the bar to the right.

ModBoxplot (modified box plot) plots one-variable data,

like the regular box plot, except points that are 1.5

Interquartile Range beyond the quartiles. (The Interquartile

Range is defined as the difference between the third

quartile

and the first quartile Q

.) These points are

plotted individually beyond the whisker, using the

Mark

(

›

or +

) you select. You can trace these points, which

are called outliers.

The prompt for outlier points is

x=, except when the outlier

is the maximum point (

maxX) or the minimum point

(

minX). When outliers exist, the end of each whisker will

display

x=. When no outliers exist, minX and maxX are the

prompts for the end of each whisker.

, Med (median),

and

define the box (page 12

29).

Box plots are plotted with respect to

Xmin and Xmax, but

ignore

Ymin and Ymax. When two box plots are plotted, the

first one plots at the top of the screen and the second plots

in the middle. When three are plotted, the first one plots at

the top, the second in the middle, and the third at the

bottom.

(Histogram)

(ModBoxplot)

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Boxplot (regular box plot) plots one-variable data. The

whiskers on the plot extend from the minimum data point

in the set (

minX) to the first quartile (Q

) and from the third

quartile (

) to the maximum point (maxX). The box is

defined by

, Med (median), and Q

(page 12

29).

Box plots are plotted with respect to

Xmin and Xmax, but

ignore

Ymin and Ymax. When two box plots are plotted, the

first one plots at the top of the screen and the second plots

in the middle. When three are plotted, the first one plots at

the top, the second in the middle, and the third at the

bottom.

NormProbPlot (normal probability plot) plots each

observation

X in Data List versus the corresponding

quantile

z of the standard normal distribution. If the plotted

points lie close to a straight line, then the plot indicates

that the data are normal.

Enter a valid list name in the

Data List field. Select X or Y

for the Data Axis setting.

•

If you select

X, the TI

83 plots the data on the x-axis and

the z-values on the y-axis.

•

If you select

Y, the TI

83 plots the data on the y-axis and

the z-values on the x-axis.

(Boxplot)

(NormProbPlot)

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To define a plot, follow these steps.

1. Press

[

STAT PLOT

]. The

STAT PLOTS

menu is

displayed with the current plot definitions.

2. Select the plot you want to use. The stat plot editor is

displayed for the plot you selected.

3. Press

to select On if you want to plot the

statistical data immediately. The definition is stored

whether you select

On or Off.

4. Select the type of plot. Each type prompts for the

options checked in this table.

Plot Type

XList YList Mark Freq

Data

List

Data

Axis

Scatter

œœœ

xyLine

œœœ

Histogram

œœœœ

ModBoxplot

œœœ

Boxplot

œœœœ

NormProbPlot

œœœ

5. Enter list names or select options for the plot type.

•

Xlist (list name containing independent data)

•

Ylist (list name containing dependent data)

•

Mark (

›

or + or

)

•

Freq (frequency list for Xlist elements; default is 1)

•

Data List (list name for NormProbPlot)

•

Data Axis (axis on which to plot Data List)

Defining the

Plots

Statistics 12-35

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Each stat plot has a unique stat plot editor. The name of

the current stat plot (

Plot1, Plot2, or Plot3) is highlighted in

the top line of the stat plot editor. To display the stat plot

editor for a different plot, press

}

, and

to move the

cursor onto the name in the top line, and then press

The stat plot editor for the selected plot is displayed, and

the selected name remains highlighted.

PlotsOn and PlotsOff allow you to turn on or turn off stat

plots from the home screen or a program. With no plot

number,

PlotsOn turns on all plots and PlotsOff turns off all

plots. With one or more plot numbers (

1, 2, and 3), PlotsOn

turns on specified plots, and PlotsOff turns off specified

plots.

PlotsOff [1,2,3]

PlotsOn [1,2,3]

Note:

You also can turn on and turn off stat plots in the top line of the

Y= editor (Chapter 3).

Displaying Other

Stat Plot Editors

Turning On and

Turning Off Stat

Plots

12-36 Statistics

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Stat plots are displayed on the current graph. To define the

viewing window, press

and enter values for the

window variables.

ZoomStat redefines the viewing window

to display all statistical data points.

When you trace a scatter plot or xyLine, tracing begins at

the first element in the lists.

When you trace a histogram, the cursor moves from the

top center of one column to the top center of the next,

starting at the first column.

When you trace a box plot, tracing begins at

Med (the

median). Press

to trace to

and minX. Press

to trace

and maxX.

When you press

}

†

to move to another plot or to

another

function, tracing moves to the current or

beginning point on that plot (not the nearest pixel).

The

ExprOn/ExprOff format setting applies to stat plots

(Chapter 3).When

ExprOn is selected, the plot number and

plotted data lists are displayed in the top-left corner.

Defining the

Viewing Window

Tracing a Stat

Plot

Statistics 12-37

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To display a stat plot from a program, define the plot, and

then display the graph.

To define a stat plot from a program, begin on a blank line

in the program editor and enter data into one or more lists;

then, follow these steps.

1. Press

[

STAT PLOT

] to display the

STAT PLOTS

menu.

2. Select the plot to define, which pastes Plot1(, Plot2(, or

Plot3( to the cursor location.

3. Press

[

STAT PLOT

]

to display the

STAT TYPE

menu.

4. Select the type of plot, which pastes the name of the

plot type to the cursor location.

Statistical Plotting in a Program

Defining a Stat

Plot in a Program

12-38 Statistics

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PM Page 38 of 38

5. Press

. Enter the list names, separated by commas.

6. Press

[

STAT PLOT

]

to display the

STAT PLOT MARK

menu. (This step is not necessary if

you selected

3:Histogram or 5:Boxplot in step 4.)

Select the type of mark (

›

or + or

) for each data point.

The selected mark symbol is pasted to the cursor

location.

7. Press

to complete the command line.

To display a plot from a program, use the DispGraph

instruction (Chapter 16) or any of the

ZOOM

instructions

(Chapter 3).

Displaying a Stat

Plot from a

Program

Inferential Statistics and Distributions 13-1

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Page 1 of 36

Inferential Statistics

and Distributions

Getting Started: Mean Height of a Population

............

13-2

Inferential Stat Editors

...................................

13-6

STAT TESTS

......................................

13-9

Inferential Statistics Input Descriptions

..................

13-26

Test and Interval Output Variables

.......................

13-28

Distribution Functions

...................................

13-29

Distribution Shading

.....................................

13-35

Contents

13-2 Inferential Statistics and Distributions

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Page 2 of 36

Getting Started is a fast-paced introduction. Read the chapter for details.

Suppose you want to estimate the mean height of a population of women given

the random sample below. Because heights among a biological population tend

to be normally distributed, a

distribution confidence interval can be used

when estimating the mean. The 10 height values below are the first 10 of 90

values, randomly generated from a normally distributed population with an

assumed mean of 165.1 cm. and a standard deviation of 6.35 cm.

(

randNorm(165.1,6.35,90) with a seed of 789).

Height (in cm.) of Each of 10 Women

169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53

1. Press

…

to display the stat list

editor.

Press

}

to move the cursor onto

, and

then press

[

INS

]. The Name= prompt is

displayed on the bottom line. The

cursor

indicates that alpha-lock is on. The

existing list name columns shift to the

right.

Note:

Your stat editor may not look like the one

pictured here, depending on the lists you have

already stored.

2. Enter [

] [

] at the Name= prompt,

and then press

. The list to which

you will store the women’s height data is

created.

Press

†

to move the cursor onto the first

row of the list.

HGHT(1)=

is displayed on the

bottom line.

3. Press 169

43 to enter the first height

value. As you enter it, it is displayed on the

bottom line.

Press

. The value is displayed in the

first row, and the rectangular cursor

moves to the next row.

Enter the other nine height values the

same way.

Getting Started: Mean Height of a Population

Inferential Statistics and Distributions 13-3

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Page 3 of 36

4. Press

…

to display the

STAT TESTS

menu, and then press

†

until 8:TInterval is

highlighted.

5. Press

to select 8:TInterval. The

inferential stat editor for

TInterval is

displayed. If

Data is not selected for Inpt:,

press

to select

Data.

Press

†

and [

] [

] at the List:

prompt (alpha-lock is on).

Press

†

99 to enter a 99 percent

confidence level at the

Level: prompt.

6. Press

†

to move the cursor onto Calculate,

and then press

. The confidence

interval is calculated, and the

TInterval

results are displayed on the home screen.

Interpret the results.

The first line,

(159.74,173.94), shows that the 99 percent confidence interval for

the population mean is between about 159.74 cm. and 173.94 cm. This is about

a 14.2 cm. spread.

The .99 confidence level indicates that in a very large number of samples, we

expect 99 percent of the intervals calculated to contain the population mean.

The actual mean of the population sampled is 165.1 cm. (introduction; page

2), which is in the calculated interval.

The second line gives the mean height of the sample

used to compute this

interval. The third line gives the sample standard deviation

Sx. The bottom line

gives the sample size

13-4 Inferential Statistics and Distributions

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Page 4 of 36

To obtain a more precise bound on the population mean

of women’s heights,

increase the sample size to 90. Use a sample mean

of 163.8 and sample

standard deviation

Sx of 7.1 calculated from the larger random sample

(introduction; page 13

2). This time, use the

Stats (summary statistics) input

option.

7. Press

…

8 to display the inferential

stat editor for

TInterval.

Press

to select

Inpt:Stats. The

editor changes so that you can enter

summary statistics as input.

8. Press

†

163

to store 163.8 to

Press

to store 7.1 to Sx.

Press

to store 90 to n.

9. Press

†

to move the cursor onto Calculate,

and then press

to calculate the new

99 percent confidence interval. The results

are displayed on the home screen.

If the height distribution among a population of women is normally distributed

with a mean

of 165.1 cm. and a standard deviation

of 6.35 cm., what height

is exceeded by only 5 percent of the women (the 95th percentile)?

10. Press

‘

to clear the home screen.

Press

[

DISTR

] to display the

DISTR

(distributions) menu.

Inferential Statistics and Distributions 13-5

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Page 5 of 36

11. Press 3 to paste invNorm( to the home

screen.

Press

165

.95 is the area, 165.1 is

, and 6.35 is

The result is displayed on the home screen; it shows that five percent of the

women are taller than 175.5 cm.

Now graph and shade the top 5 percent of the population.

12. Press

and set the window

variables to these values.

Xmin=145 Ymin=

.02 Xres=1

Xmax=185 Ymax=.08

Xscl=5 Yscl=0

13. Press

[

DISTR

]

to display the

DISTR

DRAW

menu.

14. Press

to paste ShadeNorm( to the

home screen.

Press

[

ANS

]

[

] 99

165

Ans (175.5448205 from step 11) is the

lower bound. 1

99 is the upper bound. The

normal curve is defined by a mean

165.1 and a standard deviation

of 6.35.

15. Press

to plot and shade the normal

curve.

Area is the area above the 95th percentile.

low is the lower bound. up is the upper

bound.

13-6 Inferential Statistics and Distributions

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Page 6 of 36

When you select a hypothesis test or confidence interval

instruction from the home screen, the appropriate

inferential statistics editor is displayed. The editors vary

according to each test or interval’s input requirements.

Below is the inferential stat editor for

Test.

Note:

When you select the

ANOVA(

instruction, it is pasted to the

home screen.

ANOVA(

does not have an editor screen.

To use an inferential stat editor, follow these steps.

1. Select a hypothesis test or confidence interval from the

STAT TESTS

menu. The appropriate editor is displayed.

2. Select

Data or Stats input, if the selection is available.

The appropriate editor is displayed.

3. Enter real numbers, list names, or expressions for each

argument in the editor.

4. Select the alternative hypothesis (

, <, or >) against

which to test, if the selection is available.

5. Select

No or Yes for the Pooled option, if the selection is

available.

6. Select

Calculate or Draw (when Draw is available) to

execute the instruction.

•

When you select

Calculate, the results are displayed

on the home screen.

•

When you select

Draw, the results are displayed in a

graph.

This chapter describes the selections in the above steps for

each hypothesis test and confidence interval instruction.

Inferential Stat Editors

Displaying the

Inferential Stat

Editors

Using an

Inferential Stat

Editor

Inferential Statistics and Distributions 13-7

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Page 7 of 36

Most inferential stat editors prompt you to select one of

two types of input. (

PropZInt and 2

PropZTest, 1

PropZInt

and 2

PropZInt,

Test

, and LinRegTTest do not.)

•

Select

Data to enter the data lists as input.

•

Select

Stats to enter summary statistics, such as

, Sx,

and n, as input.

To select

Data or Stats, move the cursor to either Data or

Stats, and then press

Inferential stat editors require a value for every argument.

If you do not know what a particular argument symbol

represents, see the tables on pages 13

26 and 13

27.

When you enter values in any inferential stat editor, the

83 stores them in memory so that you can run many

tests or intervals without having to reenter every value.

Most of the inferential stat editors for the hypothesis tests

prompt you to select one of three alternative hypotheses.

•

The first is a

alternative hypothesis, such as

mƒm

for

the Z

Test.

•

The second is a

< alternative hypothesis, such as

for the 2

SampTTest.

•

The third is a

> alternative hypothesis, such as p1>p2 for

the 2

PropZTest.

To select an alternative hypothesis, move the cursor to the

appropriate alternative, and then press

Selecting Data or

Stats

Entering the

Values for

Arguments

Selecting an

Alternative

Hypothesis

(

< >)

Enter values for

arguments

Select an alternative

hypothesis

Select

Calculate

Draw

output

Select

Data

Stats

input

13-8 Inferential Statistics and Distributions

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Page 8 of 36

Pooled (2

SampTTest and 2

SampTInt only) specifies

whether the variances are to be pooled for the calculation.

•

Select

No if you do not want the variances pooled.

Population variances can be unequal.

•

Select

Yes if you want the variances pooled. Population

variances are assumed to be equal.

To select the

Pooled option, move the cursor to Yes, and

then press

After you have entered all arguments in an inferential stat

editor for a hypothesis test, you must select whether you

want to see the calculated results on the home screen

(

Calculate) or on the graph screen (Draw).

•

Calculate calculates the test results and displays the

outputs on the home screen.

•

Draw draws a graph of the test results and displays the

test statistic and p-value with the graph. The window

variables are adjusted automatically to fit the graph.

To select

Calculate or Draw, move the cursor to either

Calculate or Draw, and then press

. The instruction is

immediately executed.

After you have entered all arguments in an inferential stat

editor for a confidence interval, select

Calculate to display

the results. The

Draw option is not available.

When you press

Calculate calculates the confidence

interval results and displays the outputs on the home

screen.

To paste a hypothesis test or confidence interval

instruction to the home screen without displaying the

corresponding inferential stat editor, select the instruction

you want from the

CATALOG

menu. Appendix A describes

the input syntax for each hypothesis test and confidence

interval instruction.

Note:

You can paste a hypothesis test or confidence interval

instruction to a command line in a program. From within the program

editor, select the instruction from either the

CATALOG

(Chapter 15)

or the

STAT TESTS

menu.

Selecting the

Pooled Option

Selecting

Calculate or Draw

for a Hypothesis

Test

Selecting

Calculate for a

Confidence

Interval

Bypassing the

Inferential Stat

Editors

Inferential Statistics and Distributions 13-9

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Page 9 of 36

To display the

STAT TESTS

menu, press

…

. When you

select an inferential statistics instruction, the appropriate

inferential stat editor is displayed.

Most

STAT TESTS

instructions store some output variables

to memory. Most of these output variables are in the

TEST

secondary menu (

VARS

menu; 5:Statistics). For a list of

these variables, see page 13

28.

EDIT CALC TESTS

1: Z-Test...

Test for 1

, known

2: T-Test...

Test for 1

, unknown

3: 2-SampZTest...

Test comparing 2

’s, known

’s

4: 2-SampTTest...

Test comparing 2

’s, unknown

’s

5: 1-PropZTest...

Test for 1 proportion

6: 2-PropZTest...

Test comparing 2 proportions

7: ZInterval...

Confidence interval for 1

, known

8: TInterval...

Confidence interval for 1

, unknown

9: 2-SampZInt...

Conf. int. for diff. of 2

’s, known

’s

0: 2-SampTInt...

Conf. int. for diff. of 2

’s, unknown

’s

A: 1-PropZInt...

Confidence int. for 1 proportion

B: 2-PropZInt...

Confidence int. for diff. of 2 props

2-Test...

Chi-square test for 2-way tables

D: 2-Samp

Test...

Test comparing 2

’s

E: LinRegTTest...

test for regression slope and

F: ANOVA(

One-way analysis of variance

Note:

When a new test or interval is computed, all previous output

variables are invalidated.

In this chapter, the description of each

STAT TESTS

instruction shows the unique inferential stat editor for that

instruction with example arguments.

•

Descriptions of instructions that offer the

Data/Stats

input choice show both types of input screens.

•

Descriptions of instructions that do not offer the

Data/Stats input choice show only one input screen.

The description then shows the unique output screen for

that instruction with the example results.

•

Descriptions of instructions that offer the

Calculate/Draw output choice show both types of

screens: calculated and graphic results.

•

Descriptions of instructions that offer only the

Calculate

output choice show the calculated results on the home

screen.

STAT TESTS Menu

STAT TESTS

Inferential Stat

Editors for the

STAT TESTS

Instructions

13-10 Inferential Statistics and Distributions

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Page 10 of 36

Test (one-sample

test; item 1) performs a hypothesis

test for a single unknown population mean

when the

population standard deviation

is known. It tests the null

hypothesis H

against one of the alternatives below.

•

mƒm

(

ƒm

)

•

(

)

•

(

)

In the example:

={299.4 297.7 301 298.9 300.2 297}

Data Stats

Input:

Calculated results:

Drawn results:

Note:

All examples on pages13

10 through 13

25 assume a fixed-

decimal mode setting of

(Chapter 1). If you set the decimal mode to

Float

or a different fixed-decimal setting, your output may differ from

the output in the examples.

Test

Inferential Statistics and Distributions 13-11

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Page 11 of 36

Test (one-sample

test; item 2) performs a hypothesis

test for a single unknown population mean

when the

population standard deviation

is unknown. It tests the

null hypothesis H

against one of the alternatives

below.

•

mƒm

(

ƒm

)

•

(

)

•

(

)

In the example:

TEST={91.9 97.8 111.4 122.3 105.4 95}

Data Stats

Input:

Calculated results:

Drawn results:

Test

13-12 Inferential Statistics and Distributions

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Page 12 of 36

SampZTest (two-sample

test; item 3) tests the equality

of the means of two populations (

and

) based on

independent samples when both population standard

deviations (

and

) are known. The null hypothesis

is tested against one of the alternatives below.

•

ƒm

(

ƒm

)

•

(

1:<

)

•

(

1:>

)

In the example:

LISTA={154 109 137 115 140}

LISTB={108 115 126 92 146}

Data Stats

Input:

Calculated results:

Drawn results:

SampZTest

Inferential Statistics and Distributions 13-13

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 13 of 36

SampTTest (two-sample

test; item 4) tests the equality

of the means of two populations (

and

) based on

independent samples when neither population standard

deviation (

) is known. The null hypothesis

is tested against one of the alternatives below.

•

ƒm

(

ƒm

)

•

(

1:<

)

•

(

1:>

)

In the example:

SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}

SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}

Data Stats

Input:

Calculated results:

Drawn results:

SampTTest

13-14 Inferential Statistics and Distributions

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 14 of 36

PropZTest (one-proportion

test; item 5) computes a test

for an unknown proportion of successes

(prop). It takes as

input the count of successes in the sample

and the count

of observations in the sample

PropZTest tests the null

hypothesis H

: prop=p

against one of the alternatives

below.

•

: prop

(prop:

)

•

: prop<p

(prop:<p

)

•

: prop>p

(prop:>p

)

Input:

Calculated results:

Drawn results:

)

1-PropZTest

Inferential Statistics and Distributions 13-15

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 15 of 36

PropZTest (two-proportion

test; item 6) computes a test

to compare the proportion of successes (p

and p

) from

two populations. It takes as input the count of successes in

each sample (

and

) and the count of observations in

each sample (

and

). 2

PropZTest tests the null

hypothesis H

: p

(using the pooled sample proportion

) against one of the alternatives below.

•

: p

(p1:

p2)

•

: p

(p1:<p2)

•

: p

(p1:>p2)

Input:

Calculated results:

Drawn results:

2-PropZTest

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Page 16 of 36

ZInterval (one-sample

confidence interval; item 7)

computes a confidence interval for an unknown population

mean

when the population standard deviation

known. The computed confidence interval depends on the

user-specified confidence level.

In the example:

={299.4 297.7 301 298.9 300.2 297}

Data Stats

Input:

Calculated results:

ZInterval

Inferential Statistics and Distributions 13-17

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 17 of 36

TInterval (one-sample

confidence interval; item 8)

computes a confidence interval for an unknown population

mean

when the population standard deviation

unknown. The computed confidence interval depends on

the user-specified confidence level.

In the example:

={1.6 1.7 1.8 1.9}

Data Stats

Input:

Calculated results:

TInterval

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Page 18 of 36

SampZInt (two-sample

confidence interval; item 9)

computes a confidence interval for the difference between

two population means (

) when both population

standard deviations (

and

) are known. The computed

confidence interval depends on the user-specified

confidence level.

In the example:

LISTC={154 109 137 115 140}

LISTD={108 115 126 92 146}

Data Stats

Input:

Calculated results:

2-SampZInt

Inferential Statistics and Distributions 13-19

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 19 of 36

SampTInt (two-sample

confidence interval; item 0)

computes a confidence interval for the difference between

two population means (

) when both population

standard deviations (

and

) are unknown. The

computed confidence interval depends on the user-

specified confidence level.

In the example:

SAMP1={12.207 16.869 25.05 22.429 8.456 10.589}

SAMP2={11.074 9.686 12.064 9.351 8.182 6.642}

Data Stats

Input:

Calculated results:

2-SampTInt

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Page 20 of 36

PropZInt (one-proportion

confidence interval; item A)

computes a confidence interval for an unknown proportion

of successes. It takes as input the count of successes in the

sample

and the count of observations in the sample

The computed confidence interval depends on the user-

specified confidence level.

Input:

Calculated results:

)

1-PropZInt

Inferential Statistics and Distributions 13-21

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 21 of 36

PropZInt (two-proportion

confidence interval; item B)

computes a confidence interval for the difference between

the proportion of successes in two populations (p

). It

takes as input the count of successes in each sample

(

and

) and the count of observations in each sample

(

and

). The computed confidence interval depends on

the user-specified confidence level.

Input:

Calculated results:

2-PropZInt

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Page 22 of 36

Test

(chi-square test; item C) computes a chi-square test

for association on the two-way table of counts in the

specified

Observed

matrix. The null hypothesis H

for a

two-way table is: no association exists between row

variables and column variables. The alternative hypothesis

is: the variables are related.

Before computing a

Test, enter the observed counts in a

matrix. Enter that matrix variable name at the

Observed:

prompt in the

Test editor; default=

[A]. At the Expected:

prompt, enter the matrix variable name to which you want

the computed expected counts to be stored; default=

[B].

Matrix editor:

Note:

Press



select

1:[A]

from the MATRX

EDIT menu.

Input:

Note:

Press



[B]

display matrix

[B]

Calculated results:

Drawn results:

-Test

Inferential Statistics and Distributions 13-23

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 23 of 36

Samp

Test (two-sample

-test; item D) computes an

-test to compare two normal population standard

deviations (

and

). The population means and standard

deviations are all unknown.

Samp

Test, which uses the

ratio of sample variances Sx1

/Sx2

, tests the null

hypothesis H

against one of the alternatives below.

•

ƒs

(

ƒs

)

•

(

1:<

)

•

(

1:>

)

In the example:

SAMP4={ 7

41817

5 1 10 11

SAMP5={

112

552

Data Stats

Input:

Calculated results:

Drawn results:

2-Samp

Test

13-24 Inferential Statistics and Distributions

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Page 24 of 36

LinRegTTest (linear regression

test; item E) computes a

linear regression on the given data and a

test on the value

of slope

and the correlation coefficient

for the equation

x. It tests the null hypothesis H

=0 (equivalently,

=0) against one of the alternatives below.

•

bƒ

0 and

rƒ

0 (

)

•

<0 and

<0 (

:<0

)

•

>0 and

>0 (

:>0

)

The regression equation is automatically stored to

RegEQ

(

VARS Statistics EQ

secondary menu). If you enter a

variable name at the RegEQ: prompt, the calculated

regression equation is automatically stored to the specified

equation. In the example below, the regression equation

is stored to

, which is then selected (turned on).

In the example:

={38 56 59 64 74}

={41 63 70 72 84}

Input:

Calculated results:

When LinRegTTest is executed, the list of residuals is

created and stored to the list name

RESID automatically.

RESID is placed on the

LIST NAMES

menu.

Note:

For the regression equation, you can use the fix-decimal mode

setting to control the number of digits stored after the decimal point

(Chapter 1). However, limiting the number of digits to a small number

could affect the accuracy of the fit.

LinRegTTest

Inferential Statistics and Distributions 13-25

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 25 of 36

ANOVA( (one-way analysis of variance; item F) computes a

one-way analysis of variance for comparing the means of

two to 20 populations. The

ANOVA

procedure for

comparing these means involves analysis of the variation

in the sample data. The null hypothesis H

=...=

tested against the alternative H

: not all

...

are equal.

ANOVA(

list1

list2

[

...

list20

]

)

In the example:

={7 4 6 6 5}

={6 5 5 8 7}

={4 7 6 7 6}

Input:

Calculated results:

Note:

is sum of squares and

is mean square.

ANOVA(

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Page 26 of 36

The tables in this section describe the inferential statistics inputs discussed in

this chapter. You enter values for these inputs in the inferential stat editors.

The tables present the inputs in the same order that they appear in this

chapter.

Input Description

Hypothesized value of the population mean that you are

testing.

The known population standard deviation; must be a real

number > 0.

List

The name of the list containing the data you are testing.

Freq

The name of the list containin

the frequency values for the

data in

List

. Default=1. All elements must be integers

Calculate

Draw

Determines the type of output to

enerate for tests and

intervals.

Calculate

displays the output on the home screen.

In tests,

Draw

draws a graph of the results.

Summary statistics

(

mean, standard deviation, and sample

size) for the one-sample tests and intervals.

The known population standard deviation from the first

population for the two-sample tests and intervals. Must be

a real number > 0.

The known population standard deviation from the second

population for the two-sample tests and intervals. Must be

a real number > 0.

List1

List2

The names of the lists containin

the data you are testin

for the two-sample tests and intervals. Defaults are

and

, respectively.

Freq1

Freq2

The names of the lists containin

the frequencies for the

data in

List1

and

List2

for the two-sample tests and

intervals. Defaults=1. All elements must be integers

Sx1

Sx2

Summary statistics

(

mean, standard deviation, and sample

size

)

for sample one and sample two in the two-sample

tests and intervals.

Pooled

Specifies whether variances are to be pooled for

SampTTest

and

SampTInt

instructs the TI

83 not to

pool the variances.

Yes

instructs the TI

83 to pool the

ariances.

Inferential Statistics Input Descriptions

Inferential Statistics and Distributions 13-27

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 27 of 36

Input Description

The expected sample proportion for

PropZTest

. Must be

real number, such that 0 <

< 1.

The count of successes in the sample for the

PropZTest

and

PropZInt

. Must be an integer

‚

The count of observations in the sample for the

PropZTest

and

PropZInt

. Must be an integer > 0.

The count of successes from sample one for the

PropZTest

and

PropZInt

. Must be an integer

‚

The count of successes from sample two for the

PropZTest

and

PropZInt

. Must be an integer

‚

The count of observations in sample one for the

PropZTest

and

PropZInt

. Must be an integer > 0.

The count of observations in sample two for the

PropZTest

and

PropZInt

. Must be an integer > 0.

Level

The confidence level for the interval instructions. Must be

‚

0 and <100. If it is

‚

1, it is assumed to be given as a

percent and is divided by 100. Default=0.95.

Observed (Matrix)

The matrix name that represents the columns and rows for

the observed values of a two-way table of counts for the

Test

Observed

must contain all integers

‚

0. Matrix

dimensions must be at least 2×2.

Expected (Matrix)

The matrix name that specifies where the expected values

should be stored.

Expected

is created upon successful

completion of the

Test

Xlist

Ylist

The names of the lists containing the data for

LinRegTTest

Defaults are

and

, respectively. The dimensions of

Xlist

and

Ylist

must be the same.

RegEQ

The prompt for the name of the

variable where the

calculated regression equation is to be stored. If a

variable is specified, that equation is automatically

selected (turned on). The default is to store the regression

equation to the

RegEQ

variable only.

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Page 28 of 36

The inferential statistics variables are calculated as indicated below. To access

these variables for use in expressions, press



5 (5:Statistics), and then

select the

VARS

menu listed in the last column below.

Variables Tests Intervals

LinRegTTest,

ANOVA

VARS

p-value pp

TEST

test statistics z, t,

TEST

degrees of freedom df df df

TEST

sample mean of x values for

sample 1 and sample 2

TEST

sample standard deviation of x

for sample 1 and sample 2

Sx1,

Sx2

Sx1,

Sx2

TEST

number of data points for sample

1 and sample 2

n1, n2 n1, n2

TEST

pooled standard deviation SxP SxP SxP

TEST

estimated sample proportion

ÇÇ

TEST

estimated sample proportion for

population 1

TEST

estimated sample proportion for

population 2

TEST

confidence interval pair lower,

upper

TEST

mean of x values

sample standard deviation of x Sx Sx

number of data points nn

standard error about the line s

TEST

regression/fit coefficients a, b

correlation coefficient r

coefficient of determination r

regression equation RegEQ

Test and Interval Output Variables

Inferential Statistics and Distributions 13-29

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Page 29 of 36

To display the

DISTR

menu, press

[

DISTR

DISTR DRAW

1: normalpdf(

Normal probability density

2: normalcdf(

Normal distribution probability

3: invNorm(

Inverse cumulative normal distribution

4: tpdf(

Student-

probability density

5: tcdf(

Student-

distribution probability

pdf(

Chi-square probability density

cdf

Chi-square distribution probability

pdf( Û

probability density

cdf( Û

distribution probability

0: binompdf(

Binomial probability

A: binomcdf(

Binomial cumulative density

B: poissonpdf(

Poisson probability

C: poissoncdf(

Poisson cumulative density

D: geometpdf(

Geometric probability

E: geometcdf(

Geometric cumulative density

Note:

99 and 1

99 specify infinity. If you want to view the area left

upperbound

, for example, specify

lowerbound

99.

norwmalpdf(

computes the probability density function

(pdf) for the normal distribution at a specified

value. The

defaults are mean

=0 and standard deviation

=1. To plot

the normal distribution, paste

normalpdf(

to the

editor.

The probability density function (pdf) is:

fx e

()

−

πσ

()

normalpdf(

[

]

)

Note:

For this example,

Xmin = 28

Xmax = 42

Ymin = 0

Ymax = .25

Tip:

For plotting the normal distribution, you can set window variables

Xmin

and

Xmax

so that the mean

falls between them, and then

select

0:ZoomFit

from the

ZOOM

menu.

Distribution Functions

DISTR menu

normalpdf(

13-30 Inferential Statistics and Distributions

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Page 30 of 36

normalcdf( computes the normal distribution probability

between

lowerbound

and

upperbound

for the specified

mean

and standard deviation

. The defaults are

and

=1.

normalcdf(

lowerbound

upperbound

[

])

invNorm( computes the inverse cumulative normal

distribution function for a given

area

under the normal

distribution curve specified by mean

and standard

deviation

. It calculates the

value associated with an

area

to the left of the

value. 0



area 

1 must be true.

The defaults are

=0 and

=1.

invNorm(

area

[

])

tpdf( computes the probability density function (pdf) for

the Student-

distribution at a specified

value.

(degrees

of freedom) must be >0. To plot the Student-

distribution,

paste

tpdf( to the

editor. The probability density

function (pdf) is:

xdf

()

[( ) ]

()

−+

tpdf(

)

Note:

For this example,

Xmin =

4.5

Xmax = 4.5

Ymin = 0

Ymax = .4

normalcdf(

invNorm(

tpdf(

Inferential Statistics and Distributions 13-31

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Page 31 of 36

tcdf( computes the Student-

distribution probability

between

lowerbound

and

upperbound

for the specified

(degrees of freedom), which must be > 0.

tcdf(

lowerbound

upperbound

)

pdf( computes the probability density function (pdf) for

the

(chi-square) distribution at a specified

value.

(degrees of freedom) must be an integer > 0. To plot the

distribution, paste

pdf( to the

editor. The probability

density function (pdf) is:

xex

df df x

()

(1/2)=≥

−−

221 2

// /

pdf(

)

Note:

For this example,

Xmin = 0

Xmax = 30

Ymin =

.02

Ymax = .132

cdf( computes the

(chi-square) distribution probability

between

lowerbound

and

upperbound

for the specified

(degrees of freedom), which must be an integer > 0.

cdf(

lowerbound

upperbound

)

tcdf(

pdf(

cdf(

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Page 32 of 36

pdf(

computes the probability density function (pdf) for

the

distribution at a specified

value.

numerator df

(degrees of freedom) and

denominator df

must be integers

> 0. To plot the

distribution, paste

pdf(

to the

editor.

The probability density function (pdf) is:

xnxd x

nnd

()

[( ) ]

()()

()













+≥

−−+

ΓΓ

21 2

where

= numerator degrees of freedom

= denominator degrees of freedom

pdf(

numerator df

denominator df

)

Note:

For this example,

Xmin = 0

Xmax = 5

Ymin = 0

Ymax = 1

cdf(

computes the

distribution probability between

lowerbound

and

upperbound

for the specified

numerator

(degrees of freedom) and

denominator df

numerator

and

denominator df

must be integers >0.

cdf(

lowerbound

upperbound

numerator df

denominator df

)

pdf(

cdf(

Inferential Statistics and Distributions 13-33

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 33 of 36

binompdf( computes a probability at

for the discrete

binomial distribution with the specified

numtrials

and

probability of success (

) on each trial.

can be an integer

or a list of integers. 0

p

1 must be true.

numtrials

must be

an integer > 0. If you do not specify

, a list of probabilities

from 0 to

numtrials

is returned. The probability density

function (pdf) is:

pp x n

xnx

() ( )













−=

−

101

,,,,



where

n = numtrials

binompdf(

numtrials

[

]

)

binomcdf( computes a cumulative probability at

for the

discrete binomial distribution with the specified

numtrials

and probability of success (

) on each trial.

can be a real

number or a list of real numbers. 0

p

1 must be true.

numtrials

must be an integer > 0. If you do not specify

, a

list of cumulative probabilities is returned.

binomcdf(

numtrials

[

]

)

poissonpdf( computes a probability at

for the discrete

Poisson distribution with the specified mean

, which must

be a real number > 0.

can be an integer or a list of

integers. The probability density function (pdf) is:

fx e x x

() !==

−µ

/, ,,,

012



poissonpdf(

)

binompdf(

binomcdf(

poissonpdf(

13-34 Inferential Statistics and Distributions

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Page 34 of 36

poissoncdf( computes a cumulative probability at

for the

discrete Poisson distribution with the specified mean

which must be a real number > 0.

can be a real number

or a list of real numbers.

poissoncdf(

)

geometpdf( computes a probability at

, the number of the

trial on which the first success occurs, for the discrete

geometric distribution with the specified probability of

success

. 0

p

1 must be true.

can be an integer or a list

of integers. The probability density function (pdf) is:

fx p p x

() ( )

=− =

−

112

,,,



geometpdf(

)

geometcdf( computes a cumulative probability at

, the

number of the trial on which the first success occurs, for

the discrete geometric distribution with the specified

probability of success

. 0

p

1 must be true.

can be a

real number or a list of real numbers.

geometcdf(

)

poissoncdf(

geometpdf(

geometcdf(

Inferential Statistics and Distributions 13-35

8313INFE.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:47 PM Printed: 02/19/01 1:38 PM

Page 35 of 36

To display the

DISTR DRAW

menu, press

[

DISTR

]

DISTR DRAW

instructions draw various types of density

functions, shade the area specified by

lowerbound

and

upperbound

, and display the computed area value.

To clear the drawings, select

1:ClrDraw from the

DRAW

menu (Chapter 8).

Note

: Before you execute a

DISTR DRAW

instruction, you must set

the window variables so that the desired distribution fits the screen.

DISTR DRAW

1: ShadeNorm(

Shades normal distribution.

2:Shade_t(

Shades Student-

distribution.

3:Shade

(

Shades

distribution.

4:Shade

(

Shades

distribution.

Note:

99 and 1

99 specify infinity. If you want to view the area left

upperbound

, for example, specify

lowerbound

99.

ShadeNorm( draws the normal density function specified

by mean

and standard deviation

and shades the area

between

lowerbound

and

upperbound

. The defaults are

=0 and

=1.

ShadeNorm(

lowerbound

upperbound

[

]

)

Note:

For this example,

Xmin = 55

Xmax = 72

Ymin =

.05

Ymax = .2

Distribution Shading

DISTR DRAW

ShadeNorm(

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Page 36 of 36

Shade_t( draws the density function for the Student-

distribution specified by

(degrees of freedom) and

shades the area between

lowerbound

and

upperbound

Shade_t(

lowerbound

upperbound

)

Note:

For this example,

Xmin =

Xmax = 3

Ymin =

.15

Ymax = .5

Shade

( draws the density function for the

(chi-square)

distribution specified by

(degrees of freedom) and shades

the area between

lowerbound

and

upperbound

Shade

(

lowerbound

upperbound

)

Note:

For this example,

Xmin = 0

Xmax = 35

Ymin =

.025

Ymax = .1

Shade

(

draws the density function for the

distribution

specified by

numerator df

(degrees of freedom)

and

denominator df

and shades the area between

lowerbound

and

upperbound

Shade

(

lowerbound

upperbound

numerator df

denominator df

)

Note:

For this example,

Xmin = 0

Xmax = 5

Ymin =

.25

Ymax = .9

Shade_t(

Shade

(

Shade

(

Financial Functions 14-1

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 1 of 14

Financial

Functions

Getting Started: Financing a Car

.........................

14-2

Getting Started: Computing Compound Interest

..........

14-3

Using the

TVM Solver

....................................

14-4

Using the Financial Functions

...........................

14-5

Calculating Time Value of Money (

TVM

)

.................

14-6

Calculating Cash Flows

..................................

14-8

Calculating Amortization

................................

14-9

Calculating Interest Conversion

..........................

14-12

Finding Days between Dates/Defining Payment Method

.....

14-13

Using the

TVM

Variables

.................................

14-14

Contents

14-2 Financial Functions

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 2 of 14

Getting Started is a fast-paced introduction. Read the chapter for details.

You have found a car you would like to buy. The car costs 9,000. You can

afford payments of 250 per month for four years. What annual percentage rate

(APR) will make it possible for you to afford the car?

1. Press

†

to set the

fixed-decimal mode setting to

2. The TI

will display all numbers with two decimal

places.

2. Press

[

FINANCE

] to display the

FINANCE CALC

menu.

3. Press

to select 1:TVM Solver. The

TVM Solver

is displayed.

Press

to store 48 months to

Press

†

9000

to store 9,000 to PV.

Press

250

to store

250 to PMT.

(Negation indicates cash outflow.) Press

to store 0 to

FV. Press 12

store 12 payments per year to

P/Y and 12

compounding periods per year to

C/Y.

Setting

P/Y to 12 will compute an annual

percentage rate (compounded monthly)

for

. Press

†

to select PMT:END,

which indicates that payments are due at

the end of each period.

4. Press

}

to move the cursor

to the

prompt. Press

[

SOLVE

] to

solve for

. What APR should you look

for?

Getting Started: Financing a Car

Financial Functions 14-3

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 3 of 14

At what annual interest rate, compounded monthly, will 1,250 accumulate to

2,000 in 7 years?

Note:

Because there are no payments when you solve compound interest problems,

PMT

must be set to

and

P/Y

must be

set to

1. Press

[

FINANCE

] to display the

FINANCE CALC

menu.

2. Press

to select

1:TVM Solver

. Press

to enter the number of periods in years.

Press

†

1250

to enter the present

value as a cash outflow (investment).

Press

†

to specify no payments. Press

†

2000

to enter the future value as a cash

inflow (return). Press

†

to enter

payment periods per year. Press

†

set compounding periods per year to

3. Press

}

to place the cursor on

the

prompt.

4. Press

[

SOLVE

] to solve for

, the

annual interest rate.

Getting Started: Computing Compound Interest

14-4 Financial Functions

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 4 of 14

The

TVM Solver

displays the time-value-of-money (

TVM

)

variables. Given four variable values, the

TVM Solver

solves

for the fifth variable.

The

FINANCE VARS

menu section (page 14

14) describes

the five

TVM

variables (

, PV, PMT, and FV) and P/Y and

C/Y.

PMT: END BEGIN in the

TVM Solver

corresponds to the

FINANCE CALC

menu items Pmt_End (payment at the end

of each period) and

Pmt_Bgn (payment at the beginning of

each period).

To solve for an unknown

TVM

variable, follow these steps.

1. Press

[

FINANCE

]

to display the

TVM Solver

. The

screen below shows the default values with the fixed-

decimal mode set to two decimal places.

2. Enter the known values for four

TVM

variables.

Note

: Enter cash inflows as positive numbers and cash

outflows as negative numbers.

3. Enter a value for P/Y, which automatically enters the

same value for

C/Y; if P/Y

C/Y, enter a unique value for

C/Y.

4. Select

END or BEGIN to specify the payment method.

5. Place the cursor on the

TVM

variable for which you

want to solve.

6. Press

[

SOLVE

]. The answer is computed,

displayed in the

TVM Solver

, and stored to the

appropriate

TVM

variable. An indicator square in the left

column designates the solution variable.

Using the TVM Solver

Using the TVM

Solver

Financial Functions 14-5

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 5 of 14

When using the TI

83 financial functions, you must enter

cash inflows (cash received) as positive numbers and cash

outflows (cash paid) as negative numbers. The TI

follows this convention when computing and displaying

answers.

To display the

FINANCE CALC

menu, press

[

FINANCE

CALC VARS

1: TVM Solver

...

Displays the

TVM Solver.

2: tvm_Pmt

Computes the amount of each payment.

3: tvm_

Computes the interest rate per year.

4: tvm_PV

Computes the present value.

5: tvm_

Computes the number of payment periods.

6: tvm_FV

Computes the future value.

7: npv(

Computes the net present value.

8: irr(

Computes the internal rate of return.

9: bal(

Computes the amortization sched. balance.

Prn(

Computes the amort. sched. principal sum.

Int(

Computes the amort. sched. interest sum.

Nom(

Computes the nominal interest rate.

Eff(

Computes the effective interest rate.

D: dbd(

Calculates the days between two dates.

E: Pmt_End

Selects ordinary annuity (end of period).

F: Pmt_Bgn

Selects annuity due (beginning of period).

Use these functions to set up and perform financial

calculations on the home screen.

TVM Solver

displays the

TVM Solver

(page 14

4).

Using the Financial Functions

Entering Cash

Inflows and Cash

Outflows

FINANCE CALC

TVM Solver

14-6 Financial Functions

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 6 of 14

Use time-value-of-money (

TVM

) functions (menu items 2

through 6) to analyze financial instruments such as

annuities, loans, mortgages, leases, and savings.

Each

TVM

function takes zero to six arguments, which

must be real numbers. The values that you specify as

arguments for these functions are not stored to the

TVM

variables (page 14

14).

Note:

To store a value to a

TVM

variable, use the

TVM Solver

(page

4) or use

and any

TVM

variable on the

FINANCE VARS

menu (page 14

14).

If you enter less than six arguments, the TI

83 substitutes a

previously stored

TVM

variable value for each unspecified

argument.

If you enter any arguments with a

TVM

function, you must

place the argument or arguments in parentheses.

tvm_Pmt computes the amount of each payment.

tvm_Pmt[(

P/Y

C/Y

)]

Note:

In the example above, the values are stored to the

TVM

variables in the

TVM Solver

. Then the payment (

tvm_Pmt

) is

computed on the home screen using the values in the

TVM Solver

Next, the interest rate is changed to 9.5 to illustrate the effect on the

payment amount.

Calculating Time Value of Money (TVM)

Calculating Time

Value of Money

tvm_Pmt

Financial Functions 14-7

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 7 of 14

tvm_

computes the annual interest rate.

tvm_

[(

PMT

P/Y

C/Y

)]

tvm_PV computes the present value.

tvm_PV[(

PMT

P/Y

C/Y

)]

tvm_

computes the number of payment periods.

tvm_

[(

PMT

P/Y

C/Y

)]

tvm_FV computes the future value.

tvm_FV[(

PMT

P/Y

C/Y

)]

tvm_

tvm_PV

tvm_

tvm_FV

14-8 Financial Functions

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 8 of 14

Use the cash flow functions (menu items 7 and 8) to

analyze the value of money over equal time periods. You

can enter unequal cash flows, which can be cash inflows or

outflows. The syntax descriptions for

npv(

and irr(

use

these arguments.

•

interest rate

is the rate by which to discount the cash

flows (the cost of money) over one period.

•

CF0

is the initial cash flow at time 0; it must be a real

number.

•

CFList

is a list of cash flow amounts after the initial

cash flow

CF0

•

CFFreq

is a list in which each element specifies the

frequency of occurrence for a grouped (consecutive)

cash flow amount, which is the corresponding element

CFList

. The default is 1; if you enter values, they

must be positive integers < 10,000.

For example, express this uneven cash flow in lists.

2000

4000

2000

- 3000

4000

CF0

2000

CFList

{2000,

3000,4000}

CFFreq

{2,1,2}

npv(

(net present value) is the sum of the present values

for the cash inflows and outflows. A positive result for

npv

indicates a profitable investment.

npv(

interest rate

CF0

CFList

[

CFFreq

]

)

irr( (internal rate of return) is the interest rate at which the

net present value of the cash flows is equal to zero.

irr(

CF0

CFList

[

CFFreq

]

)

3000

5000

1000

- 2000

- 2500

Calculating Cash Flows

Calculating a

Cash Flow

npv(, irr(

Financial Functions 14-9

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 9 of 14

Use the amortization functions (menu items 9, 0, and A) to

calculate balance, sum of principal, and sum of interest for

an amortization schedule.

bal( computes the balance for an amortization schedule

using stored values for

, PV, and PMT.

npmt

is the

number of the payment at which you want to calculate a

balance. It must be a positive integer < 10,000.

roundvalue

specifies the internal precision the calculator uses to

calculate the balance; if you do not specify

roundvalue

then the TI

83 uses the current

Float/Fix decimal-mode

setting.

bal(

npmt

[

roundvalue

]

)

Prn(

computes the sum of the principal during a specified

period for an amortization schedule using stored values for

, PV, and PMT.

pmt1

is the starting payment.

pmt2

is the

ending payment in the range.

pmt1

and

pmt2

must be

positive integers < 10,000.

roundvalue

specifies the internal

precision the calculator uses to calculate the principal; if you

do not specify

roundvalue

, the TI

83 uses the current

Float/Fix decimal-mode setting.

Note:

You must enter values for

PMT

, and before computing

the principal.

Prn(

pmt1

pmt2

[

roundvalue

]

)

Int( computes the sum of the interest during a specified

period for an amortization schedule using stored values for

, PV, and PMT.

pmt1

is the starting payment.

pmt2

is the

ending payment in the range.

pmt1

and

pmt2

must be

positive integers < 10,000.

roundvalue

specifies the

internal precision the calculator uses to calculate the

interest; if you do not specify

roundvalue

, the TI

83 uses

the current

Float/Fix decimal-mode setting.

Int(

pmt1

pmt2

[

roundvalue

]

)

Calculating Amortization

Calculating an

Amortization

Schedule

bal(

Prn(,

Int(

14-10 Financial Functions

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 10 of 14

You want to buy a home with a 30-year mortgage at 8

percent APR. Monthly payments are 800. Calculate the

outstanding loan balance after each payment and display

the results in a graph and in the table.

1. Press

. Press

†

to set the

fixed-decimal mode setting to

2. Press

†

select

Par graphing mode.

2. Press

[

FINANCE

]

to display the

TVM Solver

3. Press

360 to enter number of payments. Press

†

8 to

enter the interest rate. Press

†

800 to enter the

payment amount. Press

†

0 to enter the future value of

the mortgage. Press

†

12 to enter the payments per

year, which also sets the compounding periods per year

12. Press

†

to select PMT:END.

4. Press

}

to place the cursor on the PV prompt.

Press

[

SOLVE

] to solve for the present value.

5. Press

to display the parametric

editor. Turn off all

stat plots. Press

„

to define

as T. Press

†

[

FINANCE

] 9

„¤

to define Y

as bal(T).

Amortization

Example:

Calculating an

Outstanding

Loan Balance

Financial Functions 14-11

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 11 of 14

6. Press

to display the window variables. Enter

the values below.

Tmin=0 Xmin=0 Ymin=0

Tmax=360 Xmax=360 Ymax=125000

Tstep=12 Xscl=50 Yscl=10000

7. Press

to draw the graph and activate the trace

cursor. Press

and

to explore the graph of the

outstanding balance over time. Press a number and then

press

to view the balance at a specific time

8. Press

[

TBLSET

] and enter the values below.

TblStart=0

Tbl=12

9. Press

[

TABLE

] to display the table of outstanding

balances (

10.Press

†

to select G

split-screen mode, in which the graph and table are

displayed simultaneously.

Press

to display

(time) and Y

(balance) in

the table.

14-12 Financial Functions

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 12 of 14

Use the interest conversion functions (menu items B and

C) to convert interest rates from an annual effective rate to

a nominal rate (

Nom(

) or from a nominal rate to an annual

effective rate (

Eff(

Nom(

computes the nominal interest rate.

effective rate

and

compounding periods

must be real numbers.

compounding periods

must be >0.

Nom(

effective rate

compounding periods

)

Eff(

computes the effective interest rate.

nominal rate

and

compounding periods

must be real numbers.

compounding periods

must be >0.

Eff(

nominal rate

compounding periods

)

Calculating Interest Conversion

Calculating an

Interest

Conversion

Nom(

Eff(

Financial Functions 14-13

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 13 of 14

Use the date function dbd( (menu item D) to calculate the

number of days between two dates using the actual-day-

count method.

date1

and

date2

can be numbers or lists of

numbers within the range of the dates on the standard

calendar.

Note:

Dates must be between the years 1950 through 2049.

dbd(

date1

date2

)

You can enter

date1

and

date2

in either of two formats.

•

MM.DDYY (United States)

•

DDMM.YY (Europe)

The decimal placement differentiates the date formats.

Pmt_End and Pmt_Bgn (menu items E and F) specify a

transaction as an ordinary annuity or an annuity due. When

you execute either command, the

TVM Solver

is updated.

Pmt_End (payment end) specifies an ordinary annuity,

where payments occur at the end of each payment period.

Most loans are in this category.

Pmt_End is the default.

Pmt_End

On the

TVM Solver

’s PMT:END BEGIN line, select END to set

PMT to ordinary annuity.

Pmt_Bgn (payment beginning) specifies an annuity due,

where payments occur at the beginning of each payment

period. Most leases are in this category.

Pmt_Bgn

On the

TVM Solver

’s PMT:END BEGIN line, select BEGIN to

set

PMT to annuity due.

Finding Days between Dates/Defining Payment Method

dbd(

Defining the

Payment Method

Pmt_End

Pmt_Bgn

14-14 Financial Functions

8314FINA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:50 PM Printed: 02/19/01 1:38 PM

Page 14 of 14

To display the

FINANCE VARS

menu, press

[

FINANCE

]

. You can use

TVM

variables in

TVM

functions and store

values to them on the home screen.

CALC VARS

Total number of payment periods

Annual interest rate

3: PV

Present value

4: PMT

Payment amount

5: FV

Future value

6: P/Y

Number of payment periods per year

7: C/Y

Number of compounding periods/year

, PV, PMT, and FV are the five

TVM

variables. They

represent the elements of common financial transactions,

as described in the table above.

is an annual interest rate

that is converted to a per-period rate based on the values

P/Y and C/Y.

P/Y is the number of payment periods per year in a

financial transaction.

C/Y is the number of compounding periods per year in the

same transaction.

When you store a value to

P/Y, the value for C/Y

automatically changes to the same value. To store a unique

value to

C/Y, you must store the value to C/Y after you have

stored a value to

P/Y.

Using the TVM Variables

FINANCE VARS

, PV, PMT,

P/Y and C/Y

CATALOG, Strings, Hyperbolic Functions 15-1

8315CATS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:54 PM Printed: 02/19/01 1:39

PM Page 1 of 10

CATALOG, Strin

perbolic Functions

Browsing the TI

CATALOG

...........................

15-2

Entering and Using Strings

...............................

15-3

Storing Strings to String Variables

.......................

15-4

String Functions and Instructions in the

CATALOG

......

15-6

Hyperbolic Functions in the

CATALOG

..................

15-10

Contents

15-2 CATALOG, Strings, Hyperbolic Functions

8315CATS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:54 PM Printed: 02/19/01 1:39

PM Page 2 of 10

The

CATALOG

is an alphabetical list of all functions and

instructions on the TI

83. You also can access each

CATALOG

item from a menu or the keyboard, except:

•

The six string functions (page 15

•

The six hyperbolic functions (page 15

10)

•

The

solve( instruction without the equation solver editor

(Chapter 2)

•

The inferential stat functions without the inferential stat

editors (Chapter 13)

Note:

The only

CATALOG

programming commands you can execute

from the home screen are

GetCalc(

Get(

, and

Send(

To select a

CATALOG

item, follow these steps.

1. Press

CATALOGä

to display the

CATALOG

The

in the first column is the selection cursor.

2. Press

†

}

to scroll the

CATALOG

until the selection

cursor points to the item you want.

•

To jump to the first item beginning with a particular

letter, press that letter; alpha-lock is on.

•

Items that begin with a number are in alphabetical

order according to the first letter after the number.

For example,

PropZTest( is among the items that

begin with the letter P.

•

Functions that appear as symbols, such as

, <,

and

‡

(

, follow the last item that begins with Z. To

jump to the first symbol, !, press [

3. Press

to paste the item to the current screen.

Tip:

From the top of the

CATALOG

menu, press

}

to move to the

bottom. From the bottom, press

†

to move to the top.

Browsing the TI-83 CATALOG

What Is the

CATALOG?

Selecting an Item

from the

CATALOG

CATALOG, Strings, Hyperbolic Functions 15-3

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PM Page 3 of 10

A string is a sequence of characters that you enclose within

quotation marks. On the TI

83, a string has two primary

applications.

•

It defines text to be displayed in a program.

•

It accepts input from the keyboard in a program.

Characters are the units that you combine to form a string.

•

Count each number, letter, and space as one character.

•

Count each instruction or function name, such as

sin( or

cos(, as one character; the TI

83 interprets each

instruction or function name as one character.

To enter a string on a blank line on the home screen or in a

program, follow these steps.

1. Press

[

] to indicate the beginning of the string.

2. Enter the characters that comprise the string.

•

Use any combination of numbers, letters, function

names, or instruction names to create the string.

•

To enter a blank space, press

[

•

To enter several alpha characters in a row, press

[

LOCK

] to activate alpha-lock.

3. Press

[

] to indicate the end of the string.

string

4. Press

. On the home screen, the string is displayed

on the next line without quotations. An ellipsis (

...)

indicates that the string continues beyond the screen.

To scroll the entire string, press

and

Note:

Quotation marks do not count as string characters.

Entering and Using Strings

What Is a String?

Entering a String

15-4 CATALOG, Strings, Hyperbolic Functions

8315CATS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:54 PM Printed: 02/19/01 1:39

PM Page 4 of 10

The TI

83 has 10 variables to which you can store strings.

You can use string variables with string functions and

instructions.

To display the

VARS STRING

menu, follow these steps.

1. Press



to display the

VARS

menu. Move the cursor

7:String.

2. Press

to display the

STRING

secondary menu.

Storing Strings to String Variables

String Variables

CATALOG, Strings, Hyperbolic Functions 15-5

8315CATS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:54 PM Printed: 02/19/01 1:39

PM Page 5 of 10

To store a string to a string variable, follow these steps.

1. Press

[

], enter the string, and press

[

2. Press

3. Press



7 to display the

VARS STRING

menu.

4. Select the string variable (from

Str1 to Str9, or Str0) to

which you want to store the string.

The string variable is pasted to the current cursor

location, next to the store symbol (

5. Press

to store the string to the string variable. On

the home screen, the stored string is displayed on the

next line without quotation marks.

To display the contents of a string variable on the home

screen, select the string variable from the

VARS STRING

menu, and then press

. The string is displayed.

Storing a String

to a String

Variable

Displaying the

Contents of a

String Variable

15-6 CATALOG, Strings, Hyperbolic Functions

8315CATS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 12:54 PM Printed: 02/19/01 1:39

PM Page 6 of 10

String functions and instructions are available only from

the

CATALOG

. The table below lists the string functions

and instructions in the order in which they appear among

the other

CATALOG

menu items. The ellipses in the table

indicate the presence of additional

CATALOG

items.

CATALOG

...

Equ

String(

Converts an equation to a string.

expr(

Converts a string to an expression.

...

inString(

Returns a character’s place number.

...

length(

Returns a string’s character length.

...

String

Equ(

Converts a string to an equation.

sub(

Returns a string subset as a string.

...

To concatenate two or more strings, follow these steps.

1. Enter

string1

, which can be a string or string name.

2. Press

3. Enter

string2

, which can be a string or string name. If

necessary, press

and enter

string3

, and so on.

string1

string2

string3

. . .

4. Press

to display the strings as a single string.

To select a string function or instruction and paste it to the

current screen, follow the steps on page 15

String Functions and Instructions in the CATALOG

Displaying String

Functions and

Instructions in

the CATALOG

+ (Concatenation)

Selecting a String

Function from

the CATALOG

CATALOG, Strings, Hyperbolic Functions 15-7

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PM Page 7 of 10

Equ

String( converts to a string an equation that is stored

to any

VARS Y

VARS

variable. Y

contains the equation.

Str

(from

Str1 to Str9, or Str0) is the string variable to

which you want the equation to be stored as a string.

Equ

String(Y

,Str

)

expr( converts the character string contained in

string

an expression and executes it.

string

can be a string or a

string variable.

expr(

string

)

inString( returns the character position in

string

of the first

character of

substring

string

can be a string or a string

variable.

start

is an optional character position at which to

start the search; the default is 1.

inString(

string

substring

[

start

]

)

Note:

string

does not contain

substring

, or

start

is greater than the

length of

string

inString(

returns

Equ

String(

expr(

inString(

15-8 CATALOG, Strings, Hyperbolic Functions

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length( returns the number of characters in

string

can be a string or string variable.

Note:

An instruction or function name, such as

sin(

cos(

counts as

one character.

length(

string

)

String

Equ( converts

string

into an equation and stores the

equation to

string

can be a string or string variable.

String

Equ( is the inverse of Equ

String(.

String

Equ(

string

)

length(

String

Equ(

CATALOG, Strings, Hyperbolic Functions 15-9

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sub( returns a string that is a subset of an existing

string

can be a string or a string variable.

begin

is the

position number of the first character of the subset.

length

is the number of characters in the subset.

sub(

string

begin

length

)

In a program, you can enter a function to graph during

program execution using these commands.

Note:

When you execute this program, enter a function to store to

at the

ENTRY=

prompt.

sub(

Entering a

Function to

Graph during

Program

Execution

15-10 CATALOG, Strings, Hyperbolic Functions

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The hyperbolic functions are available only from the

CATALOG

. The table below lists the hyperbolic functions in

the order in which they appear among the other

CATALOG

menu items. The ellipses in the table indicate the presence

of additional

CATALOG

items.

CATALOG

...

cosh(

Hyperbolic cosine

cosh

(

Hyperbolic arccosine

...

sinh(

Hyperbolic sine

sinh

(

Hyperbolic arcsine

...

tanh(

Hyperbolic tangent

tanh

(

Hyperbolic arctangent

...

sinh(, cosh(, and tanh( are the hyperbolic functions. Each is

valid for real numbers, expressions, and lists.

sinh(

value

)

cosh(

value

)

tanh(

value

)

sinh

( is the hyperbolic arcsine function. cosh

( is the

hyperbolic arccosine function.

tanh

( is the hyperbolic

arctangent function. Each is valid for real numbers,

expressions, and lists.

sinh

(

value

)

cosh

(

value

)

sinh

(

value

)

Hyperbolic Functions in the CATALOG

Hyperbolic

Functions

sinh(, cosh(,

tanh(

sinh

(, cosh

tanh

(

Programming 16-1

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Pro

rammin

Getting Started: Volume of a Cylinder

....................

16-2

Creating and Deleting Programs

.........................

16-4

Entering Command Lines and Executing Programs

......

16-5

Editing Programs

........................................

16-6

Copying and Renaming Programs

........................

16-7

PRGM CTL

(Control) Instructions

.......................

16-8

PRGM I/O

(Input/Output) Instructions

...................

16-16

Calling Other Programs as Subroutines

..................

16-22

Contents

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Getting Started is a fast-paced introduction. Read the chapter for details.

A program is a set of commands that the TI

83 executes sequentially, as if you

had entered them from the keyboard. Create a program that prompts for the

radius R and the height H of a cylinder and then computes its volume.

1. Press



to display the

PRGM NEW

menu.

2. Press

to select 1:Create New. The

Name= prompt is displayed, and alpha-lock

is on. Press [

] [

], and

then press

to name the program

CYLINDER.

You are now in the program editor. The

colon (

: ) in the first column of the second

line indicates the beginning of a command

line.

3. Press



2 to select 2:Prompt from

the

PRGM I/O

menu. Prompt is copied to

the command line. Press

[

]

[

] to enter the variable names for

radius and height. Press

4. Press

ãpä

[

]

[

]

[

]

to enter the expression

H and store it to the variable V.

Getting Started: Volume of a Cylinder

Programming 16-3

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5. Press



3 to select 3:Disp from the

PRGM I/O

menu. Disp is pasted to the

command line. Press

[

A.LOCK

]

ããä

[

]

[

] [

][

] [

]

ããä

[

]

to set up the program to

display the text

VOLUME IS on one line and

the calculated value of

V on the next.

6. Press

[

QUIT

] to display the home

screen.

7. Press



to display the

PRGM EXEC

menu. The items on this menu are the

names of stored programs.

8. Press

to paste prgmCYLINDER to the

current cursor location. (If

CYLINDER is

not item

1 on your

PRGM EXEC

menu,

move the cursor to

CYLINDER before you

press

9. Press

to execute the program. Enter

1.5 for the radius, and then press

Enter

3 for the height, and then press

. The text

VOLUME IS, the value of V,

and

Done are displayed.

Repeat steps 7 through 9 and enter

different values for

R and H.

16-4 Programming

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A program is a set of one or more command lines. Each

line contains one or more instructions. When you execute a

program, the TI

83 performs each instruction on each

command line in the same order in which you entered

them. The number and size of programs that the TI

83 can

store is limited only by available memory.

To create a new program, follow these steps.

1. Press



to display the

PRGM NEW

menu.

2. Press

to select 1:Create New. The Name= prompt

is displayed, and alpha-lock is on.

3. Press a letter from A to Z or

to enter the first

character of the new program name.

Note:

A program name can be one to eight characters long. The

first character must be a letter from A to Z or

. The second

through eighth characters can be letters, numbers, or

4. Enter zero to seven letters, numbers, or

to complete

the new program name.

5. Press

. The program editor is displayed.

6. Enter one or more program commands (page 16

5).

7. Press

[

QUIT

] to leave the program editor and return

to the home screen.

To check whether adequate memory is available for a

program you want to enter, press

[

MEM

], and then

select

1:Check RAM from the

MEMORY

menu (Chapter 18).

To increase available memory, press

[

MEM

], and then

select

2:Delete from the

MEMORY

menu (Chapter 18).

To delete a specific program, press

[

MEM

], select

2:Delete from the

MEMORY

menu, and then select 7:Prgm

from the

DELETE FROM

secondary menu (Chapter 18).

Creating and Deleting Programs

What Is a

Program?

Creating a New

Program

Managing

Memory and

Deleting a

Program

Programming 16-5

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You can enter on a command line any instruction or

expression that you could execute from the home screen. In

the program editor, each new command line begins with a

colon. To enter more than one instruction or expression on a

single command line, separate each with a colon.

Note:

A command line can be longer than the screen is wide; long

command lines wrap to the next screen line.

While in the program editor, you can display and select

from menus. You can return to the program editor from a

menu in either of two ways.

•

Select a menu item, which pastes the item to the

current command line.

•

Press

‘

When you complete a command line, press

. The

cursor moves to the next command line.

Programs can access variables, lists, matrices, and strings

saved in memory. If a program stores a new value to a

variable, list, matrix, or string, the program changes the

value in memory during execution.

You can call another program as a subroutine (page 16

and page 16

22).

To execute a program, begin on a blank line on the home

screen and follow these steps.

1. Press



to display the

PRGM EXEC

menu.

2. Select a program name from the

PRGM EXEC

(page 16

7).

prgm

name

is pasted to the home screen

(for example,

prgmCYLINDER).

3. Press

to execute the program. While the program

is executing, the busy indicator is on.

Last Answer (

Ans) is updated during program execution.

Last Entry is not updated as each command is executed

(Chapter 1).

The TI

83 checks for errors during program execution. It

does not check for errors as you enter a program.

To stop program execution, press

. The

ERR:BREAK

menu is displayed.

•

To return to the home screen, select

1:Quit.

•

To go where the interruption occurred, select

2:Goto.

Entering Command Lines and Executing Programs

Entering a

Program

Command Line

Executing a

Program

Breaking a

Program

16-6 Programming

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To edit a stored program, follow these steps.

1. Press



to display the

PRGM EDIT

menu.

2. Select a program name from the

PRGM EDIT

menu (page

7). Up to the first seven lines of the program are

displayed.

Note:

The program editor does not display a

to indicate that

a program continues beyond the screen.

3. Edit the program command lines.

•

Move the cursor to the appropriate location, and

then delete, overwrite, or insert.

•

Press

‘

to clear all program commands on the

command line (the leading colon remains), and then

enter a new program command.

Tip:

To move the cursor to the beginning of a command line, press

; to move to the end, press

. To scroll the cursor down

seven command lines, press

†

. To scroll the cursor up seven

command lines, press

}

To insert a new command line anywhere in the program,

place the cursor where you want the new line, press

[

INS

], and then press

. A colon indicates a new line.

To delete a command line, place the cursor on the line,

press

‘

to clear all instructions and expressions on

the line, and then press

{

to delete the command line,

including the colon.

Editing Programs

Editing a

Program

Inserting and

Deleting

Command Lines

Programming 16-7

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To copy all command lines from one program into a new

program, follow steps 1 through 5 for Creating a New

Program (page 16

4), and then follow these steps.

1. Press

[

RCL

]. Rcl is displayed on the bottom line of

the program editor in the new program (Chapter 1).

2. Press



to display the

PRGM EXEC

menu.

3. Select a name from the menu.

prgm

name

is pasted to

the bottom line of the program editor.

4. Press

. All command lines from the selected

program are copied into the new program.

Copying programs has at least two convenient

applications.

•

You can create a template for groups of instructions

that you use frequently.

•

You can rename a program by copying its contents into

a new program.

Note:

You also can copy all the command lines from one existing

program to another existing program using

RCL

The TI

83 sorts

PRGM EXEC

and

PRGM EDIT

menu items

automatically into alphanumerical order. Each menu only

labels the first 10 items using

1 through 9, then 0.

To jump to the first program name that begins with a

particular alpha character or

, press

[

letter from A

to Z or

Tip:

From the top of either the

PRGM EXEC

PRGM EDIT

menu,

press

}

to move to the bottom. From the bottom, press

†

to move to

the top. To scroll the cursor down the menu seven items, press

†

. To scroll the cursor up the menu seven items, press

}

Copying and Renaming Programs

Copying and

Renaming a

Program

Scrolling the

PRGM EXEC and

PRGM EDIT

Menus

16-8 Programming

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To display the

PRGM CTL

(program control) menu, press



from the program editor only.

CTL I/O EXEC

1: If

Creates a conditional test.

2: Then

Executes commands when If is true.

3: Else

Executes commands when If is false.

4: For(

Creates an incrementing loop.

5: While

Creates a conditional loop.

6: Repeat

Creates a conditional loop.

7: End

Signifies the end of a block.

8: Pause

Pauses program execution.

9: Lbl

Defines a label.

0: Goto

Goes to a label.

A: IS>(

Increments and skips if greater than.

B: DS<(

Decrements and skips if less than.

C: Menu(

Defines menu items and branches.

D: prgm

Executes a program as a subroutine.

E: Return

Returns from a subroutine.

F: Stop

Stops execution.

G: DelVar

Deletes a variable from within program.

H: GraphStyle(

Designates the graph style to be drawn.

These menu items direct the flow of an executing program.

They make it easy to repeat or skip a group of commands

during program execution. When you select an item from

the menu, the name is pasted to the cursor location on a

command line in the program.

To return to the program editor without selecting an item,

press

‘

Program control instructions tell the TI

83 which

command to execute next in a program.

If, While, and

Repeat check a defined condition to determine which

command to execute next. Conditions frequently use

relational or Boolean tests (Chapter 2), as in:

If A<7:A+1

If N=1 and M=1:Goto Z

PRGM CTL (Control) Instructions

PRGM CTL Menu

Controlling

Program Flow

Programming 16-9

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Use If for testing and branching. If

condition

is false (zero),

then the

command

immediately following

If is skipped. If

condition

is true (nonzero), then the next

command

executed.

If instructions can be nested.

:If

condition

command

(if true)

command

Program Output

Then following an If executes a group of

commands

condition

is true (nonzero).

End identifies the end of the

group of

commands

:If

condition

:Then

command

(if true)

command

(if true)

:End

command

Program Output

Then

16-10 Programming

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Else following If

Then executes a group of

commands

condition

is false (zero).

End identifies the end of the

group of

commands

:If

condition

:Then

command

(if true)

command

(if true)

:Else

command

(if false)

command

(if false)

:End

command

Program Output

For( loops and increments. It increments

variable

from

begin

end

increment

is optional (default

is 1) and can be negative (

end

begin

end

is a maximum

or minimum value not to be exceeded.

End identifies the

end of the loop.

For( loops can be nested.

:For(

variable

begin

end

[

increment

]

)

command

(while

end

not exceeded)

command

(while

end

not exceeded)

:End

command

Program Output

If-Then-Else

For(

Programming 16-11

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While performs a group of

commands

while

condition

true.

condition

is frequently a relational test (Chapter 2).

condition

is tested when

While is encountered. If

condition

is true (nonzero), the program executes a group

commands

End signifies the end of the group. When

condition

is false (zero), the program executes each

command

following

End. While instructions can be nested.

:While

condition

command

(while

condition

is true)

command

(while

condition

is true)

:End

command

Program Output

Repeat repeats a group of

commands

until

condition

true (nonzero). It is similar to

While, but

condition

is tested

when

End is encountered; therefore, the group of

commands

is always executed at least once.

Repeat

instructions can be nested.

:Repeat

condition

command

(until

condition

is true)

command

(until

condition

is true)

:End

ommand

Program Output

While

Repeat

16-12 Programming

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End identifies the end of a group of

commands

. You must

include an

End instruction at the end of each For(, While, or

Repeat loop. Also, you must paste an End instruction at the

end of each

Then group and each If

Then

Else group.

Pause suspends execution of the program so that you can

see answers or graphs. During the pause, the pause

indicator is on in the top-right corner. Press

resume execution.

•

Pause without a

value

temporarily pauses the program.

If the DispGraph or Disp instruction has been executed,

the appropriate screen is displayed.

•

Pause with

value

displays

value

on the current home

screen.

value

can be scrolled.

Pause [

value

]

Program Output

End

Pause

Programming 16-13

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Lbl (label) and Goto (go to) are used together for

branching.

Lbl specifies the

label

for a command.

label

can be one or

two characters (

A through Z, 0 through 99, or

Lbl

label

Goto causes the program to branch to

label

when Goto is

encountered.

Goto

label

Program Output

IS>( (increment and skip) adds 1 to

variable.

If the answer

is >

value

(which can be an expression), the next

command

is skipped; if the answer is

{

value

, the next

command

is executed.

variable

cannot be a system

variable.

:IS>(

variable

value

)

command

(if answer



value

)

command

(if answer >

value

)

Program Output

Note:

IS>(

is not a looping instruction.

Lbl, Goto

IS>(

16-14 Programming

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DS<( (decrement and skip) subtracts 1 from

variable

. If the

answer is <

value

(which can be an expression), the next

command

is skipped; if the answer is

value

, the next

command

is executed.

variable

cannot be a system

variable.

:DS<(variable,value)

command

(if answer

‚

value

)

command

(if answer <

value

)

Program Output

Note:

DS<(

is not a looping instruction.

Menu( sets up branching within a program. If Menu( is

encountered during program execution, the menu screen is

displayed with the specified menu items, the pause

indicator is on, and execution pauses until you select a

menu item.

The menu

title

is enclosed in quotation marks (

" ). Up to

seven pairs of menu items follow. Each pair comprises a

text

item (also enclosed in quotation marks) to be

displayed as a menu selection, and a

label

item to which to

branch if you select the corresponding menu selection.

Menu("

title

","

text1

label1

text2

label2

, . . .)

Program Output

The program above pauses until you select 1 or 2. If you

select

2, for example, the menu disappears and the

program continues execution at

Lbl B.

DS<(

Menu(

Programming 16-15

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Use prgm to execute other programs as subroutines (page

22). When you select

prgm, it is pasted to the cursor

location. Enter characters to spell a program

name

. Using

prgm is equivalent to selecting existing programs from the

PRGM EXEC

menu; however, it allows you to enter the

name of a program that you have not yet created.

prgm

name

Note:

You cannot directly enter the subroutine name when using

RCL

You must paste the name from the

PRGM EXEC

menu (page 16

7).

Return quits the subroutine and returns execution to the

calling program (page 16

22), even if encountered within

nested loops. Any loops are ended. An implied

Return

exists at the end of any program that is called as a

subroutine. Within the main program,

Return stops

execution and returns to the home screen.

Stop stops execution of a program and returns to the home

screen.

Stop is optional at the end of a program.

DelVar deletes from memory the contents of

variable

DelVar

variable

GraphStyle( designates the style of the graph to be drawn.

function#

is the number of the

function name in the

current graphing mode.

graphstyle

is a number from

1 to 7

that corresponds to the graph style, as shown below.

1 =

(line) 5 =

(path)

2 =

(thick) 6 =

(animate)

3 =

(shade above) 7 =

(dot)

4 =

(shade below)

GraphStyle(

function#

graphstyle

)

For example, GraphStyle(1,5) in Func mode sets the graph

style for

(path; 5).

Not all graph styles are available in all graphing modes. For

a detailed description of each graph style, see the Graph

Styles table in Chapter 3.

prgm

Return

Stop

DelVar

GraphStyle(

16-16 Programming

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To display the

PRGM I/O

(program input/output) menu,

press



from within the program editor only.

CTL I/O EXEC

1: Input

Enters a value or uses the cursor.

2: Prompt

Prompts for entry of variable values.

3: Disp

Displays text, value, or the home screen.

4: DispGraph

Displays the current graph.

5: DispTable

Displays the current table.

6: Output(

Displays text at a specified position.

7: getKey

Checks the keyboard for a keystroke.

8: ClrHome

Clears the display.

9: ClrTable

Clears the current table.

0: GetCalc(

Gets a variable from another TI

83.

A: Get(

Gets a variable from CBL 2/CBL or CBR.

B: Send(

Sends a variable to CBL 2/CBL or CBR.

These instructions control input to and output from a

program during execution. They allow you to enter values

and display answers during program execution.

To return to the program editor without selecting an item,

press

‘

Input without a variable displays the current graph. You

can move the free-moving cursor, which updates

X and Y

(and R and

for PolarGC format). The pause indicator is

on. Press

to resume program execution.

Input

Program Output

PRGM I/O (Input/Output) Instructions

PRGM I/O Menu

Displaying a

Graph with Input

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Input with

variable

displays a ? (question mark) prompt

during execution.

variable

may be a real number, complex

number, list, matrix, string, or

function. During program

execution, enter a value, which can be an expression, and

then press

. The value is evaluated and stored to

variable

, and the program resumes execution.

Input [

variable

]

You can display

text

or the contents of

Str

(a string

variable) of up to 16 characters as a prompt. During

program execution, enter a value after the prompt and then

press

. The value is stored to

variable

, and the

program resumes execution.

Input ["

text

variable

]

Input [Str

variable

]

Program Output

Note:

When a program prompts for input of lists and

functions

during execution, you must include the braces (

{ }

) around the list

elements and quotation marks (

) around the expressions.

Storing a

Variable Value

with Input

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During program execution, Prompt displays each

variable

one at a time, followed by

=?. At each prompt, enter a

value or expression for each

variable

, and then press

. The values are stored, and the program resumes

execution.

Prompt

variableA

variableB

,...,

variable n

]

Program Output

Note:

Y= functions are not valid with

Prompt

Disp (display) without a value displays the home screen.

To view the home screen during program execution, follow

the

Disp instruction with a Pause instruction.

Disp

with one or more

values

displays the value of each.

Disp [

valueA

valueB

valueC

,...,

value n

]

•

value

is a variable, the current value is displayed.

•

value

is an expression, it is evaluated and the result is

displayed on the right side of the next line.

•

value

is text within quotation marks, it is displayed on

the left side of the current display line.

is not valid as

text.

Program Output

If Pause is encountered after Disp, the program halts

temporarily so you can examine the screen. To resume

execution, press

Note:

If a matrix or list is too large to display in its entirety, ellipses (

...

)

are displayed in the last column, but the matrix or list cannot be

scrolled. To scroll, use

Pause

value

(page 16

12).

Prompt

Displaying the

Home Screen

Displaying

Values and

Messages

Programming 16-19

8316PROG.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:23 PM Printed: 02/19/01 1:39

PM Page 19 of 22

DispGraph (display graph) displays the current graph. If

Pause is encountered after DispGraph, the program halts

temporarily so you can examine the screen. Press

resume execution.

DispTable (display table) displays the current table. The

program halts temporarily so you can examine the screen.

Press

to resume execution.

Output( displays

text

value

on the current home screen

beginning at

row

(

1 through 8) and

column

(1 through 16),

overwriting any existing characters.

Tip:

You may want to precede

Output(

with

ClrHome

(page 16

20).

Expressions are evaluated and values are displayed

according to the current mode settings. Matrices are

displayed in entry format and wrap to the next line.

not valid as text.

Output(

row

column

text

Output(

row

column

value

)

Program Output

For Output( on a Horiz split screen, the maximum value for

row

is 4.

DispGraph

DispTable

Output(

16-20 Programming

8316PROG.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:23 PM Printed: 02/19/01 1:39

PM Page 20 of 22

getKey returns a number corresponding to the last key

pressed, according to the key code diagram below. If no

key has been pressed,

getKey returns 0. Use getKey inside

loops to transfer control, for example, when creating video

games.

Program Output

Note:







, and

were pressed during

program execution.

Note:

You can press

at any time during execution to break the

program (page 16

5).

ClrHome (clear home screen) clears the home screen

during program execution.

ClrTable (clear table) clears the values in the table during

program execution.

getKey

TI-83 Key Code

Diagram

ClrHome,

ClrTable

Programming 16-21

8316PROG.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:23 PM Printed: 02/19/01 1:39

PM Page 21 of 22

GetCalc( gets the contents of

variable

on another TI

83 and

stores it to

variable

on the receiving TI

83.

variable

can be

a real or complex number, list element, list name, matrix

element, matrix name, string,

variable, graph database,

or picture.

GetCalc(

variable

)

Note:

GetCalc(

does not work between TI

82s and TI

83s.

Get( gets data

from the Calculator-Based Laboratory

(CBL 2

, CBL

) System or Calculator-Based Ranger

(CBR

) and stores it to

variable

on the receiving TI

83.

variable

can be a real number, list element, list name,

matrix element, matrix name, string,

variable, graph

database, or picture.

Get(

variable

)

Note:

If you transfer a program that references the

Get(

command to

the TI

83 from a TI

82, the TI

83 will interpret it as the

Get(

described

above. Use

GetCalc(

to get data from another TI

83.

Send( sends the contents of

variable

to the CBL 2/CBL or

CBR. You cannot use it to send to another TI

83.

variable

can be a real number, list element, list name, matrix

element, matrix name, string,

variable, graph database,

or picture.

variable

can be a list of elements.

Send(

variable

)

Note:

This program gets sound data

and time in seconds from

CBL 2/CBL.

Note:

You can access

Get(

Send(

, and

GetCalc(

from the

CATALOG

to execute them from the home screen (Chapter 15).

GetCalc(

Get(, Send(

16-22 Programming

8316PROG.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:23 PM Printed: 02/19/01 1:39

PM Page 22 of 22

On the TI

83, any stored program can be called from

another program as a subroutine. Enter the name of the

program to use as a subroutine on a line by itself.

You can enter a program name on a command line in either

of two ways.

•

Press



to display the

PRGM EXEC

menu and

select the name of the program (page 16

7). prgm

name

pasted to the current cursor location on a command line.

•

Select

prgm from the

PRGM CTL

menu, and then enter

the program name (page 16

15).

prgm

name

When

prgm

name

is encountered during execution, the next

command that the program executes is the first command

in the second program. It returns to the subsequent

command in the first program when it encounters either

Return or the implied Return at the end of the second

program.

Program Output

Subroutine

(

Variables are global.

label

used with

Goto and Lbl is local to the program where

it is located.

label

in one program is not recognized by

another program. You cannot use

Goto to branch to a

label

in another program.

Return exits a subroutine and returns to the calling

program, even if it is encountered within nested loops.

Calling Other Programs as Subroutines

Calling a

Program from

Another Program

Notes about

Calling Programs

Applications 17-1

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 1 of 20

Applications

Comparing Test Results Using Box Plots

................

17-2

Graphing Piecewise Functions

...........................

17-4

Graphing Inequalities

....................................

17-5

Solving a System of Nonlinear Equations

................

17-6

Using a Program to Create the Sierpinski Triangle

.......

17-7

Graphing Cobweb Attractors

............................

17-8

Using a Program to Guess the Coefficients

...............

17-9

Graphing the Unit Circle and Trigonometric Curves

......

17-10

Finding the Area between Curves

........................

17-11

Using Parametric Equations: Ferris Wheel Problem

......

17-12

Demonstrating the Fundamental Theorem of Calculus

...

17-14

Computing Areas of Regular N-Sided Polygons

..........

17-16

Computing and Graphing Mortgage Payments

...........

17-18

Contents

17-2 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 2 of 20

An experiment found a significant difference between boys

and girls pertaining to their ability to identify objects held

in their left hands, which are controlled by the right side of

their brains, versus their right hands, which are controlled

by the left side of their brains. The TI Graphics team

conducted a similar test for adult men and women.

The test involved 30 small objects, which participants were

not allowed to see. First, they held 15 of the objects one by

one in their left hands and guessed what they were. Then

they held the other 15 objects one by one in their right hands

and guessed what they were. Use box plots to compare

visually the correct-guess data from this table.

Correct Guesses

Women

Left

Women

Right

Men

Left

Men

Right

84 712

91 86

12 8 7 12

11 12 5 12

10 11 7 7

811 811

12 13 11 12

712 48

9111012

11 12 14 11

13 9

1. Press

…

to select

5:SetUpEditor

. Enter list names

WLEFT

WRGHT

MLEFT

, and

MRGHT

, separated by

commas. Press

. The stat list editor now contains

only these four lists.

2. Press

…

to select

1:Edit

3. Enter into

WLEFT

the number of correct guesses each

woman made using her left hand (

Women Left

). Press

to move to

WRGHT

and enter the number of correct

guesses each woman made using her right hand (

Women

Right

4. Likewise, enter each man’s correct guesses in

MLEFT

(

Men Left)

and

MRGHT

(

Men Right

5. Press

[

STAT PLOT

]. Select

1:Plot1

. Turn on plot 1;

define it as a modified box plot

that uses

WLEFT

Move the cursor to the top line and select

Plot2

. Turn on

plot 2; define it as a modified box plot that uses

WRGHT

Comparing Test Results Using Box Plots

Problem

Procedure

Applications 17-3

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 3 of 20

6. Press

. Turn off all functions.

7. Press

. Set

Xscl=1 and Yscl=0. Press

9 to

select

9:ZoomStat. This adjusts the viewing window and

displays the box plots for the women’s results.

8. Press

Women’s left-hand data

Women’s right-hand data

Use

and

to examine minX, Q

, Med, Q

, and maxX

for each plot. Notice the outlier to the women’s right-

hand data. What is the median for the left hand? For the

right hand? With which hand were the women more

accurate guessers, according to the box plots?

9. Examine the men’s results. Redefine plot 1 to use

MLEFT, redefine plot 2 to use MRGHT. Press

Men’s left-hand data

Men’s right-hand data

Press

and

to examine minX, Q

, Med, Q

, and maxX

for each plot. What difference do you see between the

plots?

10.Compare the left-hand results. Redefine plot 1 to use

WLEFT, redefine plot 2 to use MLEFT, and then press

to examine

minX, Q

, Med, Q

, and maxX for each

plot. Who were the better left-hand guessers, men or

women?

11.Compare the right-hand results. Define plot 1 to use

WRGHT, define plot 2 to use MRGHT, and then press

to examine

minX, Q

, Med, Q

, and maxX for each

plot. Who were the better right-hand guessers?

In the original experiment boys did not guess as well

with right hands, while girls guessed equally well with

either hand. This is not what our box plots show for

adults. Do you think that this is because adults have

learned to adapt or because our sample was not large

enough?

17-4 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 4 of 20

The fine for speeding on a road with a speed limit of 45

kilometers per hour (kph) is 50; plus 5 for each kph from

46 to 55 kph; plus 10 for each kph from 56 to 65 kph; plus

20 for each kph from 66 kph and above. Graph the

piecewise function that describes the cost of the ticket.

The fine (Y) as a function of kilometers per hour (X) is:

Y = 0 0 < X



Y = 50 + 5 (X

45) 45 < X



Y = 50 + 5

…

10 + 10 (X

55) 55 < X



Y = 50 + 5

…

10 + 10

…

10 + 20 (X

65) 65 < X

1. Press

. Select

Func and the default settings.

2. Press

. Turn off all functions and stat plots. Enter the

function to describe the fine. Use the

TEST

operations to define the piecewise function. Set the

graph style for

(dot).

3. Press

and set Xmin=

2, Xscl=10, Ymin=

5, and

Yscl=10. Ignore Xmax and Ymax; they are set by

and

in step 4.

4. Press

[

QUIT

] to return to the home screen. Store 1 to

, and then store 5 to

and

are on the

VARS Window X/Y

secondary menu.

and

specify

the horizontal and vertical distance between the centers

of adjacent pixels. Integer values for

and

produce

nice values for tracing.

5. Press

to plot the function. At what speed does

the ticket exceed 250?

Graphing Piecewise Functions

Problem

Procedure

Applications 17-5

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 5 of 20

Graph the inequality 0

3X + 5 < 0

2X + 4. Use the

TEST

menu operations to explore the values of X where the

inequality is true and where it is false.

1. Press

. Select

Dot, Simul, and the default settings.

Setting

Dot mode changes all graph style icons to

(dot) in the

editor.

2. Press

. Turn off all functions and stat plots. Enter the

left side of the inequality as

and the right side as Y

3. Enter the statement of the inequality as Y

. This

function evaluates to

1 if true or 0 if false.

4. Press

6 to graph the inequality in the standard

window.

5. Press

†

to move to

. Then press

and

to trace the inequality, observing the value of

6. Press

. Turn off Y

, Y

, and Y

. Enter equations to

graph only the inequality.

7. Press

. Notice that the values of Y

and Y

are

zero where the inequality is false.

Graphing Inequalities

Problem

Procedure

17-6 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 6 of 20

Using a graph, solve the equation X

2X = 2cos(X). Stated

another way, solve the system of two equations and two

unknowns: Y = X

2X and Y = 2cos(X). Use

ZOOM

factors

to control the decimal places displayed on the graph.

1. Press

. Select the default mode settings. Press

Turn off all functions and stat plots. Enter the functions.

2. Press

4 to select 4:ZDecimal. The display shows

that two solutions may exist (points where the two

functions appear to intersect).

3. Press

4 to select 4:SetFactors from the

ZOOM

MEMORY

menu. Set XFact=10 and YFact=10.

4. Press

2 to select 2:Zoom In. Use

}

, and

†

to move the free-moving cursor onto the apparent

intersection of the functions on the right side of the

display. As you move the cursor, notice that the

X and Y

values have one decimal place.

5. Press

to zoom in. Move the cursor over the

intersection. As you move the cursor, notice that now

the

X and Y values have two decimal places.

6. Press

to zoom in again. Move the free-moving

cursor onto a point exactly on the intersection. Notice

the number of decimal places.

7. Press

[

CALC

] 5 to select 5:intersect. Press

select the first curve and

to select the second

curve. To guess, move the trace cursor near the

intersection. Press

. What are the coordinates of

the intersection point?

8. Press

4 to select 4:ZDecimal to redisplay the

original graph.

9. Press

. Select

2:Zoom In and repeat steps 4

through 8 to explore the apparent function intersection

on the left side of the display.

Solving a System of Nonlinear Equations

Problem

Procedure

Applications 17-7

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 7 of 20

This program creates a drawing of a famous fractal, the

Sierpinski Triangle, and stores the drawing to a picture. To

begin, press



1. Name the program SIERPINS,

and then press

. The program editor is displayed.

PROGRAM:SIERPINS

:FnOff :ClrDraw

:PlotsOff

:AxesOff

Xmin:1

Xmax

Ymin:1

Ymax

Set viewing window.

:rand

X:rand

:For(K,1,3000)

:rand

Beginning of For group.

:If N



:Then

:.5X

:.5Y

:End

If/Then group

:If 1

3 <N and N



:Then

:.5(.5+X)

:.5(1+Y)

:End

If/Then group.

:If 2

3<N

:Then

:.5(1+X)

:.5Y

:End

If/Then group.

:Pt-On(X,Y)

Draw point.

:End

End of For group.

:StorePic 6

Store picture.

After you execute the program above, you can recall and

display the picture with the instruction

RecallPic 6.

Using a Program to Create the Sierpinski Triangle

Setting up the

Program

17-8 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 8 of 20

Using Web format, you can identify points with attracting

and repelling behavior in sequence graphing.

1. Press

. Select

Seq and the default mode settings.

Press

[

FORMAT

]. Select Web format and the default

format settings.

2. Press

. Clear all functions and turn off all stat plots.

Enter the sequence that corresponds to the expression

Y = K X(1

X).

)=Ku(

1)(1

1))

Min)=.01

3. Press

[

QUIT

] to return to the home screen, and then

store

2.9 to K.

4. Press

. Set the window variables.

Min=0 Xmin=0 Ymin=

.26

Max=10 Xmax=1 Ymax=1.1

PlotStart=1 Xscl=1 Yscl=1

PlotStep=1

5. Press

to display the graph, and then press

trace the cobweb. This is a cobweb with one attractor.

6. Change K to 3.44 and trace the graph to show a cobweb

with two attractors.

7. Change

K to 3.54 and trace the graph to show a cobweb

with four attractors.

Graphing Cobweb Attractors

Problem

Procedure

Applications 17-9

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 9 of 20

This program graphs the function A sin(BX) with random

integer coefficients between 1 and 10. Try to guess the

coefficients and graph your guess as C sin(DX). The

program continues until your guess is correct.

PROGRAM:GUESS

:PlotsOff :Func

:FnOff :Radian

:ClrHome

:"Asin(BX)"

:"Csin(DX)"

Define equations.

:GraphStyle(1,1)

:GraphStyle(2,5)

Set line and path

raph

styles.

:FnOff 2

:randInt(1,10)

C:0

Initialize coefficients.

Xmin

Xmax

pà

Xscl

Ymin

:10

Ymax

Yscl

Set viewing window.

:DispGraph

:Pause

Display graph.

:FnOn 2

:Lbl Z

:Prompt C,D

Prompt for guess.

:DispGraph

:Pause

Display graph.

:If C=A

:Text(1,1,"C IS OK")

:If C

:Text(1,1,"C IS WRONG")

:If D=B

:Text(1,50,"D IS OK")

:If D

:Text(1,50,"D IS WRONG")

Display results.

:DispGraph

:Pause

Display graph.

:If C=A and D=B

:Stop

:Goto Z

Quit if

uesses are

correct.

Using a Program to Guess the Coefficients

Setting Up the

Program

17-10 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 10 of 20

Using parametric graphing mode, graph the unit circle and

the sine curve to show the relationship between them.

Any function that can be plotted in

Func mode can be

plotted in

Par mode by defining the X component as T and

the

Y component as F(T).

1. Press

. Select

Par, Simul, and the default settings.

2. Press

. Set the viewing window.

Tmin=0 Xmin=

2 Ymin=

Tmax=2

Xmax=7.4 Ymax=3

Tstep=.1 Xscl=

pà

2 Yscl=1

3. Press

. Turn off all functions and stat plots. Enter the

expressions to define the unit circle centered on (0,0).

4. Enter the expressions to define the sine curve.

5. Press

. As the graph is plotting, you may press

to pause and

again to resume graphing as

you watch the sine function “unwrap” from the unit

circle.

Note:

You can generalize the unwrapping. Replace

sin(T)

with

any other trig function to unwrap that function.

Graphing the Unit Circle and Trigonometric Curves

Problem

Procedure

Applications 17-11

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 11 of 20

Find the area of the region bounded by

f(x) = 300x / (x

+ 625)

g(x) = 3cos(

1x)

x = 75

1. Press

. Select the default mode settings.

2. Press

. Set the viewing window.

Xmin=0 Ymin=

Xmax=100 Ymax=10

Xscl=10 Yscl=1

Xres=1

3. Press

. Turn off all functions and stat plots. Enter the

upper and lower functions.

=300X

+625)

=3cos(.1X)

4. Press

[

CALC

] 5 to select 5:Intersect. The graph is

displayed. Select a first curve, second curve, and guess

for the intersection toward the left side of the display.

The solution is displayed, and the value of

X at the

intersection, which is the lower limit of the integral, is

stored in

Ans and X.

5. Press

[

QUIT

] to go to the home screen. Press

[

DRAW

] 7 and use Shade( to see the area graphically.

Shade(Y

,Ans,75)

6. Press

[

QUIT

] to return to the home screen. Enter the

expression to evaluate the integral for the shaded

region.

fnInt(Y

–Y

,X,Ans,75)

The area is 325.839962.

Finding the Area between Curves

Problem

Procedure

17-12 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 12 of 20

Using two pairs of parametric equations, determine when

two objects in motion are closest to each other in the same

plane.

A ferris wheel has a diameter (d) of 20 meters and is

rotating counterclockwise at a rate (s) of one revolution

every 12 seconds. The parametric equations below

describe the location of a ferris wheel passenger at time T,

where

is the angle of rotation, (0,0) is the bottom center

of the ferris wheel, and (10,10) is the passenger’s location

at the rightmost point, when T=0.

X(T) = r cos

where

= 2

Ts and r = d

Y(T) = r + r sin

A person standing on the ground throws a ball to the ferris

wheel passenger. The thrower’s arm is at the same height as

the bottom of the ferris wheel, but 25 meters (b) to the right

of the ferris wheel’s lowest point (25,0). The person throws

the ball with velocity (v

) of 22 meters per second at an

angle (

) of 66

from the horizontal. The parametric

equations below describe the location of the ball at time T.

X(T) = b

cos

Y(T) = Tv

sin

2) T

where g =

9.8 m/ sec

1. Press

. Select Par, Simul, and the default settings.

Simul (simultaneous) mode simulates the two objects in

motion over time.

2. Press

. Set the viewing window.

Tmin=0 Xmin=

13 Ymin=0

Tmax=12 Xmax=34 Ymax=31

Tstep=.1 Xscl=10 Yscl=10

3. Press

. Turn off all functions and stat plots. Enter the

expressions to define the path of the ferris wheel and the

path of the ball. Set the graph style for

(path).

Tip:

Try setting the graph styles to

and

, which simulates a

chair on the ferris wheel and the ball flying through the air when you

press

Using Parametric Equations: Ferris Wheel Problem

Problem

Procedure

Applications 17-13

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 13 of 20

4. Press

to graph the equations. Watch closely as

they are plotted. Notice that the ball and the ferris

wheel passenger appear to be closest where the paths

cross in the top-right quadrant of the ferris wheel.

5. Press

. Change the viewing window to

concentrate on this portion of the graph.

Tmin=1 Xmin=0 Ymin=10

Tmax=3 Xmax=23.5 Ymax=25.5

Tstep=.03 Xscl=10 Yscl=10

6. Press

. After the graph is plotted, press

move near the point on the ferris wheel where the paths

cross. Notice the values of

X, Y, and T.

7. Press

†

to move to the path of the ball. Notice the

values of

X and Y (T is unchanged). Notice where the

cursor is located. This is the position of the ball when

the ferris wheel passenger passes the intersection. Did

the ball or the passenger reach the intersection first?

You can use

to, in effect, take snapshots in time

and explore the relative behavior of two objects in

motion.

17-14 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 14 of 20

Using the functions fnInt( and nDeriv( from the

MATH

to graph functions defined by integrals and derivatives

demonstrates graphically that:

F(x) =

‰

t dt = ln(x), x > 0 and that

[

‰

t dt

]

= 1

1. Press

. Select the default settings.

2. Press

. Set the viewing window.

Xmin=.01 Ymin=

1.5 Xres=3

Xmax=10 Ymax=2.5

Xscl=1 Yscl=1

3. Press

. Turn off all functions and stat plots. Enter the

numerical integral of 1

T from 1 to X and the function

ln(X). Set the graph style for

(line) and Y

(path).

4. Press

. Press

}

, and

†

to compare the

values of

and Y

5. Press

. Turn off

and Y

, and then enter the

numerical derivative of the integral of 1

X and the

function 1

X. Set the graph style for

(line) and Y

(thick).

6. Press

. Again, use the cursor keys to compare the

values of the two graphed functions,

and Y

Demonstrating the Fundamental Theorem of Calculus

Problem 1

Procedure 1

Applications 17-15

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 15 of 20

Explore the functions defined by

y =

‰

dt,

‰

dt, and

‰

1. Press

. Turn off all functions and stat plots. Use a list

to define these three functions simultaneously. Store

the function in

2. Press

6 to select 6:ZStandard.

3. Press

. Notice that the functions appear identical,

only shifted vertically by a constant.

4. Press

. Enter the numerical derivative of

in Y

5. Press

. Notice that although the three graphs

defined by

are different, they share the same

derivative.

Problem 2

Procedure 2

17-16 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 16 of 20

Use the equation solver to store a formula for the area of a

regular N-sided polygon, and then solve for each variable,

given the other variables. Explore the fact that the limiting

case is the area of a circle,

Consider the formula A = NB

sin(

pà

N) cos(

pà

N) for the

area of a regular polygon with N sides of equal length and

B distance from the center to a vertex.

N = 4 sides N = 8 sides N = 12 sides

1. Press



0 to select 0:Solver from the

MATH

menu.

Either the equation editor or the interactive solver

editor is displayed. If the interactive solver editor is

displayed, press

}

to display the equation editor.

2. Enter the formula as

0=A

sin(

/ N)cos(

/ N), and

then press

. The interactive solver editor is

displayed.

3. Enter N=4 and B=6 to find the area (A) of a square with

a distance (

B) from center to vertex of 6 centimeters.

4. Press

}

to move the cursor onto

A, and then press

[

SOLVE

]. The solution for A is displayed on the

interactive solver editor.

5. Now solve for B for a given area with various number of

sides. Enter

A=200 and N=6. To find the distance B,

move the cursor onto

B, and then press

[

SOLVE

6. Enter

N=8. To find the distance B, move the cursor onto

B, and then press

[

SOLVE

]. Find B for N=9, and

then for

N=10.

Computing Areas of Regular N-Sided Polygons

Problem

Procedure

Applications 17-17

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 17 of 20

Find the area given B=6, and N=10, 100, 150, 1000, and

10000. Compare your results with

(the area of a circle

with radius 6), which is approximately 113.097.

7. Enter

B=6. To find the area A, move the cursor onto A,

and then press

[

SOLVE

]. Find A for N=10, then

N=100, then N=150, then N=1000, and finally N=10000.

Notice that as

N gets large, the area A approaches

Now graph the equation to see visually how the area

changes as the number of sides gets large.

8. Press

. Select the default mode settings.

9. Press

. Set the viewing window.

Xmin=0 Ymin=0 Xres=1

Xmax=200 Ymax=150

Xscl=10 Yscl=10

10.Press

. Turn off all functions and stat plots. Enter the

equation for the area. Use

X in place of N. Set the graph

styles as shown.

11.Press

. After the graph is plotted, press 100

to trace to

X=100. Press 150

. Press 188

Notice that as

X increases, the value of Y converges to

, which is approximately 113.097. Y

(the area of

the circle) is a horizontal asymptote to

. The area of

an N-sided regular polygon, with r as the distance from

the center to a vertex, approaches the area of a circle

with radius r (

) as N gets large.

17-18 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 18 of 20

You are a loan officer at a mortgage company, and you

recently closed on a 30-year home mortgage at 8 percent

interest with monthly payments of 800. The new home

owners want to know how much will be applied to the

interest and how much will be applied to the principal

when they make the 240th payment 20 years from now.

1. Press

and set the fixed-decimal mode to

2 decimal

places. Set the other mode settings to the defaults.

2. Press

[

FINANCE

] 1 to display the

TVM Solver

. Enter

these values.

Note:

Enter a positive number (

800

) to show

PMT

as a cash

inflow. Payment values will be displayed as positive numbers on

the graph. Enter

for

, since the future value of a loan is 0 once

it is paid in full. Enter

PMT: END

, since payment is due at the end

of a period.

3. Move the cursor onto the PV= prompt, and then press

[

SOLVE

]. The present value, or mortgage amount,

of the house is displayed at the

PV= prompt.

Computing and Graphing Mortgage Payments

Problem

Procedure

Applications 17-19

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 19 of 20

Now compare the graph of the amount of interest with the

graph of the amount of principal for each payment.

4. Press

. Set

Par and Simul.

5. Press

. Turn off all functions and stat plots. Enter

these equations and set the graph styles as shown.

Note:

Prn(

and

Int(

are located on the

FINANCE CALC

menu.

6. Press

. Set these window variables.

Tmin=1 Xmin=0 Ymin=0

Tmax=360 Xmax=360 Ymax=1000

Tstep=12 Xscl=10 Yscl=100

Tip:

To increase the graph speed, change

Tstep

7. Press

. After the graph is drawn, press 240

to move the trace cursor to

T=240, which is equivalent

to 20 years of payments.

The graph shows that for the 240th payment (X=240),

358.03 of the 800 payment is applied to principal

(

Y=358.03).

Note:

The sum of the payments (

) is always 800.

17-20 Applications

8317APPS.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:00 PM Printed: 02/19/01 1:39 PM

Page 20 of 20

8. Press

†

to move the cursor onto the function for

interest defined by

and Y

. Enter 240.

The graph shows that for the 240th payment (X=240),

441.97 of the 800 payment is interest (

Y=441.97).

9. Press

[

QUIT

]

[

FINANCE

] 9 to paste 9:bal( to the

home screen. Check the figures from the graph.

At which monthly payment will the principal allocation

surpass the interest allocation?

Memory Management 18-1

8318MEMR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:01 PM Printed: 02/19/01 1:40

PM Page 1 of 6

Memor

Mana

ement

Checking Available Memory

.............................

18-2

Deleting Items from Memory

............................

18-3

Clearing Entries and List Elements

......................

18-4

Resetting the TI

......................................

18-5

Contents

18-2 Memory Management

8318MEMR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:01 PM Printed: 02/19/01 1:40

PM Page 2 of 6

To display the

MEMORY

menu, press

[

MEM

MEMORY

1: Check RAM

...

Reports memory availability/usage.

2: Delete

...

Displays

DELETE FROM

menu.

3: Clear Entries

Clears

ENTRY

(last-entry storage).

4: ClrAllLists

Clears all lists in memory.

5: Reset

...

Displays

RESET

menu (all/defaults).

Check RAM

displays the

Check RAM

screen. The top line

reports the total amount of available memory. The

remaining lines report the amount of memory each

variable type is using. You can check this screen to see

whether you need to delete variables from memory to

make room for new data, such as programs.

To check RAM usage, follow these steps.

1. Press

[

MEM

] to display the

MEMORY

menu.

2. Select

1:Check RAM

to display the

Check RAM

screen.

The TI

83 expresses memory quantities in bytes.

Note:

The

in the left column of

the bottom row indicates that you

can scroll or page down to view

more variable types.

Note:

Real

List

Vars

, and

Prgm

variable types never reset to

zero, even after memory is cleared.

To leave the

Check RAM

screen, press either

[

QUIT

] or

‘

. Both options display the home screen.

Checking Available Memory

MEMORY Menu

Displaying the

Check RAM

Screen

Memory Management 18-3

8318MEMR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:01 PM Printed: 02/19/01 1:40

PM Page 3 of 6

To increase available memory by deleting the contents of

any variable (real or complex number, list, matrix,

variable, program, picture, graph database, or string),

follow these steps.

1. Press

[

MEM

] to display the

MEMORY

menu.

2. Select

2:Delete to display the

DELETE FROM

secondary

menu.

3. Select the type of data you want to delete, or select 1:All

for a list of all variables of all types. A screen is

displayed listing each variable of the type you selected

and the number of bytes each variable is using.

For example, if you select

4:List, the

DELETE:List

screen

is displayed.

4. Press

}

and

†

to move the selection cursor (

) next to

the item you want to delete, and then press

. The

variable is deleted from memory. You can delete

individual variables one by one from this screen.

To leave any

DELETE:

screen without deleting anything,

press

[

QUIT

], which displays the home screen.

Note:

You cannot delete some system variables, such as the last-

answer variable

Ans

and the statistical variable

RegEQ

Deleting Items from Memory

Deleting an Item

18-4 Memory Management

8318MEMR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:01 PM Printed: 02/19/01 1:40

PM Page 4 of 6

Clear Entries clears the contents of the

ENTRY

(last entry)

storage area (Chapter 1). To clear the

ENTRY

storage area,

follow these steps.

1. Press

[

MEM

] to display the

MEMORY

menu.

2. Select

3:Clear Entries to paste the instruction to the

home screen.

3. Press

to clear the

ENTRY

storage area.

To cancel Clear Entries, press

‘

Note:

If you select

3:Clear Entries

from within a program, the

Clear

Entries

instruction is pasted to the program editor, and the

Entry

(last entry) is cleared when the program is executed.

ClrAllLists sets to 0 the dimension of each list in memory.

To clear all elements from all lists, follow these steps.

1. Press

[

MEM

] to display the

MEMORY

menu.

2. Select

4:ClrAllLists to paste the instruction to the home

screen.

3. Press

to set to

0 the dimension of each list in

memory.

To cancel ClrAllLists, press

‘

ClrAllLists does not delete list names from memory, from

the

LIST NAMES

menu, or from the stat list editor.

Note:

If you select

4:ClrAllLists

from within a program, the

ClrAllLists

instruction is pasted to the program editor. The lists are

cleared when the program is executed.

Clearing Entries and List Elements

Clear Entries

ClrAllLists

Memory Management 18-5

8318MEMR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:01 PM Printed: 02/19/01 1:40

PM Page 5 of 6

The

RESET

secondary menu gives you the option of

resetting all memory (including default settings) or

resetting the default settings while preserving other data

stored in memory, such as programs and

functions.

Resetting all memory on the TI

83 restores memory to the

factory settings. It deletes all nonsystem variables and all

programs. It resets all system variables to the default

settings.

Tip:

Before you reset all memory, consider restoring sufficient

available memory by deleting only selected data (page 18

3).

To reset all memory on the TI

83, follow these steps.

1. Press

[

MEM

] to display the

MEMORY

menu.

2. Select

5:Reset

to display the

RESET

secondary menu.

3. Select

1:All Memory

to display the

RESET MEMORY

tertiary menu.

4. Read the message below the

RESET MEMORY

menu.

•

To cancel memory reset and return to the home

screen, select

1:No

•

To erase from memory all data and programs, select

2:Reset

. All factory defaults are restored.

Mem cleared

is displayed on the home screen.

Note:

When you clear memory, the contrast sometimes changes. If

the screen is faded or blank, adjust the contrast (Chapter 1).

Resetting the TI-83

RESET

Secondary Menu

Resetting All

Memory

18-6 Memory Management

8318MEMR.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:01 PM Printed: 02/19/01 1:40

PM Page 6 of 6

When you reset defaults on the TI

83, all defaults are

restored to the factory settings. Stored data and programs

are not changed.

These are some examples of TI

83 defaults that are

restored by resetting the defaults.

•

Mode settings such as

Normal (notation); Func

(graphing); Real (numbers); and Full (screen)

•

functions off

•

Window variable values such as

Xmin=

10; Xmax=10;

Xscl=1; Yscl=1; and Xres=1

•

Stat plots off

•

Format settings such as

CoordOn (graphing coordinates

on); AxesOn; and ExprOn (expression on)

•

rand seed value to 0

To reset all TI

83 factory defaults, follow these steps.

1. Press

[

MEM

] to display the

MEMORY

menu.

2. Select

5:Reset to display the

RESET

secondary menu.

3. Select

2:Defaults to display the

RESET DEFAULTS

tertiary menu.

4. Consider the consequences of resetting defaults.

•

To cancel reset and return to the home screen, select

1:No.

•

To restore factory default settings, select

2:Reset.

Default settings are restored. Defaults set is

displayed on the home screen.

Resetting

Defaults

Communication Link 19-1

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 1 of 10

Communication

Link

Getting Started: Sending Variables

.......................

19-2

LINK

...............................................

19-3

Selecting Items to Send

..................................

19-4

Receiving Items

..........................................

19-5

Transmitting Items

.......................................

19-6

Transmitting Lists to a TI

.............................

19-8

Transmitting from a TI

82 to a TI

.....................

19-9

Backing Up Memory

.....................................

19-10

Contents

19-2 Communication Link

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 2 of 10

Getting Started is a fast-paced introduction. Read the chapter for details.

Create and store a variable and a matrix, and then transfer them to another

83.

1. On the home screen of the sending unit,

press

Q. Press

store 5.5 to

2. Press

[

]

[

] 1

[

]

[

] 3

[

]

[

]



Press

to store the matrix to

[A].

3. Connect the calculators with the link

cable. Push both ends in firmly.

4. On the receiving unit, press

[

LINK

]

display the

RECEIVE

menu. Press 1 to

select

1:Receive. The message Waiting

...

displayed and the busy indicator is on.

5. On the sending unit, press

[

LINK

] to

display the

SEND

menu.

6. Press

2 to select 2:All

. The

All

SELECT

screen is displayed.

7. Press

†

until the selection cursor (

) is

next to

[A] MATRX. Press

8. Press

†

until the selection cursor is next

Q REAL. Press

. A square dot next

[A] and Q indicates that each is selected

to send.

9. On the sending unit, press

to display the

TRANSMIT

menu.

10. On the sending unit, press 1 to select

1:Transmit and begin transmission. The

receiving unit displays the message

Receiving....When the items are

transmitted, both units display the name

and type of each transmitted variable.

Getting Started: Sending Variables

Communication Link 19-3

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 3 of 10

The TI

83 has a port to connect and communicate with

another TI

83, a TI

82, the Calculator-Based Laboratory

(CBL 2

, CBL

) System, the Calculator-Based Ranger

(CBR

), or a personal computer. The unit-to-unit link

cable is included with the TI

83. This chapter describes

how to communicate with another calculator.

You can transfer all variables and programs to another

83 or backup the entire memory of a TI

83. The

software that enables this communication is built into the

83. To transmit from one TI

83 to another, follow the

steps on pages 19

6 and 19

You can transfer from a TI

82 to a TI

83 all variables and

programs. Also, you can transfer from a TI

83 to a TI

82 lists

through L

The software that enables this communication is built into the

83. To transmit data from a TI

82 to a TI

83, follow the

steps on pages 19

6 and 19

•

You cannot perform a memory backup from a TI

82 to a

83.

•

The only data type you can transmit from a TI

83 to a

82 is list data stored in L

through L

. Use the

LINK

SEND

menu item 5:Lists to TI82 (page 19

8).

1. Insert either end of the cable into the port very firmly.

2. Insert the other end of the cable into the other

calculator’s port.

CBR and the CBL 2/CBL System are optional accessories

that connect to a TI

83 with the unit-to-unit link cable.

With a CBR or a CBL 2/CBL and a TI

83, you can collect

and analyze real-world data.

GRAPH LINK

is an optional accessory that links a TI

to enable communication with a personal computer.

TI-83 LINK

TI-83 Link

Capabilities

Linking Two

TI-83s

Linking a TI-82

and a TI-83

Connecting Two

Calculators with

the Cable

Linking to a CBR

or the CBL 2/CBL

System

Linking to a PC

or Macintosh

19-4 Communication Link

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 4 of 10

To display the

LINK SEND

menu, press

[

LINK

SEND RECEIVE

1: All+

...

Displays all items selected.

2: All

...

Displays all items deselected.

3: Prgm

...

Displays all programs names.

4: List

...

Displays all list names.

5: Lists to TI82

...

Displays list names

through

6: GDB

...

Displays all graph databases.

7: Pic

...

Displays all picture data types.

8: Matrix

...

Displays all matrix data types.

9: Real

...

Displays all real variables.

0: Complex

...

Displays all complex variables.

A: Y-Vars

...

Displays all

variables.

B: String

...

Displays all string variables.

C: Back Up

...

Selects all for backup to TI

83.

When you select an item on the

LINK SEND

menu, the

corresponding

SELECT

screen is displayed.

Note:

Each

SELECT

screen, except

All+ SELECT

, is displayed

initially with no data selected.

To select items to send on the sending unit, follow these

steps.

1. Press

[

LINK

] to display the

LINK SEND

menu.

2. Select the menu item that describes the data type to

send. The corresponding

SELECT

screen is displayed.

3. Press

}

and

†

to move the selection cursor (

) to an

item you want to select or deselect.

4. Press

to select or deselect the item. Selected

names are marked with a

5. Repeat steps 3 and 4 to select or deselect additional items.

Selecting Items to Send

LINK SEND Menu

Selecting Items

to Send

Communication Link 19-5

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 5 of 10

To display the

LINK RECEIVE

menu, press

[

LINK

]

SEND RECEIVE

1: Receive

Sets unit to receive data transmission.

When you select

1:Receive from the

LINK RECEIVE

menu on

the receiving unit, the message

Waiting... and the busy

indicator are displayed. The receiving unit is ready to

receive transmitted items. To exit the receive mode

without receiving items, press

, and then select

1:Quit

from the

Error in Xmit

menu.

To transmit, follow the steps on page 19

When transmission is complete, the unit exits the receive

mode. You can select

1:Receive again to receive more

items. The receiving unit then displays a list of items

received. Press

[

QUIT

] to exit the receive mode.

During transmission, if a variable name is duplicated, the

DuplicateName

menu is displayed on the receiving unit.

DuplicateName

1: Rename

Prompts to rename receiving variable.

2: Overwrite

Overwrites data in receiving variable.

3: Omit

Skips transmission of sending variable.

4: Quit

Stops transmission at duplicate variable.

When you select

1:Rename, the Name= prompt is displayed,

and alpha-lock is on. Enter a new variable name, and then

press

. Transmission resumes.

When you select

2:Overwrite, the sending unit’s data

overwrites the existing data stored on the receiving unit.

Transmission resumes.

When you select

3:Omit, the sending unit does not send the

data in the duplicated variable name. Transmission

resumes with the next item.

When you select

4:Quit, transmission stops, and the

receiving unit exits receive mode.

During transmission, if the receiving unit does not have

sufficient memory to receive an item, the

Memory Full

is displayed on the receiving unit.

•

To skip this item for the current transmission, select

1:Omit. Transmission resumes with the next item.

•

To cancel the transmission and exit receive mode,

select

2:Quit.

Receiving Items

LINK RECEIVE

Receiving Unit

DuplicateName

Insufficient

Memory in

Receiving Unit

19-6 Communication Link

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 6 of 10

To transmit selected items after you have selected items to

send on the sending unit (page 19

4) and set the receiving

unit to receive (page 19

5), follow these steps.

1. Press

on the sending unit to display the

TRANSMIT

menu.

2. Confirm that Waiting... is displayed on the receiving

unit, which indicates it is set to receive (page 19

5).

3. Press

to select

1:Transmit. The name and type of

each item are displayed line by line on the sending unit

as the item is queued for transmission, and then on the

receiving unit as each item is accepted.

After all selected items have been transmitted, the message

Done is displayed on both calculators. Press

}

and

†

scroll through the names.

To stop a link transmission, press

. The

Error in Xmit

menu is displayed on both units. To leave the error menu,

select

1:Quit.

A transmission error occurs after one or two seconds if:

•

A cable is not attached to the sending unit.

•

A cable is not attached to the receiving unit.

Note:

If the cable is attached, push it in firmly and try again.

•

The receiving unit is not set to receive transmission.

•

You attempt a backup between a TI

82 and a TI

83.

•

You attempt a data transfer from a TI

83 to a TI

82 with

data other than lists L

through L

or without using

menu item 5:Lists to TI82.

Although a transmission error does not occur, these two

conditions may prevent successful transmission.

•

You try to use

Get( with a calculator instead of a

CBL 2/CBL or CBR.

•

You try to use

GetCalc( with a TI

82 instead of a TI

83.

Transmitting Items

Transmitting

Items

Stopping a

Transmission

Error Conditions

Communication Link 19-7

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 7 of 10

After sending or receiving data, you can repeat the same

transmission to additional TI

83 units—from either the

sending unit or the receiving unit—without having to

reselect data to send. The current items remain selected.

Note:

You cannot repeat transmission if you selected All+ or All

To transmit to an additional TI

83, follow these steps.

1. Set the TI

83 to receive (page 19

5).

2. Do not select or deselect any new items to send. If you

select or deselect an item, all selections or deselections

from the previous transmission are cleared.

3. Disconnect the link cable from one TI

83 and connect it

to the additional TI

83.

4. Set the additional TI

83 to receive (page 19

5).

5. Press

[

LINK

] on the sending TI

83 to display the

LINK SEND

menu.

6. Select the menu item that you used for the last

transmission. The data from your last transmission is

still selected.

7. Press

to display the

LINK TRANSMIT

menu.

8. Confirm that the receiving unit is set to receive

(page 19

5).

9. Press

to select

1:Transmit

and begin transmitting.

Transmitting

Items to an

Additional TI-83

19-8 Communication Link

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 8 of 10

The only data type you can transmit from a TI

83 to a TI

is list data stored in

through L

To transmit to a TI

82 the list data that is stored to TI

lists

, L

, or L

, follow these steps.

1. Set the TI

82 to receive (page 19

5).

2. Press

[

LINK

] 5 on the sending TI

83 to select

5:Lists to TI82. The

SELECT

screen is displayed.

3. Select each list to transmit.

4. Press

to display the

LINK TRANSMIT

menu.

5. Confirm that the receiving unit is set to receive

(page 19

5).

6. Press

to select

1:Transmit and begin transmitting.

Note:

If dimension > 99 for a TI

83 list that is selected to send, the

receiving TI

82 will truncate the list at the ninety-ninth element during

transmission.

Transmitting Lists to a TI-82

Transmitting

Lists to a TI-82

Communication Link 19-9

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 9 of 10

Generally, you can transmit items to a TI

83 from a TI

82,

but differences between the two products may affect some

transmitted data. This table shows differences for which

the software built into the TI

83 automatically adjusts

when a TI

83 receives TI

82 data.

82 TI

Min PlotStart

Start

Min

Start u(

Min)

Start v(

Min)

TblMin TblStart

For example, if you transmit from a TI

82 to a TI

83 a

program that contains

Start

on a command line and then

display the program on the receiving TI

83, you will see

that

Min

has automatically replaced

Start

on the

command line.

The software built into the TI

83 cannot resolve some

differences between the TI

82 and TI

83, which are

described below. You must edit the data on the TI

83 after

you transmit to account for these differences, or the TI

will misinterpret the data.

The TI

83 reinterprets TI

82 prefix functions to include

open parentheses, which may add extraneous parentheses

to transmitted expressions.

For example, if you transmit

sin X+5

from a TI

82 to a

83, the TI

83 reinterprets it as

sin(X+5

. Without a closing

parenthesis after

, the TI

83 interprets this as

sin(X+5)

, not

the sum of

and

sin(X)

If a TI

82 instruction that the TI

83 cannot translate is

transmitted, the

ERR:INVALID

menu is displayed when the

83 attempts to execute the instruction. For example, on

the TI

82, the character group

n-1

is pasted to the cursor

location when you press

[

]. The TI

83 cannot

directly translate

n-1

to the TI

83 syntax

u(n

, so the

ERR:INVALID

menu is displayed.

Note:

83 implied multiplication rules differ from those of the TI

82.

For example, the TI

83 evaluates

, while the TI

evaluates

(Chapter 2).

Transmitting from a TI-82 to a TI-83

Resolved

Differences

between the TI-82

and TI-83

Unresolved

Differences

between the TI-82

and TI-83

19-10 Communication Link

8319LINK.DOC TI-83 Intl English, Chap 19 Bob Fedorisko Revised: 02/19/01 1:24 PM Printed: 02/19/01 1:40 PM

Page 10 of 10

To copy the exact contents of memory in the sending TI

to the memory of the receiving TI

83, put the other unit in

receive mode. Then, on the receiving unit, select

C:Back Up

from the

LINK SEND

menu.

•

Warning:

C:Back Up overwrites the memory in the

receiving unit; all information in the memory of the

receiving unit is lost.

Note:

If you do not want to do a backup, select

2:Quit

to return to

the

LINK SEND

menu.

•

Select

1:Transmit to begin transmission.

As a safety check to prevent accidental loss of memory,

the message

WARNING

Backup is displayed when the

receiving unit receives notice of a backup.

•

To continue with the backup process, select

1:Continue.

The backup transmission begins.

•

To prevent the backup, select

2:Quit.

Note:

If a transmission error is returned during a backup, the receiving

unit is reset.

When the backup is complete, both the sending calculator

and receiving calculator display a confirmation screen.

Backing Up Memory

Memory Backup

Receiving Unit

Memory Backup

Complete

Tables and Reference Information A-1

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Page 1 of 58

Tables and Reference

Information

Table of Functions and Instructions

.....................

A-2

83 Menu Map

.........................................

A-39

Variables

................................................

A-49

Statistics Formulas

......................................

A-50

Financial Formulas

......................................

A-54

Contents

A-2 Tables and Reference Information

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Page 2 of 58

Functions return a value, list, or matrix. You can use functions in an expression.

Instructions initiate an action. Some functions and instructions have arguments.

Optional arguments and accompanying commas are enclosed in brackets ( [ ] ).

For details about an item, including argument descriptions and restrictions, turn

to the page listed on the right side of the table.

From the

CATALOG

, you can paste any function or instruction to the home

screen or to a command line in the program editor. However, some functions

and instructions are not valid on the home screen. The items in this table

appear in the same order as they appear in the

CATALOG

† indicates keystrokes that are valid in the program editor only. Some keystrokes

display menus that are available only in the program editor. Others paste mode,

format, or table-set instructions only when you are in the program editor.

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

abs(

value

)

Returns the absolute value of a

real number, expression, list,

or matrix.



NUM

1:abs(

abs(

complex value

)

Returns the magnitude of a

complex number or list.



CPX

5:abs(

valueA

and

valueB

Returns 1 if both

valueA

and

valueB

are

valueA

and

valueB

can be real numbers,

expressions, or lists.

[

TEST

]

LOGIC

1:and

angle(

value

)

Returns the polar angle of a

complex number or list of

complex numbers.



CPX

4:angle(

ANOVA(

list1

list2

[

list3

...

list20

]

)

Performs a one-way analysis of

ariance for comparing the

means of two to 20

populations.

…

TESTS

F:ANOVA(

Ans

Returns the last answer.

[

ANS

] 1

Table of Functions and Instructions

Tables and Reference Information A-3

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Page 3 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

augment(

matrixA

matrixB

)

Returns a matrix, which is

matrixB

appended to

matrixA

as new columns.



MATH

7:augment(

augment(

listA

listB

)

Returns a list, which is

listB

concatenated to the end of

listA

[

LIST

]

OPS

9:augment(

AxesOff

Turns off the graph axes.

†

[

FORMAT

]

AxesOff

AxesOn

Turns on the graph axes.

†

[

FORMAT

]

AxesOn

a+b

Sets the mode to rectangular

complex number mode (a+b

†

a+b

bal(

npmt

[

roundvalue

]

)

Computes the balance at

npmt

for an amortization schedule

using stored values for

and

PMT

and rounds the

computation to

roundvalue.

[

FINANCE

]

CALC

9:bal(

binomcdf(

numtrials

[

]

)

Computes a cumulative

probability at

for the discrete

binomial distribution with the

specified

numtrials

and

probability

of success on

each trial.

[

DISTR

]

DISTR

A:binomcdf(

binompdf(

numtrials

[

]

)

Computes a probability at

for

the discrete binomial

distribution with the specified

numtrials

and probability

success on each trial.

[

DISTR

]

DISTR

0:binompdf(

cdf(

lowerbound

upperbound

)

Computes the

distribution

probability between

lowerbound

and

upperbound

for the specified degrees of

freedom

[

DISTR

]

DISTR

cdf(

A-4 Tables and Reference Information

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

pdf(

)

Computes the probability

density function (pdf) for the

distribution at a specified

alue for the specified degrees

of freedom

[

DISTR

]

DISTR

pdf(

Test(

observedmatrix

expectedmatrix

[

drawflag

]

)

Performs a chi-square test.

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

Test(

Circle(

radius

)

Draws a circle with center

(

) and

radius

[

DRAW

]

DRAW

9:Circle(

Clear Entries

Clears the contents of the Last

Entry storage area.

[

MEM

]

MEMORY

3:Clear Entries

ClrAllLists

Sets to

the dimension of all

lists in memory.

[

MEM

]

MEMORY

4:ClrAllLists

ClrDraw

Clears all drawn elements from

a graph or drawing.

[

DRAW

]

DRAW

1:ClrDraw

ClrHome

Clears the home screen.

†



I/O

8:ClrHome

ClrList

listname1

[

listname2

, ...,

listname n

]

Sets to

the dimension of one

or more

listnames

…

EDIT

4:ClrList

ClrTable

Clears all values from the

table.

†



I/O

9:ClrTable

conj(

value

)

Returns the complex conjugate

of a complex number or list of

complex numbers.



CPX

1:conj(

Connected

Sets connected plotting mode;

resets all

editor graph-style

settings to

†

Connected

Tables and Reference Information A-5

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

CoordOff

Turns off cursor coordinate

alue display.

†

[

FORMAT

]

CoordOff

CoordOn

Turns on cursor coordinate

alue display.

†

[

FORMAT

]

CoordOn

cos(

value

)

Returns cosine of a

real number, expression, or

list.

™

cos

(

value

)

Returns arccosine of a real

number, expression, or list.

[

COS

]

cosh(

value

)

Returns hyperbolic cosine of a

real number, expression, or

list.

[

CATALOG

]

cosh(

cosh

(

value

)

Returns hyperbolic arccosine

of a real number, expression,

or list.

[

CATALOG

]

cosh

(

CubicReg

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a cubic regression model

Xlistname

and

Ylistname

with frequency

freqlist

, and

stores the regression equation

regequ

…

CALC

6:CubicReg

cumSum(

list

)

Returns a list of the cumulative

sums of the elements in

list

starting with the first element.

[

LIST

]

OPS

6:cumSum(

11-12

cumSum(

matrix

)

Returns a matrix of the

cumulative sums of

matrix

elements. Each element in the

returned matrix is a cumulative

sum of a

matrix

column from

top to bottom.



MATH

0:cumSum(

dbd(

date1

date2

)

Calculates the number of days

between

date1

and

date2

using

the actual-day-count method.

[

FINANCE

]

CALC

D:dbd(

value

Dec

Displays a real or complex

number, expression, list, or

matrix in decimal format.



MATH

Dec

A-6 Tables and Reference Information

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Page 6 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Degree

Sets degree angle mode.

†

Degree

DelVar

variable

Deletes from memory the

contents of

variable

†



CTL

G:DelVar

DependAsk

Sets table to ask for

dependent-variable values.

†

[

TBLSET

]

Depend: Ask

DependAuto

Sets table to generate

dependent-variable values

automatically.

†

[

TBLSET

]

Depend: Auto

det(

matrix

)

Returns determinant of

matrix



MATH

1:det(

DiagnosticOff

Sets diagnostics-off mode;

and

are not displayed as

regression model results.

[

CATALOG

]

DiagnosticOff

DiagnosticOn

Sets diagnostics-on mode;

and

are displayed as

regression model results.

[

CATALOG

]

DiagnosticOn

dim(

listname

)

Returns the dimension of

listname

[

LIST

]

OPS

3:dim(

dim(

matrixname

)

Returns the dimension of

matrixname

as a list.



MATH

3:dim(

length

dim(

listname

)

Assigns a new dimension

(

length

) to a new or existing

listname

[

LIST

]

OPS

3:dim(

{

rows

columns

}

dim(

matrixname

)

Assigns new dimensions to a

new or existing

matrixname



MATH

3:dim(

Disp

Displays the home screen.

†



I/O

3:Disp

Disp

[

valueA

valueB

valueC

...

value n

]

Displays each value.

†



I/O

3:Disp

Tables and Reference Information A-7

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

DispGraph

Displays the graph.

†



I/O

4:DispGraph

DispTable

Displays the table.

†



I/O

5:DispTable

value

DMS

Displays

value

in DMS format.

[

ANGLE

]

ANGLE

DMS

Dot

Sets dot plotting mode; resets

all

editor graph-style settings

†

Dot

DrawF

expression

Draws

expression

(in terms of

) on the graph.

[

DRAW

]

DRAW

6:DrawF

DrawInv

expression

Draws the inverse of

expression

by plotting

values

on the y-axis and

values on

the x-axis.

[

DRAW

]

DRAW

8:DrawInv

:DS<(

variable

value

)

commandA

commands

Decrements

variable

by 1;

skips

commandA

variable

value

†



CTL

B:DS<(

e^(

power

)

Returns

raised to

power

[

]

e^(

list

)

Returns a list of

raised to a

list

of powers.

[

]

Exponent:

value

exponent

Returns

value

times 10 to the

exponent

[

]

Exponent:

list

exponent

Returns

list

elements times 10

to the

exponent

[

]

Exponent:

matrix

exponent

Returns

matrix

elements times

10 to the

exponent

[

]

Eff(

nominal rate

compounding periods

)

Computes the effective interest

rate.

[

FINANCE

]

CALC

Eff(

Else

See

If:Then:Else

A-8 Tables and Reference Information

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

End

Identifies end of

For(

Then

Else

Repeat

, or

While

loop.

†



CTL

7:End

Eng

Sets engineering display mode.

†

Eng

Equ

String(

var

,Str

)

Converts the contents of a

var

to a string and stores it in

Str

[

CATALOG

]

Equ

String(

expr(

string

)

Converts

string

to an

expression and executes it.

[

CATALOG

]

expr(

ExpReg

[

Xlistname

Ylistname

freqlist

regequ

]

Fits an exponential regression

model to

Xlistname

and

Ylistname

with frequency

reqlist

, and stores the

regression equation to

regequ

…

CALC

0:ExpReg

ExprOff

Turns off the expression

display during

TRACE

†

[

FORMAT

]

ExprOff

ExprOn

Turns on the expression

display during

TRACE

†

[

FORMAT

]

ExprOn

cdf(

lowerbound

upperbound

numerator df

denominator df

)

Computes the

distribution

probability between

lowerbound

and

upperbound

for the specified

numerator df

(degrees of freedom) and

denominator df

[

DISTR

]

DISTR

cdf(

Fill(

value

matrixname

)

Stores

value

to each element in

matrixname



MATH

4:Fill(

Fill(

value

listname

)

Stores

value

to each element in

listname

[

LIST

]

OPS

4:Fill(

Fix

# Sets fixed-decimal mode for #

of decimal places.

†

0123456789

(select one) 1

Float

Sets floating decimal mode.

†

Float

Tables and Reference Information A-9

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

fMax(

expression

variable

lower

upper

[

tolerance

]

)

Returns the value of

variable

where the local maximum of

expression

occurs, between

lower

and

upper

with

specified

tolerance



MATH

7:fMax(

fMin(

expression

variable

lower

upper

[

tolerance

]

)

Returns the value of

variable

where the local minimum of

expression

occurs, between

lower

and

upper

, with

specified

tolerance



MATH

6:fMin(

fnInt(

expression

variable

lower

upper

[

tolerance

]

)

Returns the function integral o

expression

with respect to

variable

, between

lower

and

upper

, with specified

tolerance



MATH

9:fnInt(

FnOff

[

function#

,...,

function n

]

Deselects all

functions or

specified

functions.



Y-VARS On/Off

2:FnOff

FnOn

[

function#

,...,

function n

]

Selects all

functions or

specified

functions.



Y-VARS On/Off

1:FnOn

:For(

variable

begin

end

[

increment

]

)

commands

:End

commands

Executes

commands

through

End

, incrementing

variable

from

begin

increment

until

variable

end

†



CTL

4:For(

fPart(

value

)

Returns the fractional part or

parts of a real or complex

number, expression, list, or

matrix.



NUM

4:fPart(

pdf(

numerator df

denominator df

)

Computes the

distribution

probability between

lowerbound

and

upperbound

for the specified

numerator df

(degrees of freedom) and

denominator df

[

DISTR

]

DISTR

pdf(

A-10 Tables and Reference Information

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

value

Frac

Displays a real or complex

number, expression, list, or

matrix as a fraction simplified

to its simplest terms.



MATH

Frac

Full

Sets full screen mode.

†

Full

Func

Sets function graphing mode.

†

Func

gcd(

valueA,valueB

)

Returns the greatest common

divisor of

valueA

and

valueB

which can be real numbers or

lists.



NUM

9:gcd(

geometcdf(

)

Computes a cumulative

probability at

, the number of

the trial on which the first

success occurs, for the discrete

geometric distribution with the

specified probability of success

[

DISTR

]

DISTR

E:geometcdf(

geometpdf(

)

Computes a probability at

, the

number of the trial on which the

first success occurs, for the

discrete geometric distribution

with the specified probability of

success

[

DISTR

]

DISTR

D:geometpdf(

Get(

variable

)

Gets data from the CBL 2/CBL

System or CBR and stores it in

variable

†



I/O

A:Get(

GetCalc(

variable

)

Gets contents of

variable

another TI

83 and stores it to

variable

on the receiving TI

83.

†



I/O

0:GetCalc(

getKey

Returns the key code for the

current keystroke, or

, if no

key is pressed.

†



I/O

7:getKey

Goto

label

Transfers control to

label

†



CTL

0:Goto

Tables and Reference Information A-11

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

GraphStyle(

function#

graphstyle#

)

Sets a

graphstyle

for

unction#

†



CTL

H:GraphStyle(

GridOff

Turns off grid format.

†

[

FORMAT

]

GridOff

GridOn

Turns on grid format.

†

[

FORMAT

]

GridOn

G-T

Sets graph-table vertical

split-screen mode.

†

G-T

Horiz

Sets horizontal

split-screen mode.

†

Horiz

Horizontal

Draws a horizontal line at

[

DRAW

]

DRAW

3:Horizontal

identity(

dimension

)

Returns the identity matrix of

dimension

rows ×

dimension

columns.



MATH

5:identity(

:If

condition

commandA

commands

condition

= 0 (false), skips

commandA

†



CTL

1:If

:If

condition

:Then

commands

:End

commands

Executes

commands

from

Then

End

condition

= 1

(true).

†



CTL

2:Then

:If

condition

:Then

commands

:Else

commands

:End

commands

Executes

commands

from

Then

Else

condition

= 1

(true); from

Else

End

condition

= 0 (false).

†



CTL

3:Else

imag(

value

)

Returns the imaginary

(nonreal) part of a complex

number or list of complex

numbers.



CPX

3:imag(

A-12 Tables and Reference Information

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

IndpntAsk

Sets table to ask for

independent-variable values.

†

[

TBLSET

]

Indpnt: Ask

IndpntAuto

Sets table to generate

independent-variable values

automatically.

†

[

TBLSET

]

Indpnt: Auto

Input

Displays graph.

†



I/O

1:Input

Input

[

variable

]

Input

[

text

variable

]

Prompts for value to store to

variable

†



I/O

1:Input

Input

[

Str

variable

] Displays

Str

and stores

entered value to

variable

†



I/O

1:Input

inString(

string

substring

[

start

]

)

Returns the character position

string

of the first character

substring

beginning at

start

[

CATALOG

]

inString(

int(

value

)

Returns the largest integer



real or complex number,

expression, list, or matrix.



NUM

5:int(

Int(

pmt1

pmt2

[

roundvalue

]

)

Computes the sum, rounded to

roundvalue

, of the interest

amount between

pmt1

and

mt2

for an amortization

schedule.

[

FINANCE

]

CALC

Int(

invNorm(

area

[

]

)

Computes the inverse

cumulative normal distribution

function for a given

area

under

the normal distribution curve

specified by

and

[

DISTR

]

DISTR

3:invNorm(

iPart(

value

)

Returns the integer part of a

real or complex number,

expression, list, or matrix.



NUM

3:iPart(

Tables and Reference Information A-13

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

irr(

CF0

CFList

[

CFFreq

]

)

Returns the interest rate at

which the net present value of

the cash flows is equal to zero.

[

FINANCE

]

CALC

8:irr(

:IS>(

variable

value

)

commandA

commands

Increments

variable

by 1; skips

commandA

variable

value

†



CTL

A:IS>(

listname

Identifies the next one to five

characters as a user-created

list name.

[

LIST

]

OPS

LabelOff

Turns off axes labels.

†

[

FORMAT

]

LabelOff

LabelOn

Turns on axes labels.

†

[

FORMAT

]

LabelOn

Lbl

label

Creates a

label

of one or two

characters.

†



CTL

9:Lbl

lcm(

valueA,valueB

)

Returns the least common

multiple of

valueA

and

valueB

which can be real numbers or

lists.



NUM

8:lcm(

length(

string

)

Returns the number of

characters in

string

[

CATALOG

]

length(

Line(

)

Draws a line from (

) to

(

[

DRAW

]

DRAW

2:Line(

Line(

,0)

Erases a line from (

) to

(

[

DRAW

]

DRAW

2:Line(

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

LinReg(a+bx)

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a linear regression model

Xlistname

and

Ylistname

with frequency

freqlist

, and

stores the regression equation

regequ

…

CALC

8:LinReg(a+bx)

LinReg(ax+b)

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a linear regression model

Xlistname

and

Ylistname

with frequency

freqlist

, and

stores the regression equation

regequ

…

CALC

4:LinReg(ax+b)

LinRegTTest

[

Xlistname

Ylistname

freqlist

alternative

regequ

]

Performs a linear regression

and a

-test.

alternative

;

alternative

is >.

†

…

TESTS

E:LinRegTTest

List(

list

)

Returns a list containing the

differences between

consecutive elements in

list

[

LIST

]

OPS

List(

List

matr(

listname1

...

listname n

matrixname

)

Fills

matrixname

column by

column with the elements from

each specified

listname

[

LIST

]

OPS

0:List

matr(

ln(

value

)

Returns the natural logarithm

of a real or complex number,

expression, or list.

LnReg

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a logarithmic regression

model to

Xlistname

and

Ylistname

with frequency

reqlist

, and stores the

regression equation to

regequ

…

CALC

9:LnReg

log(

value

)

Returns logarithm of a real or

complex number, expression,

or list.

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Logistic

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a logistic regression model

Xlistname

and

Ylistname

with frequency

freqlist

, and

stores the regression equation

regequ

…

CALC

B:Logistic

Matr

list(

matrix

listnameA

...

listname n

)

Fills each

listname

with

elements from each column in

matrix

[

LIST

]

OPS

A:Matr

list(

Matr

list(

matrix

column#

listname

)

Fills a

listname

with elements

from a specified

column#

matrix

[

LIST

]

OPS

A:Matr

list(

max(

valueA

valueB

)

Returns the larger of

valueA

and

valueB



NUM

7:max(

max(

list

)

Returns largest real or

complex element in

list

[

LIST

]

MATH

2:max(

max(

listA

listB

)

Returns a real or complex list of

the larger of each pair of

elements in

listA

and

listB

[

LIST

]

MATH

2:max(

max(

value,list

)

Returns a real or complex list of

the larger of

value

or each

list

element.

[

LIST

MATH

2:max(

mean(

list

[

freqlist

]

)

Returns the mean of

list

with

frequency

freqlist

[

LIST

]

MATH

3:mean(

median(

list

[

freqlist

]

)

Returns the median of

list

with

frequency

freqlist

[

LIST

]

MATH

4:median(

Med-Med

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a median-median model to

listname

and

Ylistname

with

frequency

freqlist

, and stores

the regression equation to

regequ

…

CALC

3:Med-Med

Menu("

title

","

text1

label1

[

...

text7

label7

]

)

Generates a menu of up to

seven items during program

execution.

†



CTL

C:Menu(

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

min(

valueA

valueB

)

Returns smaller of

valueA

and

valueB



NUM

6:min(

min(

list

)

Returns smallest real or

complex element in

list

[

LIST

]

MATH

1:min(

min(

listA

listB

)

Returns real or complex list of

the smaller of each pair of

elements in

listA

and

listB

[

LIST

]

MATH

1:min(

min(

value,list

)

Returns a real or complex list

of the smaller of

value

or each

list

element.

[

LIST

]

MATH

1:min(

valueA

nCr

valueB

Returns the number of

combinations of

valueA

taken

valueB

at a time.



PRB

3:nCr

value

nCr

list

Returns a list of the

combinations of

value

taken

each element in

list

at a time.



PRB

3:nCr

list

nCr

value

Returns a list of the

combinations of each element

list

taken

value

at a time.



PRB

3:nCr

listA

nCr

listB

Returns a list of the

combinations of each element

listA

taken each element in

listB

at a time.



PRB

3:nCr

nDeriv(

expression

variable

value

[

]

)

Returns approximate

numerical derivative of

expression

with respect to

variable

value

, with

specified



MATH

8:nDeriv(

Nom(

effective rate

compounding periods

)

Computes the nominal interest

rate.

[

FINANCE

]

CALC

Nom(

Normal

Sets normal display mode.

†

Normal

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

normalcdf(

lowerbound

upperbound

[

]

)

Computes the normal

distribution probability

between

lowerbound

and

upperbound

for the specified

and

[

DISTR

]

DISTR

2:normalcdf(

normalpdf(

[

]

)

Computes the probability

density function for the normal

distribution at a specified

alue for the specified

and

[

DISTR

]

DISTR

1:normalpdf(

not(

value

)

Returns

value

can be a real number,

expression, or list.

[

TEST

]

LOGIC

4:not(

valueA

nPr

valueB

Returns the number of

permutations of

valueA

taken

valueB

at a time.



PRB

2:nPr

value

nPr

list

Returns a list of the

permutations of

value

taken

each element in

list

at a time.



PRB

2:nPr

list

nPr

value

Returns a list of the

permutations of each element

list

taken

value

at a time.



PRB

2:nPr

listA

nPr

listB

Returns a list of the

permutations of each element

listA

taken each element in

listB

at a time.



PRB

2:nPr

npv(

interest rate

CF0

CFList

[

CFFreq

]

)

Computes the sum of the

present values for cash inflows

and outflows.

[

FINANCE

]

CALC

7:npv(

valueA

valueB

Returns 1 if

valueA

valueB

valueA

and

valueB

can

be real numbers, expressions,

or lists.

[

TEST

]

LOGIC

2:or

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Output(

row

column

text

Displays

text

beginning at

specified

row

and

column

†



I/O

6:Output(

Output(

row

column

value

)

Displays

value

beginning at

specified

row

and

column

†



I/O

6:Output(

Param

Sets parametric graphing

mode.

†

Par

Pause

Suspends program execution

until you press

†



CTL

8:Pause

Pause

[

value

] Displays

value

; suspends

program execution until you

press

†



CTL

8:Pause

Plot

(

type

Xlistname

Ylistname

mark

)

Defines

Plot

(

, or

) of

type

Scatter

xyLine

for

listname

and

Ylistname

using

mark

†

[

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

Plot

(

type

Xlistname

freqlist

)

Defines

Plot

(

, or

) of

type

Histogram

Boxplot

for

listname

with frequency

reqlist

†

[

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

Plot

(

type

Xlistname

freqlist

mark

)

Defines

Plot

(

, or

) of

type

ModBoxplot

for

listname

with frequency

reqlist

using

mark

†

[

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

Plot

(

type

datalistname

data axis

mark

)

Defines

Plot

(

, or

) of

type

NormProbPlot

for

datalistname

data axis

using

mark

data axis

can be

†

[

STAT PLOT

]

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

PlotsOff

[

1,2,3

] Deselects all stat plots or one

or more specified stat plots (

, or

[

STAT PLOT

]

STAT PLOTS

4:PlotsOff

PlotsOn

[

1,2,3

] Selects all stat plots or one or

more specified stat plots (

[

STAT PLOT

]

STAT PLOTS

5:PlotsOn

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Pmt_Bgn

Specifies an annuity due,

where payments occur at the

beginning of each payment

period.

[

FINANCE

]

CALC

F:Pmt_Bgn

Pmt_End

Specifies an ordinary annuity,

where payments occur at the

end of each payment period.

[

FINANCE

]

CALC

E:Pmt_End

poissoncdf(

)

Computes a cumulative

probability at

for the discrete

Poisson distribution with

specified mean

[

DISTR

]

DISTR

C:poissoncdf(

poissonpdf(

)

Computes a probability at

for

the discrete Poisson distributio

with the specified mean

[

DISTR

]

DISTR

B:poissonpdf(

Polar

Sets polar graphing mode.

†

Pol

complex value

Polar

Displays

complex value

polar format.



CPX

Polar

PolarGC

Sets polar graphing

coordinates format.

†

[

FORMAT

]

PolarGC

prgm

name

Executes the program

name

†



CTRL

D:prgm

Prn(

pmt1

pmt2

[

roundvalue

]

)

Computes the sum, rounded to

roundvalue

, of the principal

amount between

pmt1

and

mt2

for an amortization

schedule.

[

FINANCE

]

CALC

Prn(

prod(

list

[

start

end

]

)

Returns product of

list

elements between

start

and

end

[

LIST

]

MATH

6:prod(

Prompt

variableA

[

variableB

...

variable n

]

Prompts for value for

variableA

, then

variableB

, and

so on.

†



I/O

2:Prompt

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

PropZInt(

[

confidence level

]

)

Computes a one-proportion

confidence interval.

†

…

TESTS

A:1

PropZInt(

[

confidence level

]

)

Computes a two-proportion

confidence interval.

†

…

TESTS

B:2

PropZInt(

PropZTest(

[

alternative

drawflag

]

)

Computes a one-proportion

test.

alternative

is <;

alternative

;

alternative

is >.

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

5:1

PropZTest(

13-14

PropZTest(

[

alternative

drawflag

]

)

Computes a two-proportion

test.

alternative

is <;

alternative

;

alternative

is >.

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

6:2

PropZTest(

13-15

Change(

)

Reverses a point at (

[

DRAW

]

POINTS

3:Pt

Change(

Off(

[

mark

]

)

Erases a point at (

) using

mark

[

DRAW

]

POINTS

2:Pt

Off(

On(

[

mark

]

)

Draws a point at (

) using

mark

[

DRAW

]

POINTS

1:Pt

On(

PwrReg

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a power regression model

Xlistname

and

Ylistname

with frequency

freqlist

, and

stores the regression equation

regequ

…

CALC

A:PwrReg

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Pxl

Change(

row

column

)

Reverses pixel at

(

row

column

); 0



row



and 0



column



94.

[

DRAW

POINTS

6:Pxl

Change(

Pxl

Off(

row

column

)

Erases pixel at (

row

column

);



row



62 and



column



94.

[

DRAW

]

POINTS

5:Pxl

Off(

Pxl

On(

row

column

)

Draws pixel at (

row

column

);



row



62 and



column



94.

[

DRAW

]

POINTS

4:Pxl

On(

pxl

Test(

row

column

)

Returns 1 if pixel (

row

column

) is on, 0 if it is off;



row



62 and



column



94.

[

DRAW

]

POINTS

7:pxl

Test(

Rx(

)

Returns

, given polar

coordinates

and

or a list of

polar coordinates.

[

ANGLE

]

ANGLE

7:P

Rx(

Ry(

)

Returns

, given polar

coordinates

and

or a list of

polar coordinates.

[

ANGLE

]

ANGLE

8:P

Ry(

QuadReg

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a quadratic regression

model to

Xlistname

and

Ylistname

with frequency

reqlist

, and stores the

regression equation to

regequ

…

CALC

5:QuadReg

QuartReg

[

Xlistname

Ylistname

freqlist

regequ

]

Fits a quartic regression model

Xlistname

and

Ylistname

with frequency

freqlist

, and

stores the regression equation

regequ

…

CALC

7:QuartReg

Radian

Sets radian angle mode.

†

Radian

rand

[

(

numtrials

)

] Returns a random number

between 0 and 1 for a

specified number of trials

numtrials



PRB

1:rand

randBin(

numtrials

prob

[

numsimulations

]

)

Generates and displays a

random real number from a

specified Binomial distribution.



PRB

7:randBin(

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

randInt(

lower,upper

[

,numtrials

]

)

Generates and displays a

random integer within a range

specified by

lower

and

upper

integer bounds for a specified

number of trials

numtrials



PRB

5:randInt(

randM(

rows

columns

)

Returns a random matrix of

rows

(

–

) ×

columns

(

–



MATH

6:randM(

randNorm(

[

numtrials

]

)

Generates and displays a

random real number from a

specified Normal distribution

specified by

and

for a

specified number of trials

numtrials



PRB

6:randNorm(

Sets the mode to polar

complex number mode (

†

Real

Sets mode to display complex

results only when you enter

complex numbers.

†

Real

real(

value

)

Returns the real part of a

complex number or list of

complex numbers.



CPX

2:real(

RecallGDB

Restores all settings stored in

the graph database variable

GDB

[

DRAW

]

STO

4:RecallGDB

RecallPic

Displays the graph and adds

the picture stored in

Pic

[

DRAW

]

STO

2:RecallPic

complex value

Rect

Displays

complex value

or list

in rectangular format.



CPX

Rect

RectGC

Sets rectangular graphing

coordinates format.

†

[

FORMAT

]

RectGC

ref(

matrix

)

Returns the row-echelon form

of a

matrix



MATH

A:ref(

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

:Repeat

condition

commands

:End

commands

Executes

commands

until

condition

is true.

†



CTL

6:Repeat

Return

Returns to the calling program.

†



CTL

E:Return

round(

value

[

#decimals

]

)

Returns a number, expression,

list, or matrix rounded to

#decimals

(



9).



NUM

2:round(

row(

value

matrix

row

)

Returns a matrix with

row

matrix

multiplied by

value

and

stored in

row



MATH

row(

row+(

matrix

rowA

rowB

)

Returns a matrix with

rowA

matrix

added to

rowB

and

stored in

rowB



MATH

D:row+(

row+(

value

matrix

rowA

rowB

)

Returns a matrix with

rowA

matrix

multiplied by

value

added to

rowB

, and stored in

rowB



MATH

row+(

rowSwap(

matrix

rowA

rowB

)

Returns a matrix with

rowA

matrix

swapped with

rowB



MATH

C:rowSwap(

rref(

matrix

)

Returns the reduced row-

echelon form of a

matrix



MATH

B:rref(

Pr(

)

Returns

, given rectangular

coordinates

and

or a list of

rectangular coordinates.

[

ANGLE

]

ANGLE

5:R

Pr(

(

)

Returns

, given rectangular

coordinates

and

or a list of

rectangular coordinates.

[

ANGLE

]

ANGLE

6:R

(

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Samp

Test

[

listname1

listname2

freqlist1

freqlist2

alternative

drawflag

]

(Data list input)

Performs a two-sample

test.

alternative

;

alternative

;

alternative

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

D:2

Samp

Test

Samp

Test

Sx1

Sx2

[

alternative

drawflag

]

(Summary stats input)

Performs a two-sample

test.

alternative

;

alternative

;

alternative

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

D:2

Samp

Test

SampTInt

[

listname1

listname2

freqlist1

freqlist2

confidence level

pooled

]

(Data list input)

Computes a two-sample

confidence interval.

pooled

pools variances;

pooled

does

not pool variances.

†

…

TESTS

0:2

SampTInt

Sx1

Sx2

[

confidence

level

pooled

]

(Summary stats input)

Computes a two-sample

confidence interval.

pooled

pools variances;

pooled

does

not pool variances.

†

…

TESTS

0:2

SampTInt

SampTTest

[

listname1

listname2

freqlist1

freqlist2

alternative

pooled

drawflag

]

(Data list input)

Computes a two-sample

test.

alternative

;

alternative

;

alternative

pooled

pools variances;

pooled

does

not pool variances.

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

4:2

SampTTest

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

SampTTest

Sx1

Sx2

[

alternative

pooled

drawflag

]

(Summary stats input)

Computes a two-sample

test.

alternative

;

alternative

;

alternative

pooled

pools variances;

pooled

does

not pool variances.

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

4:2

SampTTest

SampZInt(

[

listname1

listname2

freqlist1

freqlist2

confidence level

]

)

(Data list input)

Computes a two-sample

confidence interval.

†

…

TESTS

9:2

SampZInt(

[

confidence level

]

)

(Summary stats input)

Computes a two-sample

confidence interval.

†

…

TESTS

9:2

SampZInt(

SampZTest(

[

listname1

listname2

freqlist1

freqlist2

alternative

drawflag

]

)

(Data list input)

Computes a two-sample

test.

alternative

;

alternative

;

alternative

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

3:2

SampZTest(

[

alternative

drawflag

]

)

(Summary stats input)

Computes a two-sample

test.

alternative

;

alternative

;

alternative

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

3:2

SampZTest(

13-12

Sci

Sets scientific notation display

mode.

†

Sci

Select(

Xlistname

Ylistname

)

Selects one or more specific

data points from a scatter plot

or xyLine plot (only), and then

stores the selected data points

to two new lists,

Xlistname

and

Ylistname

[

LIST

]

OPS

8:Select(

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Page 26 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Send(

variable

)

Sends contents of

variable

the CBL 2/CBL System or CBR.

†



I/O

B:Send(

seq(

expression

variable

begin

end

[

increment

]

)

Returns list created by

evaluating

expression

with

regard to

variable

, from

begin

end

increment.

[

LIST

]

OPS

5:seq(

Seq

Sets sequence graphing mode.

†

Seq

Sequential

Sets mode to graph functions

sequentially.

†

Sequential

SetUpEditor

Removes all list names from

the stat list editor, and then

restores list names

through

to columns

through

…

EDIT

5:SetUpEditor

SetUpEditor

listname1

[

listname2

...

listname20

]

Removes all list names from

the stat list editor, then sets it

up to display one or more

listnames

in the specified

order, starting with column

…

EDIT

5:SetUpEditor

Shade(

lowerfunc

upperfunc

[

Xleft

Xright

pattern

patres

]

)

Draws

lowerfunc

and

upperfunc

in terms of

on the

current graph and uses

attern

and

patres

to shade the

area bounded by

lowerfunc

upperfunc

Xleft

, and

Xright

[

DRAW

]

DRAW

7:Shade(

Shade

(

lowerbound

upperbound

)

Draws the density function for

the

distribution specified by

degrees of freedom

and

shades the area between

lowerbound

and

upperbound

[

DISTR

]

DRAW

3:Shade

(

Tables and Reference Information A-27

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Page 27 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Shade

(

lowerbound

upperbound

numerator df

denominator df

)

Draws the density function for

the

distribution specified by

numerator df

and

denominator df

and shades the

area between

lowerbound

and

upperbound

[

DISTR

]

DRAW

4:Shade

(

ShadeNorm(

lowerbound

upperbound

[

]

)

Draws the normal density

function specified by

and

and shades the area between

lowerbound

and

upperbound

[

DISTR

]

DRAW

1:ShadeNorm(

Shade_t(

lowerbound

upperbound

)

Draws the density function for

the Student-t distribution

specified by degrees of

freedom df, and shades the

area between

lowerbound

and

upperbound

[

DISTR

]

DRAW

2:Shade_t(

Simul

Sets mode to graph functions

simultaneously.

†

Simul

sin(

value

)

Returns the sine of a real

number, expression, or list.

sin

(

value

)

Returns the arcsine of a real

number, expression, or list.

[

SIN

]

sinh(

value

)

Returns the hyperbolic sine of

a real number, expression, or

list.

[

CATALOG

]

sinh(

sinh

(

value

)

Returns the hyperbolic arcsine

of a real number, expression,

or list.

[

CATALOG

]

sinh

(

A-28 Tables and Reference Information

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Page 28 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

SinReg

[

iterations

Xlistname

Ylistname

period

regequ

]

Attempts

iterations

times to fit

a sinusoidal regression model to

listname

and

Ylistname

using

period

guess, and stores the

regression equation to

regequ

…

CALC

C:SinReg

solve(

expression

variable

guess

lower

upper

})

Solves

expression

for

variable

given an initial

guess

and

lower

and

upper

bounds within

which the solution is sought.

†



MATH

0:solve(

SortA(

listname

)

Sorts elements of

listname

ascending order.

[

LIST

]

OPS

1:SortA(

SortA(

keylistname

dependlist1

[

dependlist2

...,

dependlist n

]

)

Sorts elements of

keylistname

in ascending order, then sorts

each

dependlist

as a dependent

list.

[

LIST

]

OPS

1:SortA(

SortD(

listname

)

Sorts elements of

listname

descending order.

[

LIST

]

OPS

2:SortD(

SortD(

keylistname

dependlist1

[

dependlist2

...

dependlist n

]

)

Sorts elements of

keylistname

in descending order, then sorts

each

dependlist

as a dependent

list.

[

LIST

]

OPS

2:SortD(

stdDev(

list

[

freqlist

]

)

Returns the standard deviation

of the elements in

list

with

frequency

freqlist

[

LIST

]

MATH

7:stdDev(

Stop

Ends program execution;

returns to home screen.

†



CTL

F:Stop

Store:

value

variable

Stores

value

variable

StoreGDB

Stores current graph in

database

GDB

[

DRAW

]

STO

3:StoreGDB

Tables and Reference Information A-29

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Page 29 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

StorePic

Stores current picture in

picture

Pic

[

DRAW

]

STO

1:StorePic

String

Equ(

string

var

)

Converts

string

into an

equation and stores it in

var

[

CATALOG

]

String

Equ(

sub(

string

begin

length

)

Returns a string that is a subset

of another

string

, from

begin

length

[

CATALOG

]

sub(

sum(

list

[

start

end

]

)

Returns the sum of elements of

list

from

start

end

[

LIST

]

MATH

5:sum(

tan(

value

)

Returns the tangent of a real

number, expression,

or list.

tan

(

value

)

Returns the arctangent of a

real number, expression, or

list.

[

TAN

]

Tangent(

expression

value

)

Draws a line tangent to

expression

value

[

DRAW

5:Tangent(

tanh(

value

)

Returns hyperbolic tangent of a

real number, expression, or list.

[

CATALOG

]

tanh(

tanh

(

value

)

Returns the hyperbolic

arctangent of a real number,

expression,

or list.

[

CATALOG

]

tanh

(

tcdf(

lowerbound

upperbound

)

Computes the Student-

distribution probability

between

lowerbound

and

upperbound

for the specified

degrees of freedom

[

DISTR

]

DISTR

5:tcdf(

Text(

row

column

text1

text2

...

text n

)

Writes

text

on graph beginning

at pixel (

row

column

), where



row



57 and



column



94.

[

DRAW

]

DRAW

0:Text(

Then

See

If:Then

A-30 Tables and Reference Information

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Page 30 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Time

Sets sequence graphs to plot

with respect to time.

†

[

FORMAT

]

Time

TInterval

[

listname

freqlist

confidence level

]

(Data list input)

Computes a

confidence

interval.

†

…

TESTS

8:TInterval

TInterval

[

confidence level

]

(Summary stats input)

Computes a

confidence

interval.

†

…

TESTS

8:TInterval

tpdf(

)

Computes the probability

density function (pdf) for the

Student-

distribution at a

specified

value with specified

degrees of freedom

[

DISTR

]

DISTR

4:tpdf(

Trace

Displays the graph and enters

TRACE

mode.

T-Test

[

listname

freqlist

alternative

drawflag

]

(Data list input)

Performs a

test with

frequency

freqlist

alternative

;

alternative

;

alternative

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

2:T-Test

T-Test

[

alternative

drawflag

]

(Summary stats input)

Performs a

test with

frequency

freqlist

alternative

is < ;

alternative

;

alternative

is >.

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

2:T-Test

Tables and Reference Information A-31

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Page 31 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

tvm_FV

[

(

PMT

P/Y

C/Y

)

]

Computes the future value.

[

FINANCE

]

CALC

6:tvm_FV

tvm_

[

(

PMT

P/Y

C/Y

)

]

Computes the annual interest

rate.

[

FINANCE

]

CALC

3:tvm_

tvm_

[

(

PMT

P/Y

C/Y

)

]

Computes the number of

payment periods.

[

FINANCE

]

CALC

5:tvm_

tvm_Pmt

[

(

P/Y

C/Y

)

]

Computes the amount of each

payment.

[

FINANCE

]

CALC

2:tvm_Pmt

tvm_PV

[

(

PMT

P/Y

C/Y

)

]

Computes the present value.

[

FINANCE

]

CALC

4:tvm_PV

uvAxes

Sets sequence graphs to plot

)

on the x-axis and

)

the y-axis.

†

[

FORMAT

]

uwAxes

Sets sequence graphs to plot

)

on the x-axis and

)

the y-axis.

†

[

FORMAT

]

1-Var

Stats

[

Xlistname

freqlist

]

Performs one-variable analysis

on the data in

Xlistname

with

frequency

freqlist

…

CALC

1:1-Var Stats

2-Var

Stats

[

Xlistname

Ylistname

freqlist

]

Performs two-variable analysis

on the data in

Xlistname

and

Ylistname

with frequency

reqlist

…

CALC

2:2-Var Stats

variance(

list

[

freqlist

]

)

Returns the variance of the

elements in

list

with frequency

reqlist

[

LIST

]

MATH

8:variance(

Vertical

Draws a vertical line

[

DRAW

]

DRAW

4:Vertical

vwAxes

Sets sequence graphs to plot

)

on the x-axis and

)

the y-axis.

†

[

FORMAT

]

Web

Sets sequence graphs to trace

as webs.

†

[

FORMAT

]

Web

A-32 Tables and Reference Information

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Page 32 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

:While

condition

commands

:End

command

Executes

commands

while

condition

is true.

†



CTL

5:While

valueA

xor

valueB

Returns 1 if only

valueA

valueB

= 0.

valueA

and

valueB

can be real numbers,

expressions, or lists.

[

TEST

]

LOGIC

3:xor

ZBox

Displays a graph, lets you draw

a box that defines a new

iewing window, and updates

the window.

†

ZOOM

1:ZBox

ZDecimal

Adjusts the viewing window so

that

X=0.1

and

Y=0.1

, and

displays the graph screen with

the origin centered on the

screen.

†

ZOOM

4:ZDecimal

ZInteger

Redefines the viewing window

using these dimensions:

X=1 Xscl=10

Y=1 Yscl=10

†

ZOOM

8:ZInteger

ZInterval

[

listname

freqlist

confidence level

]

(Data list input)

Computes a

confidence

interval.

†

…

TESTS

7:ZInterval

13-16

ZInterval

[

confidence level

]

(Summary stats input)

Computes a

confidence

interval.

†

…

TESTS

7:ZInterval

13-16

Zoom In

Magnifies the part of the graph

that surrounds the cursor

location.

†

ZOOM

2:Zoom In

Zoom Out

Displays a greater portion of

the graph, centered on the

cursor location.

†

ZOOM

3:Zoom Out

Tables and Reference Information A-33

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Page 33 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

ZoomFit

Recalculates

Ymin

and

Ymax

to include the minimum and

maximum

values, between

Xmin

and

Xmax

, of the

selected functions and replots

the functions.

†

ZOOM

0:ZoomFit

ZoomRcl

Graphs the selected functions

in a user-defined viewing

window.

†

MEMORY

3:ZoomRcl

ZoomStat

Redefines the viewing window

so that all statistical data

points are displayed.

†

ZOOM

9:ZoomStat

ZoomSto

Immediately stores the current

iewing window.

†

MEMORY

2:ZoomSto

ZPrevious

Replots the graph using the

window variables of the graph

that was displayed before you

executed the last

ZOOM

instruction.

†

MEMORY

1:ZPrevious

ZSquare

Adjusts the

window

settings so that each pixel

represents an equal width and

height in the coordinate

system, and updates the

iewing window.

†

ZOOM

5:ZSquare

ZStandard

Replots the functions

immediately, updating the

window variables to the

default values.

†

ZOOM

6:ZStandard

A-34 Tables and Reference Information

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Page 34 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Test(

[

listname

freqlist

alternative

drawflag

]

)

(Data list input)

Performs a

test with

frequency

freqlist

alternative

;

alternative

;

alternative

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

1:Z

Test(

13-10

Test(

[

alternative

drawflag

]

)

(Summary stats input)

Performs a

test.

alternative

;

alternative

;

alternative

drawflag

draws results;

drawflag

calculates results.

†

…

TESTS

1:Z

Test(

13-10

ZTrig

Replots the functions

immediately, updating the

window variables to preset

alues for plotting trig

functions.

†

ZOOM

7:ZTrig

Factorial:

value

Returns factorial of

value



PRB

4:!

Factorial:

list

Returns factorial of

list

elements.



PRB

4:!

Degrees notation:

value

Interprets

value

as degrees;

designates degrees in DMS

format.

[

ANGLE

]

ANGLE

Radian:

angle

Interprets

angle

as radians.

[

ANGLE

]

ANGLE

Transpose:

matrix

Returns a matrix in which each

element (row, column) is

swapped with the

corresponding element

(column, row) of

matrix



MATH

10-12

Tables and Reference Information A-35

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Page 35 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

root

‡

value

Returns

root

value



MATH

‡

root

‡

list

Returns

root

list

elements.



MATH

‡

list

‡

value

Returns

list

roots of

value



MATH

‡

listA

‡

listB

Returns

listA

roots of

listB



MATH

‡

Cube:

value

Returns the cube of a real or

complex number, expression,

list, or square matrix.



MATH

Cube root:

‡

(

value

)

Returns the cube root of a real or

complex number, expression, or

list.



MATH

‡

(

Equal:

valueA

valueB

Returns 1 if

valueA

valueB

Returns 0 if

valueA

valueB

valueA

and

valueB

can be real

or complex numbers,

expressions, lists, or matrices.

[

TEST

]

TEST

1:=

Not equal:

valueA

valueB

Returns 1 if

valueA

valueB

Returns 0 if

valueA

valueB

valueA

and

valueB

can be real

or complex numbers,

expressions, lists, or matrices.

[

TEST

]

TEST

Less than:

valueA

valueB

Returns 1 if

valueA

valueB

Returns 0 if

valueA

‚

valueB

valueA

and

valueB

can be real

or complex numbers,

expressions, or lists.

[

TEST

]

TEST

5:<

A-36 Tables and Reference Information

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Page 36 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Greater than:

valueA

valueB

Returns 1 if

valueA

valueB

Returns 0 if

valueA



valueB

valueA

and

valueB

can be real

or complex numbers,

expressions, or lists.

[

TEST

]

TEST

3:>

Less than or equal:

valueA



valueB

Returns 1 if

valueA



valueB

Returns 0 if

valueA

valueB

valueA

and

valueB

can be real

or complex numbers,

expressions, or lists.

[

TEST

]

TEST



Greater than or equal:

valueA

‚

valueB

Returns 1 if

valueA

‚

valueB

Returns 0 if

valueA

valueB

valueA

and

valueB

can be real

or complex numbers,

expressions, or lists.

[

TEST

]

TEST

‚

Inverse:

value

Returns 1 divided by a real or

complex number or

expression.

—

Inverse:

list

Returns 1 divided by

list

elements.

—

Inverse:

matrix

Returns

matrix

inverted.

—

Square:

value

Returns

value

multiplied by

itself.

value

can be a real or

complex number or

expression.

Square:

list

Returns

list

elements squared.

Square:

matrix

Returns

matrix

multiplied by

itself.

Powers:

value

power

Returns

value

raised to

power

value

can be a real or complex

number or expression.

›

Powers:

list

power

Returns

list

elements raised to

ower

›

Powers:

value

list

Returns

value

raised to

list

elements.

›

Tables and Reference Information A-37

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Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

Powers:

matrix

power

Returns

matrix

elements

raised to

power

›

Negation:

value

Returns the negative of a real

or complex number,

expression, list, or matrix.

Power of ten:

value

)

Returns 10 raised to the

value

power.

value

can be a real or

complex number or

expression.

[

]

Power of ten:

list

)

Returns a list of 10 raised to

the

list

power.

[

]

Square root:

‡

(

value

)

Returns square root of a real or

complex number, expression,

or list.

[

‡

]

Multiplication:

valueA

valueB

Returns

valueA

times

valueB

Multiplication:

value

list

Returns

value

times each

list

element.

Multiplication:

list

value

Returns each

list

element

times

value

Multiplication:

listA

listB

Returns

listA

elements times

listB

elements.

Multiplication:

value

matrix

Returns value times

matrix

elements.

Multiplication:

matrixA

matrixB

Returns

matrixA

times

matrixB

Division:

valueA

valueB

Returns

valueA

divided by

valueB

Division:

list

value

Returns

list

elements divided

by value.

Division:

value

list

Returns value divided by

list

elements.

Division:

listA

listB

Returns

listA

elements divided

listB

elements.

A-38 Tables and Reference Information

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Page 38 of 58

Function or Instruction/

Arguments Result

Key or Keys/

Menu or Screen/Item

ddition:

valueA

valueB

Returns

valueA

plus

valueB

ddition:

list

value

Returns list in which

value

added to each

list

element.

ddition:

listA

listB

Returns

listA

elements plus

listB

elements.

ddition:

matrixA

matrixB

Returns

matrixA

elements

plus

matrixB

elements.

Concatenation:

string1

string2

Concatenates two or more

strings.

Subtraction:

valueA

valueB

Subtracts

valueB

from

valueA

Subtraction:

value

list

Subtracts

list

elements from

value

Subtraction:

list

value

Subtracts

value

from

list

elements.

Subtraction:

listA

listB

Subtracts

listB

elements from

listA

elements.

Subtraction:

matrixA

matrixB

Subtracts

matrixB

elements

from

matrixA

elements.

Minutes notation:

degrees

minutes

seconds

Interprets

minutes

angle

measurement as minutes.

[

ANGLE

]

ANGLE

2:'

Seconds notation:

degrees

minutes

seconds

Interprets

seconds

angle

measurement as seconds.

[

]

2-23

Tables and Reference Information A-39

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Page 39 of 58

The TI

83 Menu Map begins at the top-left corner of the keyboard and follows

the keyboard layout from left to right. Default values and settings are shown.

ÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

(Func mode)

Plot1 Plot2

Plot3

Y1=

Y2=

Y3=

Y4=

...

Y9=

Y0=

(Par mode)

Plot1 Plot2

Plot3

X1T=

Y1T=

X2T=

Y2T=

...

X6T=

Y6T=

(Pol mode)

Plot1 Plot2

Plot3

r1=

r2=

r3=

r4=

r5=

r6=

(Seq mode)

Plot1 Plot2

Plot3

nMin=1

u(n)=

u(nMin)=

v(n)=

v(nMin)=

w(n)=

w(nMin)=

[

STAT PLOT

]

ÚÄÄÄÄÄ

[

STAT PLOT

]

ÚÄÄÄÄÄ

ÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

STAT PLOTS

1:Plot1…Off

L1 L2

›

2:Plot2…Off

L1 L2

›

3:Plot3…Off

L1 L2

›

4:PlotsOff

5:PlotsOn

(PRGM editor)

PLOTS

1:Plot1(

2:Plot2(

3:Plot3(

4:PlotsOff

5:PlotsOn

(PRGM editor)

TYPE

1:Scatter

2:xyLine

3:Histogram

4:ModBoxplot

5:Boxplot

6:NormProbPlot

(PRGM editor)

MARK

›

2:+

ÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

(Func mode)

WINDOW

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

Xres=1

(Par mode)

WINDOW

Tmin=0

Tmax=

Tstep=

pà

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

(Pol mode)

WINDOW

min=0

max=

step=

pà

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

(Seq mode)

WINDOW

nMin=1

nMax=10

PlotStart=1

PlotStep=1

Xmin=-10

Xmax=10

Xscl=1

Ymin=-10

Ymax=10

Yscl=1

[

TBLSET

]

ÚÄÄÄ

[

TBLSET

]

ÚÄÄÄÄ

TABLE SETUP

TblStart=0

Tbl=1

Indpnt:Auto Ask

Depend:Auto Ask

(PRGM editor)

TABLE SETUP

Indpnt:Auto Ask

Depend:Auto Ask

TI-83 Menu Map

A-40 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 40 of 58

ÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

ZOOM

1:ZBox

2:Zoom In

3:Zoom Out

4:ZDecimal

5:ZSquare

6:ZStandard

7:ZTrig

8:ZInteger

9:ZoomStat

0:ZoomFit

MEMORY

1:ZPrevious

2:ZoomSto

3:ZoomRcl

4:SetFactors…

MEMORY

(Set Factors...)

ZOOM FACTORS

XFact=4

YFact=4

[

FORMAT

]

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

(Func/Par/Pol modes)

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

(Seq mode)

Time Web uv vw uw

RectGC PolarGC

CoordOn CoordOff

GridOff GridOn

AxesOn AxesOff

LabelOff LabelOn

ExprOn ExprOff

[

CALC

]

ÚÄ

ÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

(Func mode)

CALCULATE

1:value

2:zero

3:minimum

4:maximum

5:intersect

6:dy/dx

‰

f(x)dx

(Par mode)

CALCULATE

1:value

2:dy/dx

3:dy/dt

4:dx/dt

(Pol mode)

CALCULATE

1:value

2:dy/dx

3:dr/d

(Seq mode)

CALCULATE

1:value

Normal Sci Eng

Float 0123456789

Radian Degree

Func Par Pol Seq

Connected Dot

Sequential Simul

Real a+b

re^

Full Horiz G-T

Tables and Reference Information A-41

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 41 of 58

[

LINK

]

ÚÄ

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

SEND

1:All+…

2:All

…

3:Prgm…

4:List…

5:Lists to TI82…

6:GDB…

7:Pic…

8:Matrix…

9:Real…

0:Complex…

A:Y-Vars…

B:String…

C:Back Up…

RECEIVE

1:Receive

…

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

EDIT

1:Edit…

2:SortA(

3:SortD(

4:ClrList

5:SetUpEditor

CALC

1:1-Var Stats

2:2-Var Stats

3:Med-Med

4:LinReg(ax+b)

5:QuadReg

6:CubicReg

7:QuartReg

8:LinReg(a+bx)

9:LnReg

0:ExpReg

A:PwrReg

B:Logistic

C:SinReg

TESTS

1:Z-Test…

2:T-Test…

3:2-SampZTest…

4:2-SampTTest…

5:1-PropZTest…

6:2-PropZTest…

7:ZInterval…

8:TInterval…

9:2-SampZInt…

0:2-SampTInt…

A:1-PropZInt…

B:2-PropZInt…

-Test…

D:2-Samp

Test…

E:LinRegTTest…

F:ANOVA(

A-42 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 42 of 58

[

LIST

]

ÚÄÄ

ÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿

NAMES

1:listname

2:listname

3:listname

...

OPS

1:SortA(

2:SortD(

3:dim(

4:Fill(

5:seq(

6:cumSum(

List(

8:Select(

9:augment(

0:List

matr(

A:Matr

list(

MATH

1:min(

2:max(

3:mean(

4:median(

5:sum(

6:prod(

7:stdDev(

8:variance(



ÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄ¿

MATH

Frac

Dec

‡

(

‡

6:fMin(

7:fMax(

8:nDeriv(

9:fnInt(

0:Solver…

NUM

1:abs(

2:round(

3:iPart(

4:fPart(

5:int(

6:min(

7:max(

8:lcm(

9:gcd(

CPX

1:conj(

2:real(

3:imag(

4:angle(

5:abs(

Rect

Polar

PRB

1:rand

2:nPr

3:nCr

4:!

5:randInt(

6:randNorm(

7:randBin(

[

TEST

]

ÚÄÄ

ÄÄÄÄÄÄÄÄÄ¿

TEST

1:=

3:>

‚

5:<



LOGIC

1:and

2:or

3:xor

4:not(

Tables and Reference Information A-43

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 43 of 58



ÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿

[

ANGLE

]

ÚÄÄÄ

NAMES

1:[A]

2:[B]

3:[C]

4:[D]

5:[E]

6:[F]

7:[G]

8:[H]

9:[I]

0:[J]

MATH

1:det(

3:dim(

4:Fill(

5:identity(

6:randM(

7:augment(

8:Matr

list(

9:List

matr(

0:cumSum(

A:ref(

B:rref(

C:rowSwap(

D:row+(

…

row(

…

row+(

EDIT

1:[A]

2:[B]

3:[C]

4:[D]

5:[E]

6:[F]

7:[G]

8:[H]

9:[I]

0:[J]

ANGLE

2:'

DMS

5:R

Pr(

6:R

(

7:P

Rx(

8:P

Ry(



ÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

EXEC

name

...

EDIT

name

...

NEW

1:Create New



ÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

(PRGM editor)

CTL

1:If

2:Then

3:Else

4:For(

5:While

6:Repeat

7:End

8:Pause

9:Lbl

0:Goto

A:IS>(

B:DS<(

C:Menu(

D:prgm

E:Return

F:Stop

G:DelVar

H:GraphStyle(

(PRGM editor)

I/O

1:Input

2:Prompt

3:Disp

4:DispGraph

5:DispTable

6:Output(

7:getKey

8:ClrHome

9:ClrTable

0:GetCalc(

A:Get(

B:Send(

(PRGM editor)

EXEC

1:name

2:name

...

A-44 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 44 of 58

[

DRAW

]

ÚÄÄÄÄ

ÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

DRAW

1:ClrDraw

2:Line(

3:Horizontal

4:Vertical

5:Tangent(

6:DrawF

7:Shade(

8:DrawInv

9:Circle(

0:Text(

A:Pen

POINTS

1:Pt-On(

2:Pt-Off(

3:Pt-Change(

4:Pxl-On(

5:Pxl-Off(

6:Pxl-Change(

7:pxl-Test(

STO

1:StorePic

2:RecallPic

3:StoreGDB

4:RecallGDB



ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

VARS

1:Window…

2:Zoom…

3:GDB…

4:Picture…

5:Statistics…

6:Table…

7:String…

Y-VARS

1:Function…

2:Parametric…

3:Polar…

4:On/Off…

VARS

ÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ

(Window…)

X/Y

1:Xmin

2:Xmax

3:Xscl

4:Ymin

5:Ymax

6:Yscl

7:Xres

0:XFact

A:YFact

(Window…)

1:Tmin

2:Tmax

3:Tstep

min

max

step

(Window…)

U/V/W

1:u(nMin)

2:v(nMin)

3:w(nMin)

4:nMin

5:nMax

6:PlotStart

7:PlotStep

Tables and Reference Information A-45

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 45 of 58

VARS

ÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄ

(Zoom…)

ZX/ZY

1:ZXmin

2:ZXmax

3:ZXscl

4:ZYmin

5:ZYmax

6:ZYscl

7:ZXres

(Zoom…)

ZT/Z

1:ZTmin

2:ZTmax

3:ZTstep

4:Z

min

5:Z

max

6:Z

step

(Zoom…)

1:Zu(nMin)

2:Zv(nMin)

3:Zw(nMin)

4:ZnMin

5:ZnMax

6:ZPlotStart

7:ZPlotStep

VARS

ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄ

(GDB…)

GRAPH DATABASE

1:GDB1

2:GDB2

...

9:GDB9

0:GDB0

(Picture…)

PICTURE

1:Pic1

2:Pic2

...

9:Pic9

0:Pic0

VARS

ÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄ

(Statistics…)

1:n

3:Sx

6:Sy

8:minX

9:maxX

0:minY

A:maxY

(Statistics…)

1:RegEQ

2:a

3:b

4:c

5:d

6:e

7:r

8:r

9:R

(Statistics…)

TEST

1:p

2:z

3:t

6:df

0:s

C:Sx1

D:Sx2

E:Sxp

F:n1

G:n2

H:lower

I:upper

(Statistics…)

PTS

1:x1

2:y1

3:x2

4:y2

5:x3

6:y3

7:Q

8:Med

9:Q

A-46 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 46 of 58

VARS

ÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

(Table…)

TABLE

1:TblStart

@Tbl

3:TblInput

(String…)

STRING

1:Str1

2:Str2

3:Str3

4:Str4

...

9:Str9

0:Str0

Y-VARS

ÚÄ

ÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄ¿

(Function…)

FUNCTION

1:Y

2:Y

3:Y

4:Y

...

9:Y

0:Y

(Parametric…)

PARAMETRIC

1:X

2:Y

3:X

4:Y

...

A:X

B:Y

(Polar…)

POLAR

1:r

2:r

3:r

4:r

5:r

6:r

(On/Off…)

ON/OFF

1:FnOn

2:FnOff

Tables and Reference Information A-47

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 47 of 58

[

DISTR

]

ÚÄÄ

ÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

DISTR

1:normalpdf(

2:normalcdf(

3:invNorm(

4:tpdf(

5:tcdf(

pdf(

cdf(

pdf(

cdf(

0:binompdf(

A:binomcdf(

B:poissonpdf(

C:poissoncdf(

D:geometpdf(

E:geometcdf(

DRAW

1:ShadeNorm(

2:Shade_t(

3:Shade

(

4:Shade

(

[

FINANCE

]

ÚÄÄÄ

ÄÄÄÄÄÄÄÄÄÄÄÄ¿

CALC

1:TVM Solver…

2:tvm_Pmt

3:tvm_

4:tvm_PV

5:tvm_

6:tvm_FV

7:npv(

8:irr(

9:bal(

Prn(

Int(

Nom(

Eff(

D:dbd(

E:Pmt_End

F:Pmt_Bgn

VARS

3:PV

4:PMT

5:FV

6:P/Y

7:C/Y

A-48 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 48 of 58

[

MEM

]

ÚÄÄ

MEMORY

ÚÄÄ

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÂÄÄÄÄÄÄÄÄÄÄÄÄ¿

MEMORY

1:Check RAM…

2:Delete…

3:Clear Entries

4:ClrAllLists

5:Reset…

(Check RAM…)

MEM FREE 27225

Real 15

Complex 0

List 0

Matrix 0

Y-Vars 240

Prgm 14

Pic 0

GDB 0

String 0

(Delete…)

DELETE FROM…

1:All…

2:Real…

3:Complex…

4:List…

5:Matrix…

6:Y-Vars…

7:Prgm…

8:Pic…

9:GDB…

0:String…

(Reset…)

RESET

1:All Memory…

2:Defaults…

MEMORY

(

Reset

...)

ÚÄ

ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿

[

CATALOG

]

ÚÄÄ

(All Memory…)

RESET MEMORY

1:No

2:Reset

Resetting memory

erases all data and

programs.

(Defaults…)

RESET DEFAULTS

1:No

2:Reset

CATALOG

cosh(

cosh

(

...

Equ

String(

expr(

...

inString(

...

length(

...

sinh(

sinh

(

...

String

Equ(

sub(

...

tanh(

tanh

(

Tables and Reference Information A-49

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 49 of 58

The TI

83 uses the variables listed below in various ways.

Some variables are restricted to specific data types.

The variables

A through Z and

are defined as real or

complex numbers. You may store to them. The TI

83 can

update

X, Y, R,

, and T during graphing, so you may want

to avoid using these variables to store nongraphing data.

The variables (list names)

through L

are restricted to

lists; you cannot store another type of data to them.

The variables (matrix names)

[A] through [J] are restricted

to matrices; you cannot store another type of data to them.

The variables

Pic1 through Pic9 and Pic0 are restricted to

pictures; you cannot store another type of data to them.

The variables

GDB1 through GDB9 and GDB0 are restricted

to graph databases; you cannot store another type of data

to them.

The variables

Str1 through Str9 and Str0 are restricted to

strings; you cannot store another type of data to them.

You can store any string of characters, functions,

instructions, or variables to the functions

, (

1 through 9,

and

0), X

(1 through 6), r

(

1 through 6), u(

), v(

and

) directly or through the

editor. The validity of the

string is determined when the function is evaluated.

The variables below must be real numbers. You may store

to them. Since the TI

83 can update some of them, as the

result of a

ZOOM

, for example, you may want to avoid

using these variables to store nongraphing data.

•

Xmin, Xmax, Xscl,

, XFact, Tstep, PlotStart,

Min, and

other window variables.

•

ZXmin, ZXmax, ZXscl, ZTstep, ZPlotStart, Zu(

Min), and

other

ZOOM

variables.

The variables below are reserved for use by the TI

83. You

cannot store to them.

, Sx,

, minX, maxX,

, a, b, c, RegEQ, x

, x

y1, z, t, F,

, Sx1, n1, lower, upper, r

, R

and other

statistical variables.

Variables

User Variables

System Variables

A-50 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 50 of 58

This section contains statistics formulas for the Logistic and SinReg

regressions, ANOVA, 2

Samp

Test, and 2

SampTTest.

The logistic regression algorithm applies nonlinear

recursive least-squares techniques to optimize the

following cost function:

−













−

∑

which is the sum of the squares of the residual errors,

where:

= the independent variable list

= the dependent variable list

= the dimension of the lists

This technique attempts to estimate the constants

, and

recursively to make

as small as possible.

The sine regression algorithm applies nonlinear recursive

least-squares techniques to optimize the following cost

function:

[]

Jabxcdy

=++−

∑

sin

()

which is the sum of the squares of the residual errors,

where:

= the independent variable list

= the dependent variable list

= the dimension of the lists

This technique attempts to recursively estimate the

constants

, and

to make

as small as possible.

Statistics Formulas

Logistic

SinReg

Tables and Reference Information A-51

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 51 of 58

The ANOVA

statistic is:

Factor MS

Error MS

The mean squares (

) that make up

are:

Factor MS

Factor SS

Factor df

Error MS

Error SS

Error df

The sum of squares (

) that make up the mean squares

are:

Factor SS n x x

()

=−

∑

Error SS n Sx

()

=−

∑

The degrees of freedom

that make up the mean squares

are:

Factor df I df

=−=1numerator for

Erro r df n df

( ) denominator for

=−=

∑

where:

= number of populations

= the mean of each list

Sxi

= the standard deviation of each list

= the length of each list

= the mean of all lists

ANOVA(

A-52 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 52 of 58

Below is the definition for the 2

Samp

Test.

2 = Sample standard deviations having

1 and

degrees of freedom

respectively.

-statistic =













(

x, n

, n

1) =

Ûpdf

( ) with degrees of

freedom

1, and

= reported

value

Samp

Test for the alternative hypothesis

pfxnndx

=−−

∞

∫

()

Samp

Test for the alternative hypothesis

pfxnndx

=−−

∫

()

Samp

Test for the alternative hypothesis

. Limits

must satisfy the following:

fxn n dx fxn n dx

bnd

11 11

=−−=−−

∫∫

∞

()()

,, ,,

where: [

Lbnd,Ubnd

] = lower and upper limits

The

-statistic is used as the bound producing the smallest

integral. The remaining bound is selected to achieve the

preceding integral’s equality relationship.

2-Samp

Test

Tables and Reference Information A-53

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 53 of 58

The following is the definition for the 2

SampTTest. The

two-sample

statistic with degrees of freedom

is:

−

where the computation of

and

are dependent on

whether the variances are pooled. If the variances are not

pooled:













−













−













otherwise:

nSxnSx

−+−() ()

df n n

=+−

and

Sxp

is the pooled variance.

2-SampTTest

A-54 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 54 of 58

This section contains financial formulas for computing time value of money,

amortization, cash flow, interest-rate conversions, and days between dates.

[]

=−

×+

(())

where:

PMT ƒ

C/Y

P/Y

= (.01

)

C/Y

= compounding periods per year

P/Y

= payment periods per year

= interest rate per year

iFVPV

=÷ −

−÷

()

()1

where:

PMT

The iteration used to compute

=+ ×

−+













+×+

−

PV PMT G

FV i

()

[]

ICYe

=× × −

×+

1100

(ln( ))1

where:

x=i

y = P/Y

C/Y

Gik

=+×

where:

0 for end-of-period payments

1 for beginning-of-period payments

PMT G FV i

PMT G PV i

×− ×

××













()1

where:

i ƒ

NPVFVPMT

=+÷

−

()

where:

Financial Formulas

Time Value of

Money

Tables and Reference Information A-55

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 55 of 58

PMT

PV FV

=× +

+−













−

()11

where:

i ƒ

PMT PV FV N

=+÷

−

()

where:

PMT G

−













−

×1

1()

where:

i ƒ

PV FV PMT N

=+×

−

()

where:

PMT G

iPV

PMT G

−+ × +













()

where:

i ƒ

FV PV PMT N

=+×

−

()

where:

A-56 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 56 of 58

If computing

bal

(),

pmt

2 =

npmt

Let

bal

(0) =

RND

(

)

Iterate from

= 1 to

pmt

=×−

=−−+







−

RND RND i bal m

bal m bal m RND PMT

[(())]

() ( ) ( )

12 1

then:

bal bal pmt

() ( )= 2

Pr n bal pmt bal pmt

() ( ) ( )

=−

ΣΣ

Int pmt pmt RND PMT n

() ( ) ( ) ()=−+× −211

where:

RND

= round the display to the number of

decimal places selected

RND12

= round to 12 decimal places

Balance, principal, and interest are dependent on the

values of

PMT, PV,

, and

pmt

1 and

pmt

Amortization

Tables and Reference Information A-57

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 57 of 58

npv CF CF i

() ( )

(( ))

=+ +

−+

−

∑

where:

≥











∑

Net present value is dependent on the values of the initial

cash flow (

), subsequent cash flows (

CFj

), frequency of

each cash flow (

), and the specified interest rate (

irr

() = 100

, where

satisfies

npv

() = 0

Internal rate of return is dependent on the values of the

initial cash flow (

) and subsequent cash flows (

CFj

100

Eff

() ( )

()

=× −

×+

100 1

CP xln

where:

= .01

NOM

[]

Nom

()

=×× −

÷× +

100 1

CP e

CP xln

where:

= .01

EFF

effective rate

compounding periods

NOM

nominal rate

Cash Flow

Interest Rate

Conversions

A-58 Tables and Reference Information

8399APXA.DOC TI-83 international English Bob Fedorisko Revised: 02/19/01 1:25 PM Printed: 02/19/01 1:40 PM

Page 58 of 58

With the dbd( function, you can enter or compute a date

within the range Jan. 1, 1950, through Dec. 31, 2049.

Actual/actual day-count method (assumes actual

number of days per month and actual number of days per

year):

dbd

( (days between dates) =

Number of Days II

Number of Days I

Number of Days I = (

)

365

+ (number of days

()

YYB

−

Number of Days II = (

)

365

+ (number of days

()

YYB

−

where:

1 = month of first date

1 = day of first date

1 = year of first date

2 = month of second date

2 = day of second date

2 = year of second date

= base month (January)

= base day (1)

= base year (first year after leap year)

Days between

Dates

General Information B-1

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 1 of 14

General Information

Battery Information

......................................

B-2

In Case of Difficulty

.....................................

B-4

Error Conditions

.........................................

B-5

Accuracy Information

....................................

B-10

Support and Service Information

.........................

B-12

Warranty Information

....................................

B-13

Contents

B-2 General Information

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 2 of 14

The TI

83 uses five batteries: four AAA alkaline batteries

and one lithium battery. The lithium battery provides

auxiliary power to retain memory while you replace the

AAA batteries.

When the battery voltage level drops below a usable level,

the TI

83 displays this message when you turn on the unit.

After this message is first displayed, you can expect the

batteries to function for about one or two weeks,

depending on usage. (This one-week to two-week period is

based on tests with alkaline batteries; the performance of

other kinds of batteries may vary.)

The low-battery message continues to be displayed each

time you turn on the unit until you replace the batteries. If

you do not replace the batteries within about two weeks,

the calculator may turn off by itself or fail to turn on until

you install new batteries.

Replace the lithium battery every three or four years.

Do not remove both types of batteries (AAA and lithium

auxiliary) at the same time. Do not allow the batteries to

lose power completely. If you follow these guidelines and

the steps for replacing batteries on page B

3, you can

replace either type of battery without losing any

information in memory.

Take these precautions when replacing batteries.

•

Do not mix new and used batteries. Do not mix brands

(or types within brands) of batteries.

•

Do not mix rechargeable and nonrechargeable

batteries.

•

Install batteries according to polarity (+ and

)

diagrams.

•

Do not place nonrechargeable batteries in a battery

recharger.

•

Properly dispose of used batteries immediately. Do not

leave them within the reach of children.

•

Do not incinerate batteries.

Battery Information

When to Replace

the Batteries

Effects of

Replacing the

Batteries

Battery

Precautions

General Information B-3

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 3 of 14

To replace the batteries, follow these steps.

1. Turn off the calculator. Replace the slide cover over the

keyboard to avoid inadvertently turning on the

calculator. Turn the back of the calculator toward you.

2. Hold the calculator upright. Place your thumb on the

oval indentation on the battery cover. Push down and

toward you to slide the cover about ¼ inch (6 mm). Lift

off the cover to expose the battery compartment.

Note: To avoid loss of information stored in

memory, you must turn off the calculator. Do not

remove the AAA batteries and the lithium battery

simultaneously.

3. Replace all four AAA alkaline batteries at the same

time. Or, replace the lithium battery.

•

To replace the AAA alkaline batteries, remove all

four discharged AAA batteries and install new ones

according to the polarity (+ and

) diagrams in the

battery compartment.

•

To remove the lithium battery, place your index

finger on the battery. Insert the tip of a ball-point pen

(or similar instrument) under the battery at the small

opening provided in the battery compartment.

Carefully pry the battery upward, holding it with

your thumb and finger. (There is a spring that pushes

against the underside of the battery.)

•

Install the new battery, + side up, by inserting the

battery and gently snapping it in with your finger.

Use a CR1616 or CR1620 (or equivalent) lithium

battery.

4. Replace the battery compartment cover. Turn the

calculator on and adjust the display contrast, if

necessary (step 1; page B

4).

Replacing the

Batteries

B-4 General Information

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 4 of 14

To handle a difficulty, follow these steps.

1. If you cannot see anything on the screen, the contrast

may need to be adjusted.

To darken the screen, press and release

, and then

press and hold

}

until the display is sufficiently dark.

To lighten the screen, press and release

, and then

press and hold

†

until the display is sufficiently light.

2. If an error menu is displayed, follow the steps in

Chapter 1. Refer to pages B

5 through B

9 for details

about specific errors, if necessary.

3. If a checkerboard cursor (

) is displayed, then either

you have entered the maximum number of characters in

a prompt, or memory is full. If memory is full, press

[

MEM

] 2 to select 2:Delete, and then delete some items

from memory (Chapter 18).

4. If the busy indicator (dotted line) is displayed, a graph

or program has been paused; the TI

83 is waiting for

input. Press

to continue or press

to break.

5. If the calculator does not seem to work at all, be sure

the batteries are fresh and that they are installed

properly. Refer to battery information on pages B

2 and

In Case of Difficulty

Handling a

Difficulty

General Information B-5

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 5 of 14

When the TI

83 detects an error, it displays ERR:

message

and an error menu.

Chapter 1 describes the general steps for correcting errors. This table contains

each error type, possible causes, and suggestions for correction.

Error Type Possible Causes and Suggested Remedies

ARCHIVED VAR

A function or instruction is archived and therefore cannot

be executed or edited. Use the unarchive command to

unarchive the variable before using it.

ARGUMENT

A function or instruction does not have the correct number

of arguments. See Appendix A and the appropriate chapter.

BAD GUESS

In a

CALC

operation, you specified a Guess that is not

between Left Bound and Right Bound.

For the

solve( function or the equation solver, you

specified a

guess

that is not between

lower

and

upper

Your guess and several points around it are undefined.

Examine a graph of the function. If the equation has a

solution, change the bounds and/or the initial guess.

BOUND

In a

CALC

operation or with Select(

you defined

Left Bound > Right Bound.

fMin(, fMax(, solve(, or the equation solver, you

entered

lower

‚

upper

BREAK

You pressed the

key to break execution of a program,

to halt a

DRAW

instruction, or to stop evaluation of an

expression.

DATA TYPE

You entered a value or variable that is the wrong data type.

For a function

(

includin

implied multiplication

)

or an

instruction, you entered an ar

ument that is an invalid

data type, such as a complex number where a real

number is required. See Appendix A and the appropriate

chapter.

In an editor, you entered a type that is not allowed, such

as a matrix entered as an element in the stat list editor.

See the appropriate chapter.

You attempted to store to an incorrect data type, such as

a matrix, to a list.

DIM MISMATCH

You attempted to perform an operation that references

more than one list or matrix, but the dimensions do not

match.

DIVIDE BY 0

You attempted to divide by zero. This error is not

returned durin

raphin

. The TI

83 allows for

undefined values on a graph.

You attempted a linear regression with a vertical line.

Error Conditions

B-6 General Information

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 6 of 14

Error Type Possible Causes and Suggested Remedies

DOMAIN

You specified an ar

ument to a function or instruction

outside the valid ran

e. This error is not returned durin

raphin

. The TI

83 allows for undefined values on a

graph. See Appendix A and the appropriate chapter.

You attempted a lo

arithmic or power re

ression with a

or an exponential or power regression with a

You attempted to compute

Prn(

Int(

with

pmt2

pmt1

Duplicate Name

A variable you attempted to transmit cannot be transmitted

because a variable with that name already exists in the

receiving unit.

Error in Xmit

The TI

83 was unable to transmit an item. Check to see

that the cable is firmly connected to both units and that

the receiving unit is in receive mode.

You pressed

to break during transmission.

You attempted to perform a backup from a TI

82 to a

83.

You attempted to transfer data

(

other than

throu

) from a TI

83 to a TI

82.

You attempted to transfer

throu

from a TI

83 to

a TI

82 without usin

5:Lists to TI82

on the

LINK SEND

menu.

ILLEGAL NEST

You attempted to use an invalid function in an ar

ument to

a function, such as

seq(

within

expression

for

seq(

INCREMENT

The increment in

seq(

is 0 or has the wron

n. This

error is not returned durin

raphin

. The TI

83 allows

for undefined values on a graph.

The increment in a

For(

loop is 0.

INVALID

You attempted to reference a variable or use a function

where it is not valid. For example,

cannot reference

Xmin

, or

TblStart

You attempted to reference a variable or function that

was transferred from the TI

82 and is not valid for the

83. For example, you may have transferred

the TI

83 from the TI

82 and then tried to reference it.

Seq

mode, you attempted to

raph a phase plot

without defining both equations of the phase plot.

General Information B-7

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 7 of 14

Error Type Possible Causes and Suggested Remedies

INVALID (cont.)

Seq

mode, you attempted to

raph a recursive

sequence without havin

input the correct number of

initial conditions.

Seq

mode, you attempted to reference terms other

than

(

You attempted to desi

nate a

raph style that is invalid

within the current graph mode.

You attempted to use

Select(

without havin

selected

(turned on) at least one xyLine or scatter plot.

INVALID DIM

You specified dimensions for an ar

ument that are not

appropriate for the operation.

You specified a list dimension as somethin

other than

an integer between 1 and 999.

You specified a matrix dimension as somethin

other

than an integer between 1 and 99.

You attempted to invert a matrix that is not square.

ITERATIONS

The

solve(

function or the equation solver has exceeded

the maximum number of permitted iterations. Examine

raph of the function. If the equation has a solution,

change the bounds, or the initial guess, or both.

irr(

has exceeded the maximum number of permitted

iterations.

When computin

, the maximum number of iterations

was exceeded.

LABEL

The label in the

Goto

instruction is not defined with a

Lbl

instruction in the program.

MEMORY

Memory is insufficient to perform the instruction or

function. You must delete items from memory

(

Chapter 18

)

before executing the instruction or function.

Recursive problems return this error; for example,

graphing the equation

Branchin

out of an

Then

For(

While

, or

Repeat

loop with

Goto

also can return this error because the

End

statement

that terminates the loop is never reached.

B-8 General Information

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 8 of 14

Error Type Possible Causes and Suggested Remedies

MemoryFull

You are unable to transmit an item because the receivin

unit’s available memory is insufficient. You may skip the

item or exit receive mode.

Durin

a memory backup, the receivin

unit’s available

memory is insufficient to receive all items in the sendin

unit’s memory. A messa

e indicates the number of bytes

the sendin

unit must delete to do the memory backup.

Delete items and try again.

MODE

You attempted to store to a window variable in another

raphin

mode or to perform an instruction while in the

wron

mode; for example,

DrawInv

in a

raphin

mode

other than

Func

NO SIGN CHNG

The

solve(

function or the equation solver did not detect

a sign change.

You attempted to compute

when

(

Úä

PMT

)

, and

are all

‚

0, or when

, (

Úä

PMT

), and

are all



You attempted to compute

irr(

when neither

CFList

nor

CFO

is > 0, or when neither

CFList

nor

CFO

is < 0.

NONREAL ANS

Real

mode, the result of a calculation yielded a complex

result. This error is not returned durin

raphin

. The TI

allows for undefined values on a graph.

OVERFLOW

You attempted to enter, or you have calculated, a number

that is beyond the ran

e of the calculator. This error is not

returned durin

raphin

. The TI

83 allows for undefined

alues on a graph.

RESERVED

You attempted to use a system variable inappropriately.

See Appendix A.

SINGULAR MAT

A sin

ular matrix

(

determinant = 0

)

is not valid as the

argument for

The

SinReg

instruction or a polynomial re

ression

enerated a sin

ular matrix

(

determinant = 0

)

because it

could not find a solution, or a solution does not exist.

This error is not returned durin

raphin

. The TI

allows for undefined values on a graph.

General Information B-9

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 9 of 14

Error Type Possible Causes and Suggested Remedies

SINGULARITY

expression

in the

solve(

function or the equation solver

contains a sin

ularity

(

a point at which the function is not

defined

)

. Examine a

raph of the function. If the equation

has a solution, chan

e the bounds or the initial

uess or

both.

STAT

You attempted a stat calculation with lists that are not

appropriate.

Statistical analyses must have at least two data points.

Med

must have at least three points in each

partition.

When you use a

frequency list, its elements must be

‚

(

Xmax

Xmin

)

Xscl

must be



47 for a histogram.

STAT PLOT

You attempted to display a

raph when a stat plot that uses

an undefined list is turned on.

SYNTAX

The command contains a syntax error. Look for misplaced

functions, ar

uments, parentheses, or commas. See

Appendix A and the appropriate chapter.

TOL NOT MET

You requested a tolerance to which the al

orithm cannot

return an accurate result.

UNDEFINED

You referenced a variable that is not currently defined. For

example, you referenced a stat variable when there is no

current calculation because a list has been edited, or you

referenced a variable when the variable is not valid for the

current calculation, such as

after

Med

WINDOW RANGE

A problem exists with the window variables.

You defined

Xmax



Xmin

Ymax



Ymin

You defined

max



min

and

step

(or vice versa).

You attempted to define

Tstep=0

You defined

Tmax



Tmin

and

Tstep

(or vice versa).

Window variables are too small or too lar

e to

raph

correctly. You may have attempted to zoom in or zoom

out to a point that exceeds the TI

83’s numerical range.

ZOOM

A point or a line, instead of a box, is defined in

ZBox.

ZOOM

operation returned a math error.

B-10 General Information

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 10 of 14

To maximize accuracy, the TI

83 carries more digits

internally than it displays. Values are stored in memory

using up to 14 digits with a two-digit exponent.

•

You can store a value in the window variables using up

to 10 digits (12 for

Xscl, Yscl, Tstep, and

step

•

Displayed values are rounded as specified by the mode

setting with a maximum of 10 digits and a two-digit

exponent.

•

RegEQ displays up to 14 digits in Float mode. Using a

fixed-decimal setting other than Float causes RegEQ

results to be rounded and stored with the specified

number of decimal places.

Xmin is the center of the leftmost pixel, Xmax is the center

of the next-to-the-rightmost pixel. (The rightmost pixel is

reserved for the busy indicator.)

is the distance

between the centers of two adjacent pixels.

•

Full screen mode,

X is calculated as

(Xmax

Xmin)

94. In G

T split-screen mode,

calculated as (Xmax

Xmin)

46.

•

If you enter a value for

from the home screen or a

program in Full screen mode, Xmax is calculated as

Xmin +

…

94. In G

T split-screen mode, Xmax is

calculated as Xmin +

…

46.

Ymin is the center of the next-to-the-bottom pixel; Ymax is

the center of the top pixel.

is the distance between the

centers of two adjacent pixels.

•

Full screen mode,

is calculated as

(Ymax

Ymin)

62. In Horiz split-screen mode,

calculated as (Ymax

Ymin)

30. In G

T split-screen

mode,

is calculated as (Ymax

Ymin)

50.

•

If you enter a value for

from the home screen or a

program in Full screen mode, Ymax is calculated as

Ymin +

…

62. In Horiz split-screen mode, Ymax is

calculated as Ymin +

…

30. In G

T split-screen mode,

Ymax is calculated as Ymin +

…

50.

Accuracy Information

Computational

Accuracy

Graphing

Accuracy

General Information B-11

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 11 of 14

Cursor coordinates are displayed as eight-character

numbers (which may include a negative sign, decimal

point, and exponent) when

Float mode is selected. X and Y

are updated with a maximum accuracy of eight digits.

minimum and maximum on the

CALCULATE

menu are

calculated with a tolerance of 1

‰

f(x)dx

is calculated at

3. Therefore, the result displayed may not be accurate to

all eight displayed digits. For most functions, at least five

accurate digits exist. For

fMin(, fMax(, and fnInt( on the

MATH

menu and solve( in the

CATALOG

, the tolerance can

be specified.

Function Range of Input Values

sin

, cos

, tan



| < 10

(radian or degree)

sin

, cos



, log

100

< 10

100



230.25850929940

100

< 100

sinh

, cosh



230.25850929940

tanh

| < 10

100

sinh

| < 5 × 10

cosh



< 5 × 10

tanh

1 <

< 1

‡

(real mode) 0



< 10

100

‡

(complex mode) |

| < 10

100



69, where

is a multiple of .5

Function Range of Result

sin

, tan

to 90

Lpà

2 to

pà

2 (radians)

cos

to 180

or 0 to

(radians)

Function Limits

Function Results

B-12 General Information

8399APXB.DOC TI-83 Intl English, Appendix B Bob Fedorisko Revised: 02/19/01 1:12 PM Printed: 02/19/01 1:41

PM Page 12 of 14

Product Support

Customers in the U.S., Canada, Puerto Rico, and the Virgin Islands

For general questions, contact Texas Instruments Customer Support:

phone:

800

CARES (1

800

842

2737)

e-mail: [email protected]

For technical questions, call the Programming Assistance Group of Customer

Support:

phone:

972

917

8324

Customers outside the U.S., Canada, Puerto Rico, and the Virgin Islands

Contact TI by e-mail or visit the TI calculator home page on the World Wide Web.

e-mail:

[email protected]

Internet: education.ti.com

Product Service

Customers in the U.S. and Canada Only

lways contact Texas Instruments Customer Support before returning a product

for service.

Customers outside the U.S. and Canada

Refer to the leaflet enclosed with this product or contact your local Texas

Instruments retailer/distributor.

Other TI Products and Services

isit the TI calculator home page on the World Wide Web.

education.ti.com

Refer to the leaflet enclosed with this product or contact your local Texas

Instruments retailer/distributor.

Support and Service Information

General Information B-13

8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed:

02/27/01 12:25 PM Page 12 of 13

Warranty Information

Customers in the U.S. and Canada Only

One-Year Limited Warranty for Electronic Product

This Texas Instruments (“TI”) electronic product warranty extends only to the original

purchaser and user of the product.

Warranty Duration.

This TI electronic product is warranted to the original purchaser

for a period of one (1) year from the original purchase date.

Warranty Coverage.

This TI electronic product is warranted against defective

materials and construction.

THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN

DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER

SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS

OR CONSTRUCTION.

Warranty Disclaimers.

ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE,

INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF

MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED

IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL

NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL

OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE

CONSUMER OR ANY OTHER USER.

Some states/provinces do not allow the exclusion or limitation of implied warranties or

consequential damages, so the above limitations or exclusions may not apply to you.

Legal Remedies.

This warranty gives you specific legal rights, and you may also have

other rights that vary from state to state or province to province.

Warranty Performance.

During the above one (1) year warranty period, your defective

product will be either repaired or replaced with a reconditioned model of an equivalent

quality (at TI’s option) when the product is returned, postage prepaid, to Texas

Instruments Service Facility. The warranty of the repaired or replacement unit will

continue for the warranty of the original unit or six (6) months, whichever is longer.

Other than the postage requirement, no charge will be made for such repair and/or

replacement. TI strongly recommends that you insure the product for value prior to

mailing.

Software.

Software is licensed, not sold. TI and its licensors do not warrant that the

software will be free from errors or meet your specific requirements.

All software is

provided “AS IS.”

The software and any documentation supplied with this product are

protected by copyright.

B-14 General Information

8299APPB.DOC TI-82, Appendix B, English Bob Fedorisko Revised: 02/27/01 12:20 PM Printed:

02/27/01 12:25 PM Page 13 of 13

Australia & New Zealand Customers only

One-Year Limited Warranty for Commercial Electronic Product

This Texas Instruments electronic product warranty extends only to the

original purchaser and user of the product.

Warranty Duration.

This Texas Instruments electronic product is warranted

to the original purchaser for a period of one (1) year from the original

purchase date.

Warranty Coverage.

This Texas Instruments electronic product is warranted

against defective materials and construction. This warranty is void if the

product has been damaged by accident or unreasonable use, neglect, improper

service, or other causes not arising out of defects in materials or construction.

Warranty Disclaimers. Any implied warranties arising out of this sale,

including but not limited to the implied warranties of merchantability

and fitness for a particular purpose, are limited in duration to the

above one-year period. Texas Instruments shall not be liable for loss

of use of the product or other incidental or consequential costs,

expenses, or damages incurred by the consumer or any other user.

Some jurisdictions do not allow the exclusion or limitation of implied

warranties or consequential damages, so the above limitations or exclusions

may not apply to you.

Legal Remedies. This warranty gives you specific legal rights, and you may

also have other rights that vary from jurisdiction to jurisdiction.

Warranty Performance.

During the above one (1) year warranty period,

your defective product will be either repaired or replaced with a new or

reconditioned model of an equivalent quality (at TI’s option) when the product

is returned to the original point of purchase. The repaired or replacement unit

will continue for the warranty of the original unit or six (6) months, whichever

is longer. Other than your cost to return the product, no charge will be made

for such repair and/or replacement. TI strongly recommends that you insure

the product for value if you mail it.

Software.

Software is licensed, not sold. TI and its licensors do not warrant

that the software will be free from errors or meet your specific requirements.

All software is provided “AS IS.”

The software and any documentation supplied with this product

are protected by copyright.

All Customers Outside the U.S. and Canada

For information about the length and terms of the warranty, refer to your package

and/or to the warranty statement enclosed with this product, or contact your local Texas

Instruments retailer/distributor.

Index-1

Index

8399INDX.DOC TI-83 international English Bob Fedorisko Revised: 02/20/01 10:54 AM Printed: 02/21/01 8:40

AM Page 1 of 16

(addition),

2-3

A-38

cdf(

(chi-square cdf),

13-31

A-3

pdf(

(chi-square pdf),

13-31

A-4

Test

(chi-square test),

13-22

A-4

(colon),

6, 16-5

(concatenation),

15-6

A-38

(cube),

2-6, A-35

‡

(

(cube root),

2-6, A-35

(degrees notation),

2-3

A-34

(division),

2-3, A-37

(equal-to relational test),

2-25,

A-35

(factorial),

2-21

A-34

(graph style, animate),

3-9

(graph style, dot),

3-9

(graph style, line),

3-9

(greater than),

2-25, A-35

‚

(greater than or equal to),

2-25,

A-35

(inverse),

2-3

8-9

10-10, A-36

(less than),

2-25, A-35



(less than or equal to),

2-25, A-36

{ }

(list indicator),

11-4

[ ]

(matrix indicator),

10-7

(minutes notation),

2-23, A-38

(multiplication),

2-3, A-37

(negation),

1-23, 2-4, A-37

(not equal to),

2-25, A-35

( )

(parentheses),

1-23

(pi),

2-4

›

(pixel mark),

8-15, 12-34

(pixel mark),

8-15, 12-34

(pixel mark),

8-15, 12-34

(plot type, box),

12-33

(plot type, histogram),

12-32

(plot type, modified box),

12-32

(plot type, normal probability),

12-33

(power),

2-3

A-36

A-37

(power of ten),

2-4

A-37

‡

(root),

2-6, A-35

(seconds notation),

2-23, A-38

(square) ,

2 - 3 , A-36

‡

(

(square root) ,

2 - 3 , A-37

Store,

1-14, A-28

" "

(string indicator),

15-3

(subtraction),

2-3, A-38

a+b

(rectangular complex mode),

1-12, 2-16

A-3

above graph style(

3-9

abs(

(absolute value),

2-13

2-19

10-10

A-2

accuracy information

computational and graphing,

B-10

graphing,

3-17

function limits and results,

B-11

addition (

2-3

A-38

alpha cursor,

1-5

alpha key,

alpha-lock,

1-8

alternative hypothesis,

13-7

amortization

bal(

(amortization balance),

14-9

A-3

calculating schedules,

14-9

formula,

A-56

Int(

(sum of interest),

A-12

Prn(

(sum of principal),

14-9

A-19

and

(Boolean operator),

2-26

A-2

angle(

2-19

A-2

ANGLE

menu,

2-23

angle modes,

1-11

animate graph style (

3-9

ANOVA(

(one-way variance analysis),

13-25

A-2

formula,

A-51

Ans

(last answer),

1-18

A-2

APD

(Automatic Power Down™),

1-2

applications.

See

examples,

applications

arccosine (

cos

(

2-3

arcsine (

sin

(

2-3

arctangent (

tan

(

2-3

augment(

10-14

11-15

A-3

Automatic Power Down™ (APD

1-2

automatic regression equation,

12-22

automatic residual list (

RESID

12-22

axes format, sequence graphing,

6-8

axes, displaying (

AxesOn

AxesOff

3-14

A-3

AxesOff

3-14

A-3

AxesOn

3-14

A-3

Index-2

8399INDX.DOC TI-83 international English Bob Fedorisko Revised: 02/20/01 10:54 AM Printed: 02/21/01 8:40

AM Page 2 of 16

backing up calculator memory,

19-4,

19-10

bal(

(amortization balance),

14-9

A-3

batteries,

1-2

B-2

below graph style (

3-9

binomcdf(

13-33

A-3

binompdf(

13-33

A-3

Boolean logic,

2-26

box pixel mark (

›

8-15, 12-34

Boxplot

plot type (

12-33

busy indicator,

1-4

CALCULATE

menu,

3-25

Calculate

output option,

13-6, 13-8

cash flow

calculating,

14-8

formula,

A-57

irr(

(internal rate of return),

14-8

A-13

npv(

(net present value),

14-8

A-17

CATALOG

15-2

CBL 2/CBL System,

16-21, 19-3

A-10

CBR,

16-21, 19-3

A-10

Check RAM

(memory screen),

18-2

chi-square cdf (

cdf(

13-31

A-3

chi-square pdf (

pdf(

13-31

A-4

chi-square test (

Test

13-22

A-4

Circle(

(draw circle),

8-11

A-4

Clear Entries

18-4

A-4

clearing

entries (

Clear Entries

18-4

A-4

all lists (

ClrAllLists

18-4

A-4

drawing (

ClrDraw

8-4

A-4

home screen (

ClrHome

16-20

A-4

list (

ClrList

12-20

A-4

table (

ClrTable

16-20

A-4

ClrAllLists

(clear all lists),

18-4

A-4

ClrDraw

(clear drawing),

8-4

A-4

ClrHome

(clear home screen),

16-20

A-4

ClrList

(clear list),

12-20

A-4

ClrTable

(clear table),

16-20

A-4

coefficients of determination (

12-23

colon separator (

6, 16-5

combinations (

nCr

2-21

A-16

C (continued)

complex

modes (

a+b

1-12, 2-16

A-3

A-22

numbers,

1-12

2-16

2-18

A-22

compounding-periods-per-year variable

(

C/Y

14-4, 14-14

concatenation (

15-6

A-38

confidence intervals,

13-8, 13-16

conj(

(conjugate),

2-18

A-4

Connected

(plotting mode),

1-11

A-4

contrast (display),

1-3

convergence, sequence graphing,

6-12

conversions

Dec

(to decimal),

2-5

A-5

DMS

(to degrees/minutes/ seconds),

2-24, A-7

Eff

(to effective interest rate),

14-12, A-7

Equ

String(

(equation-to-string

conversion),

15-7, A-8

Frac

(to fraction conversion),

2-5,

A-10

List

matr(

(list-to-matrix

conversion),

10-14, 11-15, A-14

Matr

list(

(matrix-to-list conversion),

10-14, 11-16, A-15

Nom

(to nominal interest rate

conversion),

14-12, A-16

Polar

(to polar conversion),

2-19,

A-19

Rx(

Ry(

(polar-to-rectangular

conversion),

2-24, A-21

Rect

(to rectangular conversion),

2-19, A-22

Pr(

(

(rectangular-to-polar

conversion),

2-24, A-23

String

Equ(

(string-to-equation

conversion),

15-8, A-29

CoordOff

3-14, A-5

CoordOn

3-14, A-5

correlation coefficient (

12-23, 12-25

cos(

(cosine),

2-3, A-5

cos

(

(arccosine),

2-3, A-5

cosh(

(hyperbolic cosine),

15-10, A-5

Index-3

8399INDX.DOC TI-83 international English Bob Fedorisko Revised: 02/20/01 10:54 AM Printed: 02/21/01 8:40

AM Page 3 of 16

D (continued)

cosh

(

(hyperbolic arccosine),

15-10,

A-5

cosine (

cos(

2-3, A-5

cross pixel mark (

8-15, 12-34

cube (

2-6, A-35

cube root (

‡

(

2-6, A-35

CubicReg

(cubic regression),

12-26,

A-5

cubic regression (

CubicReg

12-26,

A-5

cumulative sum (

cumSum(

10-15

11-12, A-5

cumSum(

(cumulative sum),

10-15

11-12, A-5

cursors,

1-5

1-8

C/Y

(compounding-periods-per-year

variable),

14-4, 14-14

Data input option,

13-6, 13-7

days between dates (

dbd(

14-13, A-5,

A-58

dbd(

(days between dates),

14-13, A-5,

A-58

Dec

(to decimal conversion),

2-5, A-5

decimal mode (float or fixed),

1-10

decrement and skip (

DS<(

16-14, A-7

definite integral,

2-7, 3-28, 4-8, 5-6

Degree

angle mode,

1-11

2-23, A-6

degrees notation (

2-3

A-34

DELETE FROM

menu,

18-3

delete variable contents (

DelVar

16-15, A-6

DelVar

(delete variable contents),

16-15, A-6

DependAsk

7-3, 7-5, A-6

DependAuto

7-3, 7-5, A-6

derivative.

See

numerical derivative

det(

(determinant),

10-12, A-6

determinant (

det(

10-12, A-6

DiagnosticOff

12-23, A-6

DiagnosticOn

12-23, A-6

diagnostics display mode(

12-23

differentiation,

2-8, 3-28, 4-8, 5-6

D (continued)

dimensioning a list or matrix,

10-12

10-13

11-11, A-6

dim(

(dimension),

10-12

11-11, A-6

dim(

(assign dimension),

10-13

11-11, A-6

Disp

(display),

16-18, A-6

DispGraph

(display graph),

16-19, A-7

display contrast,

1-3

display cursors,

1-5

DispTable

(display table),

16-19, A-7

DISTR

(distributions menu),

13-29

DISTR DRAW

(distributions drawing

menu),

13-35

distribution functions

binomcdf(

13-33, A-3

binompdf(

13-33, A-3

cdf(

13-31, A-3

pdf(

13-31, A-4

cdf(

13-32, A-8

pdf(

13-32, A-9

geometcdf(

13-34, A-10

geometpdf(

13-34, A-11

invNorm(

13-30, A-12

normalcdf(

13-30, A-17

normalpdf(

13-29, A-17

poissoncdf(

13-34, A-99

poissonpdf(

13-33, A-19

tcdf(

13-31, A-29

tpdf(

13-30, A-29

distribution shading instructions

Shade

(

13-36, A-26

Shade

(

13-36, A-27

ShadeNorm(

13-35, A-27

Shade_t(

13-36, A-27

division (

2-3, A-37

DMS (degrees/minutes/seconds entry

notation),

2-23, A-38

DMS

(to degrees/minutes/seconds),

2-24, A-7

dot graph style (

3-9

dot pixel mark (

8-15, 12-34

Dot

(plotting mode),

1-11, A-7

DrawF

(draw a function),

8-9, A-7

Index-4

8399INDX.DOC TI-83 international English Bob Fedorisko Revised: 02/20/01 10:54 AM Printed: 02/21/01 8:40

AM Page 4 of 16

D (continued)

drawing on a graph

circles (

Circle(

8-11

functions and inverses (

DrawF

DrawInv

8-9

lines (

Horizontal

Line(

Vertical

8-6, 8-7

line segments (

Line(

8-5

pixels (

Pxl

Change

Pxl

Off

Pxl

pxl

Test

8-16

points (

Change

Off

8-14

tangents (

Tangent

8-8

text (

Text

8-12

using

Pen

8-13

DrawInv

(draw inverse),

8-9, A-7

DRAW

menu,

8-3

DRAW

instructions,

8-3

Draw output option,

13-6

DRAW POINTS

menu,

8-14

DRAW STO

(draw store menu),

8-17

dr/d

operation on a graph,

5-6

DS<(

(decrement and skip),

16-14, A-7

DuplicateName

menu,

19-5

dx/dt

operation on a graph,

3-28, 4-8

dy/dx

operation on a graph,

3-28, 4-8,

5-6

(constant)

, 2-4

e^(

(exponential),

2-4, A-7

å (exponent),

1-7, 1-10, A-7

edit keys table,

1-8

Eff(

(to effective interest rate),

14-12,

A-7

Else

16-10

End

16-12, A-8

Eng

(engineering notation mode),

1-10,

A-8

entry cursor,

1-5

ENTRY

(last entry key),

1-16

EOS

(Equation Operating System),

1-22

eqn

(equation variable),

2-8, 2-12

equal-to relational test (

2-25, A-35

Equation Operating System (EOS

1-22

Equation Solver

2-8

equations with multiple roots,

2-12

E (continued)

Equ

String(

(equation-to-string

conversion),

15-7, A-8

errors

diagnosing and correcting,

1-24

messages,

B-5

examples—applications

area between curves,

17-11

areas of regular n-sided polygons,

17-16

box plots,

17-2

cobweb attractors,

17-8

fundamental theorem of calculus,

17-14

guess the coefficients,

17-9

inequalities,

17-5

mortgage payments

parametric equations: ferris wheel

problem,

17-12

piecewise functions,

17-4

Sierpinski triangle,

17-7

solving a system of nonlinear

equations,

17-6

unit circle and trig curves,

17-10

examples—Getting Started

box with lid

9 to 16

defining a,

defining a table of values,

finding calculated maximum,

setting the viewing window,

tracing the graph,

zooming in on the graph,

zooming in on the table,

coin flip,

2-2

compound interest,

14-3

drawing a tangent line,

8-2

financing a car,

14-2

forest and trees,

6-2

generating a sequence,

11-2

graphing a circle,

3-2

mean height of a population,

13-2

path of a ball,

4-2

pendulum lengths and periods,

12-2

polar rose,

5-2

Index-5

8399INDX.DOC TI-83 international English Bob Fedorisko Revised: 02/20/01 10:54 AM Printed: 02/21/01 8:40

AM Page 5 of 16

E (continued)

examples—Getting Started (continued)

quadratic formula

converting to a fraction,

displaying complex results,

entering a calculation,

roots of a,

7-2

sending variables,

19-2

solving a system of linear equations,

10-2

unit circle,

9-2

volume of a cylinder,

16-2

examples—miscellaneous

convergence,

6-12

daylight hours in Alaska,

12-28

calculating outstanding loan

balances,

14-10

predator-prey model,

6-13

exponential regression (

ExpReg

12-26, A-8

expr(

(string-to-expression conversion),

15-7, A-8

ExpReg

(exponential regression),

12-26, A-8

expression,

1-6

converting from string (

expr(

15-7,

A-8

turning on and off (

ExprOn

ExprOff

3-14, A-8

ExprOff

(expression off),

3-14, A-8

ExprOn

(expression on),

3-14, A-8

‰

f(x)dx

operation on a graph,

3-28

factorial (

2-21

A-34

family of curves,

3-16

cdf(

13-32, A-8

Fill(

10-13, A-8

FINANCE CALC

menu,

14-5

FINANCE VARS

menu,

14-14

financial functions

amortization schedules,

14-9

cash flows,

14-8

days between dates,

14-13

interest rate conversions,

14-12

payment method,

14-13

time value of money (

TVM

14-6

F (continued)

Fix

(fixed-decimal mode),

1-10, A-8

fixed-decimal mode (

Fix

1-10, A-8

Float

(floating-decimal mode),

1-10,

A-8

floating-decimal mode (

Float

1-10,

A-8

fMax(

(function maximum),

2-6, A-9

fMin(

(function minimum),

2-6, A-9

fnInt(

(function integral),

2-7, A-9

FnOff

(function off),

3-8, A-9

FnOn

(function on),

3-8, A-9

For(

16-10, A-9

format settings,

3-13, 6-8

formulas

amortization,

A-56

ANOVA

A-51

cash flow,

A-57

days between dates,

A-58

factorial,

2-21

interest rate conversions,

A-57

logistic regression,

A-50

sine regression,

A-50

time value of money,

A-54

two-sample

-Test,

A-52

two-sample

test,

A-53

fPart(

(fractional part),

2-14

10-11, A-9

pdf(

13-32, A-9

Frac

(to fraction),

2-5, A-10

free-moving cursor,

3-17

frequency,

12-24

Full

(full-screen mode),

1-12, A-10

full-screen mode (

Full

1-12, A-10

Func

(function graphing mode),

1-11,

A-10

function, definition of,

1-7

function graphing,

3-1

3-28

accuracy,

3-17

CALC

(calculate menu),

3-25

defining and displaying,

3-3

defining in the Y= editor,

3-5

defining on the home screen, in a

program,

3-6

deselecting,

3-7

displaying,

3-3

3-11

3-15

evaluating,

3-6

family of curves,

3-16

format settings,

3-13

Index-6

8399INDX.DOC TI-83 international English Bob Fedorisko Revised: 02/20/01 10:54 AM Printed: 02/21/01 8:40

AM Page 6 of 16

F (continued)

Function graphing (continued)

free-moving cursor,

3-17

graph styles,

3-9

maximum of (

fMax(

A-

minimum of (

fMin(

A-

modes,

1-11

3-4

A-10

moving the cursor to a value,

3-19

overlaying functions on a graph,

3-16

panning,

3-19

pausing or stopping a graph,

3-15

Quick Zoom,

3-19

selecting,

3-7

3-8, A-9

shading,

3-10

Smart Graph,

3-15

tracing,

3-18

window variables,

3-11

3-12

Y= editor,

3-5

viewing window,

3-11

and

window variables,

3-12

ZOOM

menu,

3-20

ZOOM MEMORY

menu,

3-23

function integral (

fnInt(

2-7, A-9

functions and instructions table,

A-2

future value,

14-5

14-7, 14-14

present value,

14-5

14-7, 14-14

(future-value variable),

14-4, 14-14

gcd(

(greatest common divisor),

2-15,

A-10

GDB

(graph database),

8-19

geometcdf(

13-34, A-10

geometpdf(

13-34, A-10

Get(

(get data from CBL 2/CBL or

CBR),

16-21, A-10

GetCalc(

(get data from TI

83),

16-21,

A-10

getKey

16-20, A-10

Getting Started,