Texas instruments TI-82 Stats User Manual

TI-82 STATS

GRAPHING CALCULATOR

GUIDEBOOK

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This manual describes how to use the TI-82 STATS Graphing Calculator. Getting Started is an overview of TI-82 STATS features. Chapter 1 describes how the TI-82 STATS operates. Other chapters describe various interactive features. Chapter 17 shows how to combine these features to solve problems.

Getting Started: Do This First!

TI-82 STATS Keyboard..................................................................................... 2

TI-82 STATS Menus First Steps

.................................................................................................................... 5

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-82 STATS Features

............................................................................................ 4

................................. 6

............................ 7

................... 8

............................................................. 9

............................................. 10

.................................................. 11

......................................... 12

............................. 13

................................................. 15

.............................. 16

.......................................................................... 17

Chapter 1: Operating the TI-82 STATS

Turning On and Turning Off the TI-82 STATS Setting the Display Contrast The Display

................................................................................................................ 1-4

Entering Expressions and Instructions TI-82 STATS Edit Keys Setting Modes

........................................................................................................... 1-9

Using TI-82 STATS Variable Names Storing Variable Values Recalling Variable Values

............................................................................ 1-3

...................................................... 1-6

..................................................................................... 1-8

....................................................... 1-13

..................................................................................... 1-14

................................................................................ 1-15

................................. 1-2

ENTRY (Last Entry) Storage Area.............................................................. 1-16

Ans (Last Answer) Storage Area.................................................................. 1-18

TI-82 STATS Menus

............................................................................................ 1-19

VARS and VARS Y.VARS Menus.............................................................. 1-21

Equation Operating System (EOSé) Error Conditions

...................................................................................................... 1-24

......................................................... 1-22

Introduction iii

Table of Contents (continued)

Chapter 2: Math, Angle, and Test Operations

Chapter 3: Function Graphing

Chapter 4: Parametric Graphing

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........................................................................ 2-25

TEST LOGIC (Boolean) Operations .......................................................... 2-26

Getting Started: Graphing a Circle Defining Graphs Setting the Graph Modes Defining Functions

...................................................................................................... 3-3

................................................................................... 3-4

................................................................................................ 3-5

Selecting and Deselecting Functions Setting Graph Styles for Functions Setting the Viewing Window Variables Setting the Graph Format Displaying Graphs

.................................................................................................. 3-15

Exploring Graphs with the Free-Moving Cursor Exploring Graphs with

TRACE..................................................................... 3-18

Exploring Graphs with the

ZOOM MEMORY.................................................................................... 3-23

Using Using the

CALC (Calculate) Operations.................................................. 3-25

Getting Started: Path of a Ball Defining and Displaying Parametric Graphs Exploring Parametric Graphs

.............................................................. 3-2

.......................................................... 3-7

.............................................................. 3-9

................................................... 3-11

.................................................................................. 3-13

................................ 3-17

ZOOM Instructions .................................. 3-20

........................................................................ 4-2

........................................ 4-4

.......................................................................... 4-7

Chapter 5: Polar Graphing

iv Introduction

Getting Started: Polar Rose

.............................................................................. 5-2

Defining and Displaying Polar Graphs Exploring Polar Graphs

...................................................................................... 5-6

..................................................... 5-3

Chapter 6: Sequence Graphing

Getting Started: Forest and Trees................................................................. 6-2

Defining and Displaying Sequence Graphs Selecting Axes Combinations Exploring Sequence Graphs Graphing Web Plots

.............................................................................................. 6-11

......................................................................... 6-8

............................................................................. 6-9

Using Web Plots to Illustrate Convergence Graphing Phase Plots

........................................................................................... 6-13

Comparing TI-82 STATS and TI.82 Sequence Variables Keystroke Differences Between TI-82 STATS and TI-82

........................................... 6-3

........................................... 6-12

........... 6-15

.......... 6-16

Chapter 7: Tables

Chapter 8: DRAW Operations

Chapter 9: Split Screen

Getting Started: Roots of a Function Setting Up the Table

............................................................................................. 7-3

Defining the Dependent Variables Displaying the Table

............................................................................................. 7-5

Getting Started: Drawing a Tangent Line Using the Clearing Drawings Drawing Line Segments

DRAW Menu...................................................................................... 8-3

................................................................................................. 8-4

..................................................................................... 8-5

Drawing Horizontal and Vertical Lines Drawing Tangent Lines

...................................................................................... 8-8

Drawing Functions and Inverses Shading Areas on a Graph Drawing Circles

....................................................................................................... 8-11

Placing Text on a Graph

................................................................................ 8-10

..................................................................................... 8-12

Using Pen to Draw on a Graph Drawing Points on a Graph Drawing Pixels Storing Graph Pictures ( Recalling Graph Pictures ( Storing Graph Databases (

......................................................................................................... 8-16

Pic)............................................................................ 8-17

Pic)....................................................................... 8-18

GDB)................................................................... 8-19

Recalling Graph Databases (

Getting Started: Exploring the Unit Circle Using Split Screen

.................................................................................................. 9-3

.......................................................... 7-2

............................................................... 7-4

............................................... 8-2

................................................... 8-6

................................................................... 8-9

...................................................................... 8-13

.............................................................................. 8-14

GDB).............................................................. 8-20

............................................. 9-2

Horiz (Horizontal) Split Screen ..................................................................... 9-4

G-T (Graph-Table) Split Screen.................................................................... 9-5

TI-82 STATS Pixels in

Horiz and G-T Modes .................................... 9-6

Introduction v

Table of Contents (continued)

Chapter 10: Matrices

Chapter 11: Lists

Chapter 12: Statistics

Getting Started: Systems of Linear Equations ..................................... 10-2

Defining a Matrix Viewing and Editing Matrix Elements Using Matrices with Expressions Displaying and Copying Matrices Using Math Functions with Matrices Using the

Getting Started: Generating a Sequence Naming Lists Storing and Displaying Lists Entering List Names Attaching Formulas to List Names Using Lists in Expressions

................................................................................................... 10-3

...................................................... 10-4

................................................................. 10-7

................................................................ 10-8

......................................................... 10-9

MATRX MATH Operations ....................................................... 10-12

.................................................. 11-2

.............................................................................................................. 11-3

........................................................................... 11-4

............................................................................................. 11-6

.............................................................. 11-7

................................................................................ 11-9

LIST OPS Menu...................................................................................................... 11-10

LIST MATH Menu.................................................................................................. 11-17

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

....................................................................... 12-10

.................................................................................. 12-11

.............................................................. 12-14

...................................................... 12-16

............................................................ 12-17

.................................................................................... 12-18

................................ 12-2

STAT EDIT Menu .................................................................................................. 12-20

Regression Model Features

.............................................................................. 12-22

STAT CALC Menu ................................................................................................ 12-24

Statistical Variables Statistical Analysis in a Program Statistical Plotting Statistical Plotting in a Program

............................................................................................... 12-29

.................................................................. 12-30

................................................................................................... 12-31

.................................................................... 12-37

Chapter 13: Inferential Statistics and Distributions

vi Introduction

Getting Started: Mean Height of a Population Inferential Stat Editors

......................................................................................... 13-6

..................................... 13-2

STAT TESTS Menu ............................................................................................. 13-9

Inferential Statistics Input Descriptions Test and Interval Output Variables Distribution Functions Distribution Shading

......................................................................................... 13-29

............................................................................................. 13-35

................................................... 13-26

.............................................................. 13-28

Chapter 14: Financial Functions

Getting Started: Financing a Car................................................................... 14-2

Getting Started: Computing Compound Interest Using the Using the Financial Functions Calculating Time Value of Money ( Calculating Cash Flows Calculating Amortization Calculating Interest Conversion

TVM Solver ......................................................................................... 14-4

........................................................................ 14-5

TVM).............................................. 14-6

...................................................................................... 14-8

................................................................................... 14-9

.................................................................... 14-12

Finding Days between Dates/Defining Payment Method Using the

TVM Variables................................................................................... 14-14

................................ 14-3

....................... 14-13

Chapter 15:

CATALOG,

Strings, Hyperbolic Functions

Chapter 16: Programming

Chapter 17: Applications

Browsing the TI-82 STATS Entering and Using Strings Storing Strings to String Variables String Functions and Instructions in the Hyperbolic Functions in the

Getting Started: Volume of a Cylinder Creating and Deleting Programs Entering Command Lines and Executing Programs Editing Programs

.................................................................................................... 16-6

Copying and Renaming Programs

CATALOG.................................................. 15-2

............................................................................... 15-3

.............................................................. 15-4

CATALOG........................ 15-6

CATALOG.................................................. 15-10

..................................................... 16-2

................................................................... 16-4

........................ 16-5

............................................................... 16-7

PRGM CTL (Control) Instructions.............................................................. 16-8

PRGM I/O (Input/Output) Instructions..................................................... 16-16

Calling Other Programs as Subroutines

Comparing Test Results Using Box Plots Graphing Piecewise Functions Graphing Inequalities

........................................................................................... 17-5

Solving a System of Nonlinear Equations Using a Program to Create the Sierpinski Triangle Graphing Cobweb Attractors

.......................................................................... 17-8

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

................................................... 16-22

............................................... 17-2

....................................................................... 17-4

.............................................. 17-6

.......................... 17-7

........................................... 17-9

...................... 17-10

................................................................ 17-11

........................ 17-12

.................. 17-14

................................ 17-16

................................... 17-18

Introduction vii

Table of Contents (continued)

Chapter 18: Memory Management

Chapter 19: Communication Link

Appendix A: Tables and Reference Information

Appendix B: General Information

Checking Available Memory.......................................................................... 18-2

Deleting Items from Memory Clearing Entries and List Elements Resetting the TI-82 STATS

Getting Started: Sending Variables TI-82 STATS

LINK ............................................................................................... 19-3

Selecting Items to Send Receiving Items Transmitting Items

....................................................................................................... 19-5

................................................................................................. 19-6

Transmitting Lists to a TI-82 Transmitting from a TI-82 to a TI-82 STATS Backing Up Memory

Table of Functions and Instructions Menu Map Variables Statistical Formulas Financial Formulas

Battery Information

................................................................................................................... A-39

....................................................................................................................... A-49

............................................................................................... A-50

................................................................................................ A-54

............................................................................................... B-2

In Case of Difficulty Error Conditions

...................................................................................................... B-5

Accuracy Information Support and Service Information Warranty Information

......................................................................... 18-3

............................................................. 18-4

............................................................................. 18-5

............................................................. 19-2

....................................................................................... 19-4

.......................................................................... 19-8

..................................... 19-9

............................................................................................ 19-10

............................................................ A-2

............................................................................................. B-4

.......................................................................................... B-10

.................................................................. B-12

.......................................................................................... B-13

Index

viii Introduction

Getting Started: Do This First!

Contents

TI-82 STATS Keyboard..................................................................................... 2

TI-82 STATS Menus First Steps

.................................................................................................................... 5

............................................................................................ 4

................................. 6

............................ 7

................... 8

............................................................. 9

............................................. 10

.................................................. 11

......................................... 12

............................. 13

................................................. 15

.............................. 16

.......................................................................... 17

Getting Started 1

TI-82 STATS Keyboard

Generally, the keyboard is divided into these zones: graphing keys, editing keys, advanced function keys, and scientific calculator keys.

Keyboard Zones

Graphing Key

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.

Editing Key

dvance

Function Keys

Scientifi Calculator Keys

2 Getting Started

Using the Color.Coded Keyboard

The keys on the TI-82 STATS 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.

Using the y and ƒ Keys

The y key accesses the second function printed in yellow above each key.

The ƒ key accesses the alpha function printed in green above each key.

The secondary function of each key is printed in yellow above the key. When you press the yellow y key, the character, abbreviation, or word printed in yellow above the other keys becomes active for the next keystroke. For example, when you press y and then , the guidebook describes this keystroke combination as y [

TEST menu is displayed. This

TEST].

The alpha function of each key is printed in green above the key. When you press the green ƒ key, the alpha character printed in green above the other keys becomes active for the next keystroke. For example, when you press ƒ and then , the letter keystroke combination as ƒ [

A is entered. This guidebook describes this

A].

Getting Started 3

TI-82 STATS Menus

Displaying a Menu

While using your TI-82 STATS, 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.

After 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

ress 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 ( in the last displayed item. If you scroll beyond the last displayed item, an up arrow ( colon in the first item displayed.You can select an item in either of two ways.

¦ Press † or } to move the cursor to the number

or letter of the item; press Í.

¦ Press the key or key combination for the

number or letter next to the item.

$ ) replaces the colon ( : )

# ) replaces the

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 y [

QUIT] to return to the home screen.

¦ Press a key for another menu or screen.

4 Getting Started

First Steps

Before starting the sample problems in this chapter, follow the steps on this page to reset the TI-82 STATS 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-82 STATS, follow these steps.

1. Press É to turn on the calculator.

2. Press and release y, and then press [MEM]

(above Ã).

When you press y, you access the operation

rinted in yellow above the next key that you ress. [MEM] is the y operation of the Ã

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-82 STATS, the display contrast is reset.

¦ If the screen is very light or blank, press

and release y, and then press and hold } to darken the screen.

¦ If the screen is very dark, press and release

y, and then press and hold † to lighten the screen.

Getting Started 5

Entering a Calculation: The Quadratic Formula

Use the quadratic formula to solve the quadratic equations 3X2 + 5X + 2 = 0 and 2X N X + 3 = 0. Begin with the equation 3 X2 + 5X + 2 = 0.

1. Press 3 ¿ ƒ [A] (above ) to

store the coefficient of the X

term.

2. Press ƒ [ : ] (above Ë). The colon allows

you to enter more than one instruction on a line.

3. Press

5 ¿ ƒ [B] (above ) to

store the coefficient of the X term. Press ƒ [ same line. Press

: ] to enter a new instruction on the

2 ¿ ƒ [C] (above

) to store the constant.

4. Press Í 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 £ Ì ƒ [B] Ã y [‡] ƒ [B]

¡ ¹

4 ƒ [A] ƒ [C] ¤ ¤ ¥ £ 2

ƒ [A] ¤ to enter the expression for one

of the solutions for the quadratic formula,

−

+−bb ac

6. Press Í 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.

6 Getting Started

Converting to a Fraction: The Quadratic Formula

You can show the solution as a fraction.

1. Press  to display the

2. Press 1 to select 1:4Frac from the MATH menu.

When you press the home screen.

1, Ans4Frac is displayed on

Ans is a variable that

contains the last calculated answer.

3. Press Í 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 y [

ENTRY] (above Í) to recall the

fraction conversion entry, and then press y [

ENTRY] again to recall the quadratic-formula

expression,

−

+−bb ac

MATH menu.

5. Press } to move the cursor onto the + sign in

the formula. Press ¹ to edit the quadraticformula expression to become:

−

6. Press Í to find the other solution for the

quadratic equation 3X

−−bb ac

+ 5X + 2 = 0.

Getting Started 7

Displaying Complex Results: The Quadratic Formula

Now solve the equation 2X2 N X + 3 = 0. When you set a+bi complex number mode, the TI-82 STATS displays complex results.

1. Press z † † † † † † (6 times), and

then press ~ to position the cursor over Press Í to select

a+b

complex-numbe

mode.

2. Press y [QUIT] (above z) to return to the

home screen, and then press ‘ to clear it.

3. Press 2 ¿ ƒ [A] ƒ [ : ] Ì 1

¿ ƒ [B] ƒ [ : ] 3 ¿ ƒ [

C] Í.

The coefficient of the X2term, the coefficient of the X term, and the constant for the new equation are stored to A, B, and C, respectively.

4. Press y [ENTRY] to recall the store

instruction, and then press y [ to recall the quadratic-formula expression,

−

−−bb ac

a+b

ENTRY] again

5. Press Í to find one solution for the

equation 2X

N X + 3 = 0.

6. Press y [ENTRY] repeatedly until this

quadratic-formula expression is displayed:

−

+−bb ac

7. Press Í to find the other solution for the

quadratic equation: 2X

Note: An alternative for solving equations for real numbers is to use the built-in Equation Solver (Chapter 2).

N X + 3 = 0.

8 Getting Started

Defining a Function: Box with Lid

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 volume of the box.

From the diagram: 2X + A = 20

2X + 2B = 25

V = A B X

Substituting: V = (20 N 2X) (25à 2 N X) X

1. Press o to display the Y= editor, which is

where you define functions for tables and graphing.

2. Press £ 20 ¹ 2 „ ¤ £ 25 ¥ 2 ¹

„ ¤ „ Í to define the volume function as

Y1 in terms of X.

„ lets you enter X quickly, without having to press ƒ. The highlighted indicates that

Y1 is selected.

= sign

X B X B

Getting Started 9

Defining a Table of Values: Box with Lid

The table feature of the TI-82 STATS 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 y [

the

2. Press Í to accept TblStart=0.

3. Press 1 Í to define the table increment

@Tbl=1. Leave Indpnt: Auto and Depend: Auto so that the table will be

generated automatically.

4. Press y [TABLE] (above s) to display

the table.

Notice that the maximum value for volume) occurs when and 5.

5. Press and hold † to scroll the table until a

negative result for

Notice that the maximum length of X for this

roblem occurs where the sign of Y1 (box’s volume) changes from positive to negative, between

6. Press y [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 displayed in the table is 6.)

TBLSET] (above p) to display

TABLE SETUP menu.

Y1 (box’s

X is about 4, between 3

Y1 is displayed.

10 and 11.

10 Getting Started

Zooming In on the Table: Box with Lid

You can adjust the way a table is displayed to get more information about a defined function. With smaller values for

1. Press 3 Í to set TblStart. Press Ë 1 Í to set @Tbl.

This adjusts the table setup to get a more accurate estimate of

Y1.

X for maximum volume

2. Press y [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

4. Press y [TBLSET]. Press 3 Ë 6 Í to set

TblStart. Press Ë 01 Í to set @Tbl.

5. Press y [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.

@Tbl, you can zoom in on the table.

Y1 is

3.6<X<3.8.

6. Press † and } to move the cursor to 3.67. Press ~ to move the cursor into the

column.

The value of bottom line in full precision as

Y1 at X=3.67 is displayed on the

410.261226.

7. Press † to display the other maximums.

The value of Y1 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 occu at 3.68 if you could measure and cut the paper at .01-cm. increments.

Getting Started 11

Setting the Viewing Window: Box with Lid

You also can use the graphing features of the TI-82 STATS 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 p 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.

Ymin, and Ymax define the boundaries of the

display.

Xscl and Yscl define the distance

Xmin, Xmax,

etween tick marks on the X and Y axes. Xres

controls resolution.

2. Press 0 Í to define Xmin.

3. Press 20 ¥ 2 to define Xmax using an expression.

4. Press Í. The expression is evaluated, and

10 is stored in Xmax. Press Í to accept Xscl as 1.

5. Press 0 Í 500 Í 100 Í 1 Í to define the remaining window variables.

Xmin

Ymax

Xscl

Xmax

Yscl

Ymin

12 Getting Started

Displaying and Tracing the Graph: Box with Lid

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 s to graph the selected function in the viewing window.

The graph of 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 freemoving cursor to the apparent maximum of the function.

As you move the cursor, the coordinate values are updated continually.

Y1=(20N2X)(25à2NX)X is

X and Y

Getting Started 13

Displaying and Tracing the Graph: Box with Lid (cont.)

4. Press r. The trace cursor is displayed on the

Y1 function.

The function that you are tracing is displayed in the top-left corner.

5. Press | and ~ to trace along a time, evaluating

Y1 at each X.

You also can enter your estimate for the maximum value of

6. Press 3 Ë 8. When you press a number key while in

TRACE, the X= prompt is displayed in

the bottom-left corner.

7. Press Í.

The trace cursor jumps to the point on the Y1 function evaluated at X=3.8.

8. Press | and ~ until you are on the maximum

Y value.

This is the maximum of Y1(X) for the X pixel values. The actual, precise maximum may lie between pixel values.

Y1, one X dot at

14 Getting Started

Zooming In on the Graph: Box with Lid

To help identify maximums, minimums, roots, and intersections of functions, you can magnify the viewing window at a specific location using the

1. Press q to display the ZOOM menu.

This menu is a typical TI-82 STATS 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 Í.

2. Press 2 to select 2:Zoom In.

The graph is displayed again. The cursor has changed to indicate that you are using a

ZOOM

instruction.

3. With the cursor near the maximum value of the function (as in step 8 on page 14), press Í.

The new viewing window is displayed. Both

XmaxNXmin and YmaxNYmin have been

adjusted by factors of 4, the default values for the zoom factors.

4. Press p to display the new window settings.

ZOOM instructions.

Getting Started 15

Finding the Calculated Maximum: Box with Lid

You can use a CALCULATE menu operation to calculate a local maximum of a function.

1. Press y [

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 Í.

4 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 Í.

3 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 Í.

Or, press a guess for the maximum.

When you press a number key in

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.

CALC] (above r) to display the

3 Ë 8, and then press Í to enter

TRACE, the

16 Getting Started

Other TI-82 STATS Features

Getting Started has introduced you to basic TI-82 STATS operation. This guidebook describes in detail the features you used in Getting Started. It also covers the other features and capabilities of the TI-82 STATS.

Graphing

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).

Sequences

Tables

Split Screen

Matrices

Lists

Statistics

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

Y= 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).

Getting Started 17

Other TI-82 STATS Features (continued)

Inferential Statistics

Financial Functions

CATALOG

Programming

Linking to a PC or Macintoshë

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-82 STATS. 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).

You can connect your TI-82 STATS to a personal computer using TI Connect™ software and a TI Connectivity cable. The software is included on the CD in the TI-82 STATS package.

When you connect to the TI Connect™ software, the TI-82 STATS calculator will be identified by TI Connect™ as a TI-83 calculator. Everything else should function as expected.

For more information, consult the TI Connect™ Help.

The TI-82 STATS has a port to connect and communicate with another TI-82 STATS, a TI.82, the Calculator-Based Laboratoryé (CBLé) System, a Calculator-Based Rangeré (CBRé), or a personal computer. The unit-to-unit link cable is included with the TI-82 STATS (Chapter 19).

18 Getting Started

Operatin

Contents

the TI-82 STATS

Turning On and Turning Off the TI-82 STATS ................................. 2

Setting the Display Contrast The Display Entering Expressions and Instructions TI-82 STATS Edit Keys Setting Modes Using TI-82 STATS Variable Names Storing Variable Values Recalling Variable Values

ENTRY (Last Entry) Storage Area.............................................................. 16

Ans (Last Answer) Storage Area................................................................. 18

TI-82 STATS Menus

VARS and VARS Y.VARS Menus.............................................................. 21

Equation Operating System (EOSé) Error Conditions

................................................................................................................ 4

........................................................................................................... 9

...................................................................................................... 24

............................................................................ 3

...................................................... 6

..................................................................................... 8

....................................................... 13

..................................................................................... 14

................................................................................ 15

............................................................................................ 19

......................................................... 22

Operating the TI-82 STATS 1-1

Turning On and Turning Off the TI-82 STATS

Turning On the Calculator

Turning Off the Calculator

Batteries

To turn on the TI-82 STATS, press É.

• If you previously had turned off the calculator by pressing

OFF], the TI-82 STATS displays the home screen as it

y [ was when you last used it and clears any error.

• If Automatic Power Down™ (APDé) had previously turned

off the calculator, the TI-82 STATS 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-82 STATS automatically after about five minutes without any activity.

To turn off the TI-82 STATS manually, press y [

OFF].

• All settings and memory contents are retained by Constant

Memoryé.

• Any error condition is cleared.

The TI-82 STATS 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.

1-2 Operating the TI-82 STATS

Setting the Display Contrast

Adjusting the Display Contrast

When to Replace Batteries

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-82 STATS has 40 contrast settings, so each number 0 through 9 represents four settings.

The TI-82 STATS retains the contrast setting in memory when it is turned off.

To adjust the contrast, follow these steps.

1. Press and release the y key.

2. Press and hold † or }, 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 0, the display may become completely blank. To restore the screen, press and release y, 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-82 STATS 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.

Operating the TI-82 STATS 1-3

The Display

Types of Displays

Home Screen

Displaying Entries and Answers

The TI-82 STATS displays both text and graphs. Chapter 3 describes graphs. Chapter 9 describes how the TI-82 STATS can display a horizontally or vertically split screen to show graphs and text simultaneously.

The home screen is the primary screen of the TI-82 STATS. 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-82 STATS 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

Y= 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.

Entr

nswer

The mode settings control the way the TI-82 STATS 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.

Entr

nswer

Returning to the Home Screen

Busy Indicator

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

QUIT].

When the TI-82 STATS 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.

1-4 Operating the TI-82 STATS

Display Cursors

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 rectangle$A character is entered at the cursor;

any existing character is overwritten

Insert Underline

A character is inserted in front of the cursor location

Second Reverse arrowÞA 2nd character (yellow on the

keyboard) is entered or a 2nd operation is executed

Alpha Reverse A

An alpha character (green on the keyboard) is entered or SOLVE is executed

Full Checkerboard

rectangle

o entry; the maximum characters are

entered at a prompt or memory is full

If you press ƒ during an insertion, the cursor becomes an underlined

A (A) If you press y during an insertion, the

underline cursor becomes an underlined # ( # ).

Graphs and editors sometimes display additional cursors, which are described in other chapters.

Operating the TI-82 STATS 1-5

Entering Expressions and Instructions

What Is an Expression?

Entering an Expression

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-82 STATS, you enter an expression in the same order as you would write it on paper. For example, pR

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 Í, regardless of the cursor location. The entire expression is evaluated according to Equation Operating System (EOSé) rules (page 1.22), and the answer is displayed.

Most TI-82 STATS 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 « letters

L, O, and G. If you enter LOG, the TI-82 STATS

interprets the entry as implied multiplication of the variables

O, and G.

Calculate 3.76 ÷ (L7.9 + ‡5) + 2 log 45.

45. Do not enter the

3 Ë 76 ¥ £ Ì 7 Ë 9 Ã

y [‡] 5 ¤ ¤ Ã 2 « 45 ¤ Í

Multiple Entries on a Line

To enter two or more expressions or instructions on a line, separate them with colons (ƒ [ stored together in last entry (

1-6 Operating the TI-82 STATS

:]). All instructions are

ENTRY; page 1.16).

Entering a Number in Scientific Notation

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 y [

EE]. å

å is pasted to the cursor location.

åå

3. If the exponent is negative, press Ì, and then enter the exponent, which can be one or two digits.

When you enter a number in scientific notation, the TI-82 STATS 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.

Functions

Instructions

Interrupting a Calculation

A function returns a value. For example,

÷, L, +, ‡(, 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-82 STATS. Most functions take at least one argument, as indicated by an open parenthesis ( one argument,

An instruction initiates an action. For example,

( ) following the name. For example, sin( requires

sin(value).

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(X,Y,radius).

To interrupt a calculation or graph in progress, which would be indicated by the busy indicator, press É.

When you interrupt a calculation, the menu is displayed.

• To return to the home screen, select

• To go to the location of the interruption, select

1:Quit.

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.

Operating the TI-82 STATS 1-7

(

TI-82 STATS Edit Keys

Keystrokes Result

~ or | Moves the cursor within an expression; these keys repeat. } or † Moves the cursor from line to line within an expression that occupies

y | Moves the cursor to the beginning of an expression. y ~ Moves the cursor to the end of an expression. Í Evaluates an expression or executes an instruction. ‘ On a line with text on the home screen, clears the current line.

{ Deletes a character at the cursor; this key repeats. y [INS] Changes the cursor to __; inserts characters in front of the underline

y Changes the cursor to Þ; the next keystroke performs a 2nd operation

ƒ Changes the cursor to Ø; the next keystroke pastes an alpha character

y [A.LOCK] Changes the cursor to Ø; sets alpha-lock; subsequent keystrokes (on an

„ Pastes an X in Func mode, a T in Par mode, a q in Pol mode, or an n in

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.

On a blank line on the home screen, clears everything on the home screen.

In an editor, clears the expression or value where the cursor is located; it does not store a zero.

cursor; to end insertion, press y [INS] or press |, }, ~, or †.

an operation in yellow above a key and to the left); to cancel 2nd,

ress y again.

a character in green above a key and to the right) or executes SOLVE Chapters 10 and 11); to cancel ƒ, press ƒ or press |, },

~, or †.

alpha key) paste alpha characters; to cancel alpha-lock, press ƒ; name prompts set alpha-lock automatically.

Seq mode with one keystroke.

1-8 Operating the TI-82 STATS

Setting Modes

Checking Mode Settings

Changing Mode Settings

Setting a Mode from a Program

Mode settings control how the TI-82 STATS displays and interprets numbers and graphs. Mode settings are retained by the Constant Memory feature when the TI-82 STATS 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 z. The current settings are highlighted. Defaults are highlighted below. The following pages describe the mode settings in detail.

Normal Sci Eng Float 0123456789 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^qi Real, rectangular cplx, or polar cplx Full Horiz G-T Full screen, two split-screen modes

umeric notation umber of decimal places

To change mode settings, follow these steps.

1. Press † or } to move the cursor to the line of the setting that you want to change.

2. Press ~ or | to move the cursor to the setting you want.

3. Press Í.

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.

Operating the TI-82 STATS 1-9

Setting Modes (continued)

Normal, Sci, Eng

Float, 0123456789

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 in

Sci (scientific) notation mode expresses numbers in two parts.

12345.67.

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

1.234567E4.

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

Note: If you select Normal notation, but the answer cannot display in 10 digits (or the absolute value is less than .001), the TI-82 STATS expresses the answer in scientific notation.

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

12.34567E3.

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 Í.

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)

1-10 Operating the TI-82 STATS

Radian, Degree

Angle modes control how the TI-82 STATS 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.

Func, Par, Pol, Seq

Connected, Dot

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

Par (parametric) graphing mode plots relations, where X and Y

X (Chapter 3).

are functions of T (Chapter 4).

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

q (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.

Operating the TI-82 STATS 1-11

Setting Modes (continued)

Sequential, Simul

Real, a+bi, re^qi

Full, Horiz, G.T

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 and plots them for the next value of

Note: Regardless of which graphing mode is selected, the TI-82 STATS will sequentially graph all stat plots before it graphs any functions.

Real mode does not display complex results unless complex

X and then evaluates

numbers are entered as input.

Two complex modes display complex results.

• a+bi (rectangular complex mode) displays complex numbers

in the form a+bi.

•

re^qi (polar complex mode) displays complex numbers in

the form re^qi.

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).

•

G.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).

1-12 Operating the TI-82 STATS

Using TI-82 STATS Variable Names

Variables and Defined Items

On the TI-82 STATS 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-82 STATS 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 A, B, . . . , Z, q

Complex numbers A, B, . . . , Z, q

Matrices ãAä, ãBä, ãCä, . . . , ãJä

Lists

L1, L2, L3, L4, L5, L6, and user-defined

names

Functions

Parametric equations

Polar functions

Y1, Y2, . . . , Y9, Y0

X1T and Y1T, . . . , X6T and Y6T

r1, r2, r3, r4, r5, r6

Sequence functions u, v, w

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

Notes about Variables

• 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 Y= functions (Chapters 3, 4, 5, and 6).

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

Y= 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).

Operating the TI-82 STATS 1-13

Storing Variable Values

Storing Values in a Variable

Displaying a Variable Value

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 ƒ and then the letter of the variable to which you want to store the value.

4. Press Í. 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 Í.

1-14 Operating the TI-82 STATS

Recalling Variable Values

Using Recall (RCL)

To recall and copy variable contents to the current cursor location, follow these steps. To leave

RCL, press ‘.

1. Press y ãRCLä. Rcl and the edit cursor are displayed on the bottom line of the screen.

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

• Press ƒ and then the letter of the variable.

• Press y ã

press y [

LISTä, and then select the name of the list, or

Ln].

• Press , and then select the name of the matrix.

• Press  to display the

display the

VARS Y.VARS menu; then select the type and

VARS menu or  ~ to

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 Í. 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.

Operating the TI-82 STATS 1-15

ENTRY (Last Entry) Storage Area

Using ENTRY (Last Entry)

Accessing a Previous Entry

When you press Í on the home screen to evaluate an expression or execute an instruction, the expression or instruction is placed in a storage area called When you turn off the TI-82 STATS,

ENTRY (last entry).

ENTRY is retained in

memory.

To recall

ENTRY, press y [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-82 STATS updates

ENTRY only when you press

Í, you can recall the previous entry even if you have begun to enter the next expression.

5 Ã 7

Í y [ENTRY]

The TI-82 STATS retains as many previous entries as possible in

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

press y [ bytes, it is retained for

ENTRY storage area.

1 ¿ ƒ A

ENTRY] repeatedly. If a single entry is more than 128

ENTRY, but it cannot be placed in the

2 ¿ ƒ B

Í y [ENTRY]

If you press y [ENTRY] after displaying the oldest stored entry, the newest stored entry is displayed again, then the nextnewest entry, and so on.

y [ENTRY]

1-16 Operating the TI-82 STATS

Reexecuting the Previous Entry

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 Í.

To reexecute the displayed entry, press Í again. Each reexecution displays an answer on the right side of the next line; the entry itself is not redisplayed.

0 ¿ ƒ N

Í ƒ N Ã 1 ¿ ƒ N ƒ ã:ä ƒ N ¡ Í Í Í

Multiple Entry Values on a Line

Clearing ENTRY

To store to ENTRY two or more expressions or instructions, separate each expression or instruction with a colon, then press Í. All expressions and instructions separated by colons are stored in

ENTRY.

When you press y [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 Í.

For the equation A=pr2, use trial and error to find the radius of a circle that covers 200 square centimeters. Use 8 as your first guess.

¿ ƒ R ƒ

[:] y [p] ƒ R ¡ Í

y [ENTRY]

y | 7 y [INS] Ë 95 Í

Continue until the answer is as accurate as you want.

Clear Entries (Chapter 18) clears all data that the TI-82 STATS

is holding in the

ENTRY storage area.

Operating the TI-82 STATS 1-17

Ans (Last Answer) Storage Area

Using Ans in an Expression

Continuing an Expression

Storing Answers

When an expression is evaluated successfully from the home screen or from a program, the TI-82 STATS 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-82 STATS, the value in

Ans is retained in memory.

You can use the variable Ans to represent the last answer in most places. Press y [

ANS] to copy the variable name Ans to the

cursor location. When the expression is evaluated, the TI-82 STATS uses the value of

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.

1 Ë 7 ¯ 4 Ë 2

Ans in the calculation.

147 ¥ y [ANS]

You can use Ans as the first entry in the next expression without entering the value again or pressing y [

ANS]. On a blank line

on the home screen, enter the function. The TI-82 STATS pastes the variable name

5 ¥ 2

Ans to the screen, then the function.

Í ¯ 9 Ë 9 Í

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.

y [p] 5 ¡ Í ¯ 3 Ë 3 Í ¿ ƒ Í

1-18 Operating the TI-82 STATS

TI-82 STATS Menus

Using a TI-82 STATS Menu

Scrolling a Menu

You can access most TI-82 STATS 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 ~ or | 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 ƒ †. To page up six menu items at a time, press ƒ }. 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 †.

Operating the TI-82 STATS 1-19

TI-82 STATS Menus (continued)

Selecting an Item from a Menu

Leaving a Menu without Making a Selection

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 † or } to move the cursor to the item you want, and

then press Í.

After you select an item from a menu, the TI-82 STATS typically displays the previous screen.

Note: On the LIST NAMES, PRGM EXEC, and PRGM EDIT menus, only items 1 through 9 and 0 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 q, press the key combination for that alpha character or q. If no items begin with that character, then the cursor moves beyond it to the next item.

Calculate 3‡27.

 † † † Í

27 ¤ Í

You can leave a menu without making a selection in any of four ways.

• Press y [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

 or y [

LIST].

• Press a key or key combination for a different screen, such

as o or y [

TABLE].

1-20 Operating the TI-82 STATS

VARS and VARS Y.VARS Menus

VARS Menu

Selecting a Variable from the VARS Menu or VARS Y.VARS Menu

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 menu 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, T/q, and U/V/W variables 2: Zoom... ZX/ZY, ZT/Zq, and ZU variables 3: GDB... Graph database variables 4: Picture... Picture variables 5: Statistics... XY, G, EQ, 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

Y= function variables.

VARS Y-VARS 1: Function... Yn functions 2: Parametric... XnT, YnT functions 3: Polar... rn functions 4: On/Off... Lets you select/deselect functions

Note: The sequence variables (u, v, w) are located on the keyboard as the second functions of ¬, −, and ®.

To select a variable from the VARS or VARS Y.VARS menu, follow these steps.

1. Display the

VARS or VARS Y.VARS menu.

• Press  to display the VARS menu.

• Press  ~ to display the

2. Select the type of variable, such as

VARS Y.VARS menu.

2:Zoom from the VARS

menu or 3:Polar from the VARS Y.VARS menu. A secondary menu is displayed.

3. If you selected

VARS menu, you can press ~ or | to display other

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

secondary menus.

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

Operating the TI-82 STATS 1-21

Equation Operating System (EOSé)

Order of Evaluation

The Equation Operating System (EOSé) defines the order in which functions in expressions are entered and evaluated on the TI-82 STATS. 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

2, M1

, !, ¡, r, and conversions

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

‡32

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(A2,A,6), are evaluated

as they are encountered.

1-22 Operating the TI-82 STATS

Implied Multiplication

The TI-82 STATS recognizes implied multiplication, so you need not press ¯ to express multiplication in all cases. For example, the TI-82 STATS interprets

(2ääää5)7 as implied multiplication.

Note: TI-82 STATS implied multiplication rules differ from those of the

TI.82. For example, the TI-82 STATS evaluates 1à2X as (1à2)ä while the TI.82 evaluates 1à2X as 1/(2ä

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

äX) (Chapter 2).

ää

äX,

ää

Parentheses

Negation

All calculations inside a pair of parentheses are completed first. For example, in the expression portion inside the parentheses, answer,

3, by 4.

4(1+2), EOS first evaluates the

1+2, and then multiplies the

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 displayconversion instructions.

Note: An open parenthesis following a list name, matrix name, or Y= 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 Y= function.

To enter a negative number, use the negation key. Press Ì and then enter the number. On the TI-82 STATS, 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 ¹ key for subtraction and the Ì key for negation. If you press ¹ to enter a negative number, as in 9 ¯ ¹ 7, or if you press Ì to indicate subtraction, as in 9 Ì 7, an error occurs. If you press ƒ A Ì ƒ B, it is interpreted as implied multiplication (Aä

äMB).

ää

Operating the TI-82 STATS 1-23

Error Conditions

Diagnosing an Error

Correcting an Error

The TI-82 STATS detects errors while performing these tasks.

• Evaluating an expression

• Executing an instruction

• Plotting a graph

• Storing a value

When the TI-82 STATS detects an error, it returns an error message as a menu title, such as

ERR:DOMAIN. Appendix B describes each error type and

ERR:SYNTAX or

possible reasons for the error.

• If you select 1:Quit (or press y [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.

1-24 Operating the TI-82 STATS

Math, Angle, and Tes

Contents

Operations

Getting Started: Coin Flip................................................................................. 2

Keyboard Math Operations

MATH Operations................................................................................................... 5

Using the Equation Solver

MATH NUM (Number) Operations.............................................................. 13

Entering and Using Complex Numbers

MATH CPX (Complex) Operations ............................................................ 18

MATH PRB (Probability) Operations........................................................ 20

ANGLE Operations................................................................................................ 23

TEST (Relational) Operations........................................................................ 24

TEST LOGIC (Boolean) Operations .......................................................... 26

.............................................................................. 3

................................................................................ 8

.................................................... 16

Math, Angle, and Test Operations 2.1

Getting Started: Coin Flip

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  | to

display the

7:randBin( (random Binomial). randBin( is

asted to the home screen. Press 10 to enter the

number of coin flips. Press ¢. Press Ë enter the probability of heads. Press ¢. Press

40 to enter the number of simulations. Press ¤.

2. Press Í 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 ¿ y ãL1ä Í to store the data to

the list name another activity, such as plotting a histogram (Chapter 12).

MATH PRB menu. Press 7 to select

5 to

L1. You then can use the data for

4. Press ~ or | 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.

2.2 Math, Angle, and Test Operations

Keyboard Math Operations

Using Lists with Math Operations

+ (Addition), N (Subtraction), ääää (Multiplication), à (Division)

Trigonometric Functions

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, Ã), N (subtraction, ¹), ä

ää

(multiplication, ¯), and à (division, ¥) with real and complex numbers, expressions, lists, and matrices. You cannot use

à with

matrices.

valueA

+valueB valueA N valueB

valueA

äääävalueB valueA à valueB

You can use the trigonometric (trig) functions (sine, ˜; cosine, ™; and tangent, š) with real numbers, expressions, and lists. The current angle mode setting affects interpretation. For example,

Degree mode it returns .5.

sin(value) cos(value) tan(value)

You can use the inverse trig functions (arcsine, y [SINL1]; arccosine, y [

sin(30) in Radian mode returns L.9880316241; in

COS

]; and arctangent, y [TANL1]) with real

numbers, expressions, and lists. The current angle mode setting affects interpretation.

sinL1(value) cosL1(value) tanL1(value)

Note: The trig functions do not operate on complex numbers.

^ (Power),

(Square),

‡( (Square Root)

(Inverse)

You can use ^ (power, ›), 2 (square, ¡), and ‡( (square root, y [

‡]) with real and complex numbers, expressions, lists, and

matrices. You cannot use

^power value

value

‡( with matrices.

‡(value)

You can use L1 (inverse, —) with real and complex numbers, expressions, lists, and matrices. The multiplicative inverse is equivalent to the reciprocal, 1àx.

value

Math, Angle, and Test Operations 2.3

Keyboard Math Operations (continued)

log(, 10^(, ln(

e^( (Exponential)

e (Constant)

L (Negation)

You can use log( (logarithm, «), 10^( (power of 10, y

[

]), and ln( (natural log, µ) with real or complex numbers,

expressions, and lists.

log(value) 10^(power) ln(value)

(exponential, y ãex]) returns the constant e raised to a

e^(

power. You can use

e^( with real or complex numbers,

expressions, and lists.

e^(power)

e (constant, y [e]) is stored as a constant on the TI-82 STATS

. Press y [ the TI-82 STATS uses 2.718281828459 for

M (negation, Ì) returns the negative of value. You can use M

e] to copy e to the cursor location. In calculations,

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

Mvalue

EOS rules (Chapter 1) determine when negation is evaluated. For example, evaluated before negation. Use parentheses to square a negated number, as in

returns a negative number, because squaring is

(LA)

Note: On the TI-82 STATS, the negation symbol (M) is shorter and higher than the subtraction sign (N), which is displayed when you press ¹.

p (Pi)

p (Pi, y [p]) is stored as a constant in the TI-82 STATS. In

calculations, the TI-82 STATS uses 3.1415926535898 for

2.4 Math, Angle, and Test Operations

MATH Operations

MATH Menu

4Frac, 4Dec

To display the MATH menu, press .

MATH NUM CPX PRB

1: 4Frac Displays the answer as a fraction. 2: 4Dec Displays the answer as a decimal.

3: 4:3‡( Calculates the cube root. 5:x‡ Calculates the x 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.

4Frac (display as a fraction) displays an answer as its rational

equivalent. You can use

Calculates the cube.

root.

4Frac 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

4Frac

following value.

value 4Frac

4Dec

(display as a decimal) displays an answer in decimal form. You can use lists, and matrices. You can only use

4Dec with real or complex numbers, expressions,

4Dec following value.

value 4Dec

Math, Angle, and Test Operations 2.5

MATH Operations (continued)

(Cube),

‡( (Cube Root)

‡ (Root)

fMin(, fMax(

(cube) returns the cube of value. You can use 3 with real or

complex numbers, expressions, lists, and square matrices.

value

‡( (cube root) returns the cube root of value. You can use 3‡(

with real or complex numbers, expressions, and lists.

‡(value)

‡ (x

root) returns the xth root of 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 1â

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 ([ ]).

L5).

2.6 Math, Angle, and Test Operations

nDeriv(

nDeriv( (numerical derivative) returns an approximate derivative

of expression with respect to variable, given the value at which to calculate the derivative and H (if not specified, the default is 1â

L3). nDeriv( is valid only for real numbers.

nDeriv(expression,variable,value[,H])

nDeriv(

uses the symmetric difference quotient method, which approximates the numerical derivative value as the slope of the secant line through these points.

(

f¢(x) =

x+H)Nf(xNH)

As H 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-82 STATS can return a false

derivative value at a nondifferentiable point.

fnInt(

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 1â

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 s.

L5). fnInt( is valid only for real numbers.

Math, Angle, and Test Operations 2.7

Using the Equation Solver

Solver

Entering an Expression in the Equation Solver

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 2.9)

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 Y= variable name from the VARS Y.VARS menu

to the equation solver.

• Press y [

VARS Y.VARS menu, and press Í. The expression is

RCL], paste a Y= variable name from the

pasted to the equation solver.

The expression is stored to the variable eqn as you enter it.

2.8 Math, Angle, and Test Operations

Entering an Expression in the Equation Solver (continued)

3. Press Í or †. 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 (

• A

$ is displayed in the first column of the bottom line if

bound={L1å

å99,1åååå99}).

åå

the editor continues beyond the screen.

Tip: To use the solver to solve an equation such as K=.5MV2, enter

eqn:0=KN.5MV

in the equation editor.

Entering and Editing Variable Values

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

Y1 or r6, and then reference the variables in the equation. The

interactive solver editor displays all variables of all

VARS Y.VARS variables, such as

Y= functions

referenced in the equation.

Math, Angle, and Test Operations 2.9

Using the Equation Solver (continued)

Solving for a Variable in the Equation Solver

To solve for a variable using the equation solver after an equation has been stored to

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 Í or †.

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-82 STATS will attempt to display the solution that is closest to your guess.

The default guess is calculated as

eqn, follow these steps.

(upper+ lower)

2.10 Math, Angle, and Test Operations

Solving for a Variable in the Equation Solver (continued)

4. Edit bound={lower,upper}. lower and upper are the bounds

between which the TI-82 STATS searches for a solution. This is optional, but it may help find the solution more quickly. The default is

bound={L1å

å99,1åååå99}.

åå

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

and press ƒ [

SOLVE] (above the Í 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.

•

leftNrt=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

leftNrt= indicates that the equation has been evaluated at

the new value of the variable for which you solved.

Math, Angle, and Test Operations 2.11

Using the Equation Solver (continued)

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

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

leftNrt=diff

disappear. Move the cursor to the variable for which you now want to solve and press ƒ [

SOLVE].

The TI-82 STATS 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 or 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 is L1â99. The default for upper is 1â99.

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 in expression, except variable, before expression is evaluated. lower and upper must be entered in list format.

2.12 Math, Angle, and Test Operations

MATH NUM (Number) Operations

MATH NUM Menu

abs(

round(

To display the MATH NUM menu, press  ~.

MATH NUM CPX PRB

1: abs( Absolute value 2: round( Roun 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, Angle, and Test Operations 2.13

MATH NUM (Number) Operations (continued)

iPart(, fPart(

int(

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.

2.14 Math, Angle, and Test Operations

min(, max(

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(, gcd(

lcm( returns the least common multiple of valueA and valueB,

both of which must be nonnegative integers. When listA and listB are specified, elements. If list and value are specified,

lcm( returns a list of the lcm of each pair of

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, elements. If list and value are specified,

gcd( returns a list of the gcd of each pair of

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)

Math, Angle, and Test Operations 2.15

Entering and Using Complex Numbers

Complex-Number Modes

Entering Complex Numbers

The TI-82 STATS displays complex numbers in rectangular form and polar form. To select a complex-number mode, press z, and then select either of the two modes.

•

a+bi (rectangular-complex mode)

• re^qi (polar-complex mode)

On the TI-82 STATS, 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 mode ln(L1) returns an error; in a+bi mode ln(L1) returns an answer.

Real mode a+bi mode

Real

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.

Note about Radian versus Degree Mode

2.16 Math, Angle, and Test Operations

Radian mode is recommended for complex number calculations. Internally, the TI-82 STATS 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 e^(iq) = cos(q) + i sin(q) are not generally true because the values for cos and sin are converted to radians, while those for e^( ) are not. For example, e^(i45) = cos(45) + i sin(45) is treated internally as e^(i45) = cos(p/4) + i sin(p/4). Complex identities are always true in radian mode.

Interpreting Complex Results

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^qi and Radian modes are set.

RectangularComplex Mode

Polar-Complex Mode

Rectangular-complex mode recognizes and displays a complex number in the form imaginary component, and i is a constant equal to

a+bi, where a is the real component, b is the

-1

To enter a complex number in rectangular form, enter the value of a (real component), press Ã or ¹, enter the value of b (imaginary component), and press y [i] (constant).

real component(

+ or N)imaginary componenti

Polar-complex mode recognizes and displays a complex number in the form re^ log,

To enter a complex number in polar form, enter the value of r (magnitude), press y [ value of

i, where r is the magnitude, e is the base of the natural

is the angle, and i is a constant equal to -1.

] (exponential function), enter the

(angle), press y [i] (constant), and then press ¤.

magnitudee^(anglei)

Math, Angle, and Test Operations 2.17

MATH CPX (Complex) Operations

MATH CPX Menu

conj(

real(

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). 6: 4Rect Displays the result in rectangular form. 7: 4Polar Displays the result in polar form.

conj( (conjugate) returns the complex conjugate of a complex

number or list of complex numbers.

conj(a+bi) returns aNbi in a+bi mode. conj(re^(

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

i)) returns re^(Lqi) in re^qi mode.

of complex numbers.

real(a+bi) returns a. real(re^(

i)) returns rä

äcos(

ää

imag(

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

complex number or list of complex numbers.

imag(a+bi) returns b. imag(re^(

i)) returns rä

2.18 Math, Angle, and Test Operations

äsin(

ää

angle(

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 +p in the second quadrant or Np in the third quadrant.

angle(a+bi) returns tan angle(re^(

i)) returns q, where Lp<q<p.

(b/a).

abs(

4Rect

4Polar

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

(real2+imag2)

, of a complex number or list of complex

numbers.

abs(a+bi) returns (a2+b2) abs(re^(

4Rect (display as rectangular) displays a complex result in

i)) returns r (magnitude).

rectangular form. It is valid only at the end of an expression. It is not valid if the result is real.

complex result

4Polar (display as polar) displays a complex result in polar form.

8Rect returns a+bi.

It is valid only at the end of an expression. It is not valid if the result is real.

complex result

8Polar returns re^(

i).

Math, Angle, and Test Operations 2.19

MATH PRB (Probability) Operations

MATH PRB Menu

rand

To display the MATH PRB menu, press  |.

MATH NUM CPXPRB 1: rand Random-number generator 2: nPr 3: nCr 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

umber of permutations umber of combinations

random numbers > 0 and < 1. To generate a list of randomnumbers, 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, randä random number > 0 and < 5.

ä5 generates a

ää

With each rand execution, the TI-82 STATS generates the same random-number sequence for a given seed value. The TI-82 STATS factory-set seed value for

rand is 0. To generate a

different random-number sequence, store any nonzero seed value to

rand or reset the defaults (Chapter 18).

Note: The seed value also affects randInt(, randNorm(, and

randBin( instructions (page 2.22).

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

2.20 Math, Angle, and Test Operations

nPr, nCr

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)

! (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)! = nän!, until n is reduced to either 0 or L1/2. At that point, the definition 0!=1 or the definition (L1à2)!=‡p is used to complete the calculation. Hence:

n!=nä(nN1)ä(nN2)ä ... ä2ä1, if n is an integer ‚0 n!= nä(nN1)ä(nN2)ä ... ä1à2ä‡p, if n+1à2 is an integer ‚0 n! is an error, if neither n nor n+1à2 is an integer ‚0.

(The variable n equals value in the syntax description above.)

Math, Angle, and Test Operations 2.21

MATH PRB (Probability) Operations (continued)

randInt(

randNorm(

randBin(

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 [mN3(s), m+3(s)]. To generate a list of random numbers, specify an integer > 1 for numtrials (number of trials); if not specified, the default is 1.

randNorm(m,

randBin( (random Binomial) generates and displays a random

[,numtrials])

integer from a specified Binomial distribution. numtrials (number of trials) must be ‚ 1. 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).

2.22 Math, Angle, and Test Operations

ANGLE Operations

ANGLE Menu

DMS Entry Notation

To display the ANGLE menu, press y [ANGLE]. The ANGLE menu displays angle indicators and instructions. The

Radian/Degree mode setting affects the TI-82 STATS

interpretation of

ANGLE 1: ¡ Degree notation 2: ' DMS minute notation

3: 4: 8DMS Displays as degree/minute/second 5: R8Pr( Returns r, given X and Y 6: R8Pq( Returns q, given X and Y 7: P8Rx( Returns x, given R and q 8: P8Ry( Returns y, given R and q

ANGLE menu entries.

Radian notation

DMS (degrees/minutes/seconds) entry notation comprises the degree symbol ( (

"). degrees must be a real number; minutes and seconds must

¡), the minute symbol ('), and the second symbol

be real numbers ‚ 0.

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-82 STATS can interpret the argument as degrees, minutes, and seconds.

Degree mode Radian mode

¡ (Degree)

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

regardless of the current angle mode setting. In you can use

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 ƒ [ã].

¡ to convert degrees to radians.

Radian mode,

Math, Angle, and Test Operations 2.23

ANGLE Operations (continued)

(Radians)

(radians) designates an angle or list of angles as radians, regardless of the current angle mode setting. In you can use

value

Degree mode

to convert radians to degrees.

Degree mode,

8DMS

R8Pr (, R8Pq (, P8Rx(, P8Ry(

8DMS (degree/minute/second) displays answer in DMS format

(page 2.23). The mode setting must be interpreted as degrees, minutes, and seconds.

Degree for answer to be

8DMS is valid

only at the end of a line.

answer

8DMS

R8Pr( converts rectangular coordinates to polar coordinates and

returns

r. R8Pq( converts rectangular coordinates to polar

coordinates and returns

R8Pr(x,y), R8Pq(x,y)

P8Rx(

converts polar coordinates to rectangular coordinates and

returns

x. P8Ry( converts polar coordinates to rectangular

coordinates and returns

P8Rx(r,q), P8Ry(r,q)

q. x and y can be lists.

Note: Radian mode is set.

y. r and

can be lists.

Note: Radian mode is set.

2.24 Math, Angle, and Test Operations

TEST (Relational) Operations

TEST Menu

=, ƒ, >, ‚, <, 

To display the TEST menu, press y [TEST].

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

TEST LOGIC 1: = Equal 2: ƒ 3: > Greater than 4: ‚ Greater than or equal to 5: < Less than 6:  Less than or equal to

Relational operators compare valueA and valueB and return the test is true or

0 if the test is false. valueA and valueB can be

real numbers, expressions, or lists. For

ot equal to

1 if

= and ƒ 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 valueAƒvalueB

valueA

>valueB valueA‚valueB

valueA

<valueB valueAvalueB

Using Tests

Relational operators are evaluated after mathematical functions according to EOS rules (Chapter 1).

• The expression

2+2=2+3 returns 0. The TI-82 STATS

performs the addition first because of EOS rules, and then it compares 4 to 5.

• The expression

2+(2=2)+3 returns 6. The TI-82 STATS

performs the relational test first because it is in parentheses, and then it adds 2, 1, and 3.

Math, Angle, and Test Operations 2.25

TEST LOGIC (Boolean) Operations

TEST LOGIC Menu

Boolean Operators

and, or, xor

To display the TEST LOGIC menu, press y ãTESTä ~.

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, or, and xor (exclusive or) return a value of 1 if an

expression is true or

0 if an expression is false, according to the

table below. valueA and valueB can be real numbers, expressions, or lists.

valueA

and valueB

valueA

or valueB

valueA

xor valueB

valueA valueB and or xor

ƒ0 ƒ0 returns 110 ƒ0 0 returns 011

0 ƒ0 returns 011

0 0 returns 000

not(

Using Boolean Operations

returns 1 if value (which can be an expression) is 0.

not(value)

Boolean logic is often used with relational tests. In the following program, the instructions store

2.26 Math, Angle, and Test Operations

4 into C.

Function

Graphin

Contents

Getting Started: Graphing a Circle.............................................................. 2

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 Exploring Graphs with the

ZOOM MEMORY.................................................................................... 23

Using Using the

...................................................................................................... 3

................................................................................... 4

................................................................................................ 5

.......................................................... 7

.............................................................. 9

................................................... 11

.................................................................................. 13

.................................................................................................. 15

................................ 17

TRACE..................................................................... 18

ZOOM Instructions .................................. 20

CALC (Calculate) Operations.................................................. 25

Function Graphing 3.1

‡

Getting Started: Graphing a Circle

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 make the functions appear as a circle.

1. In Func mode, press o to display the

Y= editor. Press y ã‡ä 100 ¹ „ ¡ ¤

Í to enter the expression Y=

which defines the top half of the circle.

The expression Y=L

ottom half of the circle. On the TI-82 STATS, you can define one function in terms of another. To define

Y2=LY1, press Ì to enter the negation

sign. Press  ~ to display the

VARS Y.VARS menu. Then press Í to

select

1:Function. The FUNCTION secondary

menu is displayed. Press

2. Press q 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 s.

Notice that the functions appear as an ellipse in the standard viewing window.

ZSquare (zoom square) to adjust the display and

(100NX2),

(100NX2) defines the

1 to select 1:Y1.

3. To adjust the display so that each pixel represents an equal width and height, press q

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 p and notice the new values for

Xmax, Ymin, and Ymax.

Xmin,

3.2 Function Graphing

Defining Graphs

TI-82 STATS— Graphing Mode Similarities

Defining a Graph

Displaying and Exploring a Graph

Saving a Graph for Later Use

Chapter 3 specifically describes function graphing, but the steps shown here are similar for each TI-82 STATS 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 z and set the appropriate graph mode (page 3.4).

2. Press o and enter, edit, or select one or more functions in

the

Y= 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 p and define the viewing window variables

(page 3.11).

6. Press y [

FORMAT] and select the graph format settings

(page 3.13).

After you have defined a graph, press s to display it. Explore the behavior of the function or functions using the TI-82 STATS tools described in this chapter.

You can store the elements that define the current graph to any of 10 graph database variables (

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

GDB1 through GDB9, and

recall the graph database to which you stored the original graph.

These types of information are stored in a

Y= functions

•

GDB.

• 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.

Function Graphing 3.3

Setting the Graph Modes

Checking and Changing the Graphing Mode

To display the mode screen, press z. 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-82 STATS 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.

Setting Modes from a Program

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 z to display the mode settings.

2. Press †, ~, |, and } to place the cursor on the mode that

3. Press Í to paste the mode name to the cursor location.

The mode is changed when the program is executed.

3.4 Function Graphing

you want to select.

Defining Functions

Displaying Functions in the

= Edito

Defining or Editing a Function

To display the Y= editor, press o. You can store up to 10 functions to the function variables

Y1 through Y9, and Y0. You

can graph one or more defined functions at once. In this example, functions

Y1 and Y2 are defined and selected.

To define or edit a function, follow these steps.

1. Press o to display the Y= 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 ƒ [X].

• 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 a user-defined function in the

Y= editor.

Yn as

4. Press Í or † to move the cursor to the next function.

Function Graphing 3.5

Defining Functions (continued)

Defining a Function from the Home Screen or a Program

Evaluating Y= Functions in Expressions

To define a function from the home screen or a program, begin on a blank line and follow these steps.

1. Press ƒ [ [

ã] again.

ã], enter the expression, and then press ƒ

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 Í to complete the instruction.

"expression"!!!!Yn

When the instruction is executed, the TI-82 STATS stores the expression to the designated variable and displays the message

Done.

You can calculate the value of a value of

Yn(value) Y

X. A list of values returns a list.

n({value1,value2,value3, . . .,value n})

Yn, selects the function,

Y= function Yn at a specified

3.6 Function Graphing

Selecting and Deselecting Functions

Selecting and Deselecting a Function

Turning On or Turning Off a Stat Plot in the Y= Editor

You can select and deselect (turn on and turn off) a function in the

Y= editor. A function is selected when the = sign is

highlighted. The TI-82 STATS graphs only the selected functions. You can select any or all functions

Y0.

Y1 through Y9, and

To select or deselect a function in the Y= editor, follow these steps.

1. Press o to display the

Y= 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 Í 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

Y= editor, use Plot1 Plot2 Plot3 (the top line of the Y= 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 press } and ~ to place the cursor on

Plot1, Plot2, or Plot3, and

Y= editor,

then press Í.

Plot1 is turned on. Plot2 and Plot3 are turned off.

Function Graphing 3.7

Selecting and Deselecting Functions (continued)

Selecting and Deselecting Functions from the Home Screen or a Program

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 Yn) 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#, . . .,function n] FnOff[function#,function#, . . .,function n]

5. Press Í. When the instruction is executed, the status of each function in the current mode is set and

Done is

displayed.

For example, in functions in the

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

Y= editor, and then turns on Y1 and Y3.

3.8 Function Graphing

Setting Graph Styles for Functions

Graph Style Icons in the Y= Editor

Setting the Graph Style

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

Y1 as a solid line, Y2

as a dotted line, and Y3 as a thick line.

Icon Style Description

ç Line A solid line connects plotted points; this is the

default in Connected mode

è Thick A thick solid line connects plotted points é Above Shading covers the area a*bove the graph ê Below Shading covers the area below the graph ë Path A circular cursor traces the leading edge of the

graph and draws a path

ì Animate A circular cursor traces the leading edge of the

graph without drawing a path

í 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 o to display the Y= 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 Í 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.

Function Graphing 3.9

Setting Graph Styles for Functions (continued)

Shading Above and Below

Setting a Graph Style from a Program

When you select é or ê for two or more functions, the TI-82 STATS rotates through four shading patterns.

• Vertical lines shade the first function with a é or ê 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 é or ê

function, repeating the order described above.

When shaded areas intersect, the patterns overlap.

Note: When é or ê 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

1 to 7 that corresponds to the graph style, as shown

below.

1 = ç (line) 2 = è (thick) 3 = é (above) 4 = ê (below) 5 = ë (path) 6 = ì (animate) 7 = í (dot)

GraphStyle(function#,graphstyle#)

For example, when this program is executed in Func mode,

GraphStyle(1,3) sets Y1 to é (above).

3.10 Function Graphing

Setting the Viewing Window Variables

The TI-82 STATS Viewing Window

Displaying the Window Variables

The viewing window is the portion of the coordinate plane defined by defines the distance between tick marks on the x-axis.

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

Yscl (Y

scale) defines the distance between tick marks on the y-axis. To turn off tick marks, set

Xmin

Ymin

Xscl=0 and Yscl=0.

Ymax

Xscl

Xmax

Yscl

To display the current window variable values, press p. 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

• At

Xres=1, functions are evaluated and graphed at each pixel

on the x-axis.

• At

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 TI-82 STATS to draw graphs more slowly.

Changing a Window Variable Value

To change a window variable value from the window editor, follow these steps.

1. Press † or } 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 Í, †, or }. If you entered an expression, the TI-82 STATS evaluates it. The new value is stored.

Note: Xmin<Xmax and Ymin<Ymax must be true in order to graph.

Function Graphing 3.11

Setting the Viewing Window Variables (continued)

Storing to a Window Variable from the Home Screen or a Program

@X and @Y

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 (T/q

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 Í to complete the instruction.

When the instruction is executed, the TI-82 STATS stores the value to the window variable and displays the value.

The variables @X and @Y (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).

Xmax, Ymin, and Ymax when you display a graph.

@X and @Y are calculated from Xmin,

@X =

You can store values to @X and @Y. If you do, Xmax and Ymax are calculated from @X, Xmin, @Y, and Ymin.

3.12 Function Graphing

(Xmax N Xmin)

@Y =

(Ymax N Ymin)

Setting the Graph Format

Displaying the Format Settings

Changing a Format Setting

RectGC, PolarGC

To display the format settings, press y [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 Í to select the highlighted setting.

RectGC (rectangular graphing coordinates) displays the cursor

location as rectangular coordinates

PolarGC (polar graphing coordinates) displays the cursor

location as polar coordinates

X and Y.

R and q.

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 q; if CoordOn format is

selected, R and q are displayed.

Function Graphing 3.13

Setting the Graph Format (continued)

CoordOn, CoordOff

GridOff, GridOn

AxesOn, AxesOff

LabelOff, LabelOn

ExprOn, ExprOff

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 (

ExprOn and ExprOff determine whether to display the

Y= expression when the trace cursor is active. This format

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

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.

3.14 Function Graphing

Displaying Graphs

Displaying a New Graph

Pausing or Stopping a Graph

Smart Graph

To display the graph of the selected function or functions, press s.

TRACE, ZOOM instructions, and CALC operations

display the graph automatically. As the TI-82 STATS 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 Í to pause; then press Í to resume.

• Press É to stop; then press s to redraw.

Smart Graph is a TI-82 STATS feature that redisplays the last graph immediately when you press s, 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-82 STATS will replot the graph based on new values when you press s.

• 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

Function Graphing 3.15

Displaying Graphs (continued)

Overlaying Functions on a Graph

Graphing a Family of Curves

On the TI-82 STATS, you can graph one or more new functions without replotting existing functions. For example, store

sin(X)

to Y1 in the Y= editor and press s. Then store cos(X) to Y2 and press s again. The function Y2 is graphed on top of Y1, the original function.

If you enter a list (Chapter 11) as an element in an expression, the TI-82 STATS 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.

3.16 Function Graphing

Exploring Graphs with the Free-Moving Cursor

Free-Moving Cursor

Graphing Accuracy

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 ‘ or Í. 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 r (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.

Free-moving cursor “on” the curve

Function Graphing 3.17

(

Exploring Graphs with TRACE

Beginning a Trace

Moving the Trace Cursor

Use TRACE to move the cursor from one plotted point to the next along a function. To begin a trace, press r. If the graph is not displayed already, press r to display it. The trace cursor is on the first selected function in the the middle displayed at the bottom of the screen if selected. The the screen, if

To move the TRACE cursor . . . do this:

X value on the screen. The cursor coordinates are

CoordOn format is

Y= expression is displayed in the top-left corner of

ExprOn format is selected.

Y= editor, at

. . . to the previous or next plotted point, press | or ~.

. . . five plotted points on a function affects this),

Xres

ress y | or y

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

then press Í.

. . . from one function to another, press } or †.

When the trace cursor moves along a function, the calculated from the undefined at an

X value; that is, Y=Yn(X). If the function is

X value, the Y value is blank.

Trace cursor on the curve

Y value is

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.

Moving the Trace Cursor from Function to Function

To move the trace cursor from function to function, press † and }. The cursor follows the order of the selected functions in the

Y= editor. The trace cursor moves to each function at the same X

value. If ExprOn format is selected, the expression is updated.

3.18 Function Graphing

Moving the Trace Cursor to Any Valid X Value

To move the trace cursor to any valid X value on the current function, enter the value. When you enter the first digit, an

prompt and the number you entered are displayed in the bottomleft 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 Í to move the cursor.

Note: This feature does not apply to stat plots.

Panning to the Left or Right

Quick Zoom

Leaving and Returning to TRACE

Using TRACE in a Program

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 Í 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

When you leave and return to displayed in the same location it was in when you left

TRACE.

TRACE, the trace cursor is

TRACE,

unless Smart Graph has replotted the graph (page 3.15).

On a blank line in the program editor, press r. 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 Í to resume program execution.

Function Graphing 3.19

Exploring Graphs with the ZOOM Instructions

ZOOM Menu

Zoom Cursor

ZBox

To display the ZOOM menu, press q. You can adjust the viewing window of the graph quickly in several ways. All

ZOOM instructions are accessible from programs.

ZOOMMEMOR

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 on the graph becomes the zoom cursor ( the free-moving cursor (

To define a new viewing window using

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

+), a smaller version of

+).

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 Í. 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 Í, press ‘.

4. When you have defined the box, press Í to replot the graph.

To use ZBox to define another box within the new graph, repeat steps 2 through 4. To cancel

3.20 Function Graphing

ZBox, press ‘.

Zoom In, Zoom Out

Zoom In magnifies the part of the graph that surrounds the

cursor location. graph, centered on the cursor location. The

Zoom Out displays a greater portion of 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 Í. The TI-82 STATS 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 Í.

• 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 Í.

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

ZSquare

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=L4.7 Ymin=L3.1 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 makes the graph of a circle look like a circle.

@X=@Y, which

Xscl and Yscl

remain unchanged. The midpoint of the current graph (not the intersection of the axes) becomes the midpoint of the new graph.

Function Graphing 3.21

Exploring Graphs with the ZOOM Instructions (cont.)

ZStandard

ZTrig

ZInteger

ZoomStat

ZStandard replots the functions immediately. It updates the

window variables to the standard values shown below.

Xmin=L10 Ymin=L10 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=L(47à24)p Ymin=L4 Xmax=(47à24)p Ymax=4 Xscl=p/2 Yscl=1

ZInteger

shown below. To use

redefines the viewing window to the dimensions

ZInteger, move the cursor to the point that

you want to be the center of the new window, and then press Í;

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

ZoomFit replots the functions immediately. ZoomFit

recalculates YMin and YMax to include the minimum and maximum

XMin and XMax. XMin and XMax are not changed.

3.22 Function Graphing

Y values of the selected functions between the current

Using ZOOM MEMORY

ZOOM MEMORY Menu

ZPrevious

ZoomSto

ZoomRcl

To display the ZOOM MEMORY menu, press q ~.

ZOOMMEMOR

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

ZXmax, ZXscl, ZYmin, ZYmax, ZYscl, and ZXres.

ZOOM variables ZXmin,

These variables apply to all graphing modes. For example, changing the value of

Par mode.

ZoomRcl graphs the selected functions in a user-defined

ZXmin in Func mode also changes it in

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.

Function Graphing 3.23

Using ZOOM MEMORY (continued)

ZOOM FACTORS

Checking XFact and YFact

Changing XFact and YFact

Using ZOOM MEMORY Menu Items from the Home Screen or a Program

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 In or Zoom Out

around a point.

To display the the current values for

ZOOM FACTORS screen, where you can review

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.

3.24 Function Graphing

Texas instruments TI-82 Stats User Manual

Specifications and Main Features

Frequently Asked Questions

User Manual

Important

Table of Contents

Getting Started: Do This First!

TI-82 STATS Keyboard

TI-82 STATS 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-82 STATS Features

Turning On and Turning Off the TI-82 STATS

Setting the Display Contrast

The Display

Entering Expressions and Instructions

TI-82 STATS Edit Keys

Setting Modes

Using TI-82 STATS Variable Names

Storing Variable Values

Recalling Variable Values

ENTRY (Last Entry) Storage Area

Ans (Last Answer) Storage Area

TI-82 STATS Menus

VARS and VARS Y.VARS Menus

Equation Operating System (EOSé)

Error Conditions

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