Texas Instruments TI-82 User Manual

26
G
RAPHING
T
ECHNOLOGY
G
UIDE
: TI-82
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Figure 2.71: Sequence mode
Of course, you could use the explicit formula for the n-th term of an arithmetic sequence, t
n
= a + (n – 1)d. First
enter values for the variables a, d, and n, then evaluate the formula by pressing ALPHA A + ( ALPHA N – 1 )
ALPHA D ENTER. For a geometric sequence whose n-th term is given by t
n
= a · r
n – 1
, enter values for the
variables a, r, and n, then evaluate the formula by pressing ALPHA A ALPHA R ^ (ALPHA N – 1 ) ENTER.
To use the explicit formula in Seq MODE, make u
n
= 7 + (n – 1) ·4 by pressing Y= and then 7 + (2nd n – 1 ) × 4.
Once more, calculate u
18
by pressing 2nd Y-
VARS
4 1 ( 18 ) ENTER.
There are more instructions for using sequence mode in the TI-82 manual.
2.7.3 Sums of Sequences: Calculate the sum
12
1
4(0.3)
n
n
=
∑
on the TI-82 by pressing 2nd LIST ► 5 2nd LIST 5 4 ×
.3 ^ ALPHA N , ALPHA N , 1 , 12 , 1) ENTER. You should get 1.714284803. The format of this command is
sum seq(expression, variable, begin, end, increment).
2.8 Parametric and Polar Graphs
2.8.1 Graphing Parametric Equations: The TI-82 plots up to six pairs of parametric equations as easily as it plots
functions. Just use the MODE menu (Figure 2.1), go to the fourth line from the top, and change the setting to Par.
Be sure, if the independent parameter is an angle measure, that MODE is set to whichever you need, Rad or Deg.
Figure 2.72: Parametric Y= menu Figure 2.73: Parametric WINDOW menu
For example, here are the keystrokes needed to graph the parametric equations x = cos
3
t and y = sin
3
t. First check
that angles are currently being measured in radians. Change to parametric mode and press Y= to examine the new
parametric equation menu (Figure 2.72). Enter the two parametric equations for X
1T
and Y
1T
by pressing ( COS
X,T,θ
) ^ 3 ENTER ( SIN
X,T,θ
) ^ 3 ENTER. Now, when you press the variable key
X,T,θ
, you get a T because the
calculator is in parametric mode.

Texas Instruments TI-82 Specifications

General

Type	Graphing calculator
Processor	Zilog Z80, 6 MHz
RAM	28 KB
ROM	128 KB
Programming	TI-BASIC
Display	Monochrome LCD
Power	4 AAA batteries

Summary

2.1 Getting Started with the TI-82

Basics

Initial setup, power, contrast, and display settings for the TI-82 calculator.

Editing

How to edit previous calculations and correct entries using cursor keys.

The MATH Menu

2.2 Functions and Graphs

Evaluating Functions

Entering and evaluating functions for calculations and tables.

Functions in a Graph Window

TRACE

ZOOM

Techniques for enlarging or reducing graph views for better analysis.

Relative Minimums and Maximums

Finding and approximating local extrema of functions on a graph.

2.3 Solving Equations and Inequalities

Intercepts and Intersections

Locating x-intercepts and points where graphs cross.

Solving Equations by Graphing

Solving Systems by Graphing

2.4 Trigonometry

Degrees and Radians

Setting angle modes (degrees/radians) for trigonometric functions.

2.5 Scatter Plots

Entering Data

Plotting Data

Regression Line

Calculating and graphing the line of best fit for data.

Exponential Growth Model

2.7 Sequences

Iteration with the ANS Key

Repeating calculations using the ANS variable.

Arithmetic and Geometric Sequences

2.10 Programming

Entering a Program

Creating and writing programs on the TI-82.

Executing a Program

Running stored programs on the calculator.

2.11 Differentiation

Limits

Numerical Derivatives

Calculating numerical approximations of derivatives.

Newton's Method

2.12 Integration

Approximating Definite Integrals

Numerically approximating definite integrals.

Areas