Texas Instruments TI-82 Manual page 27

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Also look at the new WINDOW menu (Figure 2.73). In the standard window, the values of T go from 0 to 2π in

steps of

= .1309, with the view from –10 to 10 in both directions. But here the viewing rectangle has been

changed to extend from –2 to 2 in both directions. Press GRAPH to see the parametric graph (Figure 2.74).

You may ZOOM and TRACE along parametric graphs just as you did with function graphs. As you trace along this

graph, notice that the cursor moves in the counterclockwise direction as T increases.

2.8.2 Rectangular-Polar Coordinate Conversion: The 2nd ANGLE menu provides functions for converting

between rectangular and polar coordinate systems. These functions use the current MODE settings, so it is a good

idea to check the default angle measure before any conversion. Of course, you may use the MATH menu to override

the current angle measure setting, as explained in Section 2.4.1. For the following examples, the TI-82 is set to

radian measure.

Given rectangular coordinates (x, y) = (4, –3), convert from these rectangular coordinates to polar coordinates (r, θ)

by pressing 2nd ANGLE 5 4 , (-) 3 ) ENTER to display the value of r. The value of θ is displayed after you press

2nd ANGLE 6 4, (-) 3) ENTER.

Suppose (r, θ) = (3, π). To convert from these polar coordinates to rectangular coordinates (x, y) , press 2nd

ANGLE 7 3 , 2nd π) for the x-coordinate; next press 2nd ANGLE 8 3 , 2nd π) ENTER to display the y-

coordinate.

2.8.3 Graphing Polar Equations: The TI-82 graphs a polar function in the form r = f (θ). In the fourth line of the

MODE menu, select Pol for polar graphs. You may now graph up to six different polar functions at a time.

For example, to graph r = 4sin θ, press Y= for the polar graph editing screen. Then enter the expression 4sin θ for r1

by pressing 4 sin

; note that the

X,T,θ

appropriate interval and increment for θ. In Figure 2.76, the viewing rectangle is roughly "square" and extends from

–6 to 6 horizontally and from –4 to 4 vertically.

RAPHING

ECHNOLOGY

Figure 2.74: Parametric graph of x = cos

Figure 2.75: Coordinate conversions

key produces θ in polar mode. Choose a good viewing rectangle and an

X,T,θ

: TI-82

UIDE

t and y = sin