Texas Instruments TI-92 Getting Started page 33

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Graphing Technology Guide: TI-92

Figure 5.90: Parametric graph of x = cos

t and y = sin

You may Zoom and Trace along parametric graphs just as you did with function graphs. However, unlike with

function graphs, the cursor will not move to values outside of the t range, so

will not work when t = 0, and

will not work when t = 2π. As you trace along this graph, notice that the cursor moves in the counterclockwise

direction as t increases.

5.8.2 Rectangular-Polar Coordinate Conversion: The Angle sub-menu of the MATH menu provides a function for

converting between rectangular and polar coordinate systems. These functions use the current angle measure setting,

so it is a good idea to check the default angle measure before any conversion. Of course, you may override the

current angle measure setting, as explained in Section 5.4.1. For the following examples, the TI-92 is set to radian

measure.

Given the rectangular coordinates (x, y) = (4, –3), convert to polar coordinates (r, θ) in the Home screen by pressing

2nd MATH 2[Angle] 5[R ►Pr(] 4 , (-) 3 ) ENTER. The value of r is displayed; now press 2nd MATH 2[Angle]

6[R ►Pθ(] 4, (-) 3 ) ENTER to display the value of θ (Figure 5.91). The polar coordinates are approximately (5, –

0.6435).

Suppose (r, θ) = (3, π). Convert to rectangular coordinates (x, y) by pressing 2nd MATH 2[Angle] 3[P ► Rx(] 3 ,

2nd π ) ENTER. The x-coordinate is displayed. Press 2nd MATH 2[Angle] 4[P►Ry(] 3 , 2nd π) ENTER to

display the y-coordinate (Figure 5.92). The rectangular coordinates are (–3, 0).

Figure 5.91: Rectangular to polar coordinates

Figure 5.92: Polar to rectangular coordinates

5.8.3 Graphing Polar Equations: The TI-92 graphs polar functions in the form r = f (θ) . In the Graph line of the

MODE menu, select POLAR for polar graphs. You may now graph up to ninety nine polar functions at a time. Be

sure that the angle measure has been set to whichever you need, RADIAN or DEGREE. Here we will use radian

measure.

For example, to graph r = 4 sinθ , press

Y= for the polar graph editing screen. Then enter the expression 4 sin θ

by pressing 4 SIN θ) ENTER. The θ key is on the lower right of the keyboard, near the ENTER key.

Choose a good viewing rectangle and an appropriate interval and increment for θ. In Figure 5.93, the viewing

rectangle is roughly "square" and extends from –14 to 14 horizontally and from –6 to 6 vertically. (Refer back to the

Technology Tip in Section 5.2.4.)