Display the graph of r = 4sin 3 on a calculator, using (a) The polar curve mode, (b) The parametric curve mode. (See Example 6).

Display the graph of r = 4sin 3θ on a calculator, using 

(a) The polar curve mode, 

(b) The parametric curve mode. (See Example 6).

Data from Example 6

View the graph of r = 1 − 2cosθ  on a calculator.
Using the mode feature, a polar curve is displayed using the polar graph option or the parametric graph option, depending on the calculator. (Review the manual for the calculator.) The graph displayed will be the same with either method.

With the polar graph option, the function is entered directly. The values for the viewing window are determined by settings for x, y and the angles θ  that will be used. These values are set in a manner similar to those used for parametric equations. With the parametric graph option, to graph r = f(θ), we note that x = r cosθ and y = r sinθ . This tells us that

Thus, for r = 1 − 2cos, by using

the graph can be displayed, as shown in Fig. 21.117.

x = f(0)cos0 y = f(0)sin0