Chapter 9.6, Problem 38E

To determine

To calculate: To graph the polar equationusing graphing utility and then describe the viewing window

Explanation of Solution

Given information: Polar equation is $r=-\cos 2\theta$

Formula Used:

Lima cons are the graph of below polar equations:

  $\begin{array}{l}r=a\pm b\cos \theta \\ r=a\pm b\sin \theta \end{array}$

When $\frac{a}{b}<1$ , polar equation represents limacon with inner loop

When $\frac{a}{b}=1$ , polar equation represents Cardiod

When $1<\frac{a}{b}<2$ , polar equation represents Dimpled limacon

When $\frac{a}{b}=2$ , polar equation represents convex limacon

Calculation:

Polar equation is given as

  $r=-\cos 2\theta$

Equation is of the form $r=a\cos \left(n\theta \right)$ , thus the curve is a rose curve

Since $n$ is even, thus number of petals in curve is $2n$

Hence, number of curve is $4$

Graph is a rose curve with four petals

Plotting the graph using graphing utility as follows:

  

Here, $0\le \theta \le 2\pi$

Conclusion:

Hence, graph is sketched.