Chapter 7.2, Problem 17PE

For Exercises 15-22, determine whether the tests for symmetry in Table 7-2 detect symmetry with respect to

a. The polar axis. Replace $\left(r,\theta \right)$ by $\left(r,-\theta \right)$

b. The line $\theta =\frac{\pi }{2}$ . Replace $\left(r,\theta \right)$ by $\left(r,\pi -\theta \right)$

c. The pole. Replace $\left(r,\theta \right)$ by $\left(-r,\theta \right)$

Otherwise, indicate that the test is inconclusive.

$r=3\cos 3\theta$