Chapter 8.2, Problem 15PE

For Exercises 15-22, determine whether the tests for symmetry in Table 8-2 detect symmetrywith 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.

$r^2=16\cos 2\theta$