Chapter 7, Problem 12T

For Exercises 11-12, 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.

$r=-7\sin \theta$