## Precalculus (6th Edition) Blitzer

a. not necessarily symmetric with respect to the polar axis. b. symmetric with respect to the line $\theta=\frac{\pi}{2}$. c. not necessarily symmetric with respect to the pole.
a. To test the symmetry with respect to the polar axis, replace $(r,\theta)$ with $(r,-\theta)$; we have $r=3sin(-\theta)$ or $r=-3sin(\theta)$. Thus the equation is not necessarily symmetric with respect to the polar axis. b. To test the symmetry with respect to the line $\theta=\frac{\pi}{2}$, replace $(r,\theta)$ with $(-r,-\theta)$; we have $-r=3sin(-\theta)$ or $r=3sin(\theta)$. Thus the equation is symmetric with respect to the line $\theta=\frac{\pi}{2}$. c. To test the symmetry with respect to the pole, replace $(r,\theta)$ with $(-r,\theta)$; we have $-r=3sin(\theta)$ or $r=-3sin(\theta)$. Thus the equation is not necessarily symmetric with respect to the pole.