## Precalculus (6th Edition) Blitzer

The graph is symmetric only with respect to the line $\theta =\frac{\pi }{2}$.
We make the substitutions as follows: (a) $\theta \to - \theta$ :$$r= \sin (- \theta ) \quad \Rightarrow \quad r=-\sin \theta$$ (b) $r \to -r, \quad \theta \to -\theta$ :$$-r = \sin (-\theta ) \quad \Rightarrow \quad r= \sin \theta$$ (c) $r \to -r$ :$$-r = \sin \theta \quad \Rightarrow \quad r=-\sin \theta$$