Answer
The graph is symmetric with respect to the line $\theta =\frac{\pi }{2}$.
Work Step by Step
We look for symmetry by making the following substitutions:
(a) $\theta \to - \theta$ :$$r=\sin \frac{(- \theta )}{2} \quad \Rightarrow \quad r=-\sin \frac{ \theta }{2}$$Thus, the graph does not necessarily have symmetry with respect to the polar axis.
(b) $r \to -r, \quad \theta \to -\theta$ :$$-r =\sin \frac{(-\theta )}{2} \quad \Rightarrow \quad r= \sin \frac{\theta }{2}$$Thus, the graph is symmetric with respect to the line $\theta=\frac{\pi}{2}$.
(c) $r \to -r$ :$$-r =\sin \frac{ \theta }{2}\quad \Rightarrow \quad r=-\sin \frac{ \theta }{2}$$Thus, the graph does not necessarily have symmetry with respect to the pole.
