Answer
The graph is symmetric with respect to the polar axis.
Work Step by Step
We look for symmetry by making the following substitutions:
(a) $\theta \to - \theta$ :$$r=\frac{1}{1-\cos (-\theta )} \quad \Rightarrow \quad r=\frac{1}{1-\cos \theta }$$Thus, the graph is symmetric with respect to the polar axis.
(b) $r \to -r, \quad \theta \to -\theta$ :$$-r =\frac{1}{1-\cos (-\theta )} \quad \Rightarrow \quad r=-\frac{1}{1-\cos \theta }$$Thus, the graph does not necessarily have symmetry with respect to the line $\theta=\frac{\pi}{2}$.
(c) $r \to -r$ :$$-r =\frac{1}{1-\cos \theta } \quad \Rightarrow \quad r=-\frac{1}{1-\cos \theta }$$Thus, the graph does not necessarily have symmetry with respect to the pole.
