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