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) $\theta \to - \theta$ :$$r\cos(- \theta )=-3 \quad \Rightarrow \quad r\cos \theta =-3$$Thus, the graph is symmetric with respect to the polar axis.
(b) $r \to -r, \quad \theta \to -\theta$ :$$(-r)\cos (-\theta ) =-3 \quad \Rightarrow \quad r\cos \theta =3$$Thus, the graph does not necessarily have symmetry with respect to the line $\theta=\frac{\pi}{2}$.
(c) $r \to -r$ :$$(-r)\cos \theta =-3 \quad \Rightarrow \quad r\cos \theta =3$$Thus, the graph does not necessarily have symmetry with respect to the pole.
