Answer
The graph does not necessarily have symmetry with respect to the polar axis, the line $\theta =\frac{\pi }{2}$, or the pole.
Work Step by Step
We look for symmetry by making the following substitutions:
(a) $\theta \to - \theta$ :$$r=4\sin (-\theta ) + 4\cos (- \theta ) \quad \Rightarrow \quad r=- 4\sin \theta +4\cos \theta$$Thus, the graph does not necessarily have symmetry with respect to the polar axis.
(b) $r \to -r, \quad \theta \to -\theta$ :$$-r =4\sin (-\theta )+4\cos (-\theta ) \quad \Rightarrow \quad r=4\sin \theta -4\cos \theta$$Thus, the graph does not necessarily have symmetry with respect to the line $\theta=\frac{\pi}{2}$.
(c) $r \to -r$ :$$-r =4\sin \theta +4\cos \theta \quad \Rightarrow \quad r=-4\sin \theta - 4\cos \theta$$Thus, the graph does not necessarily have symmetry with respect to the pole.
