Answer
The graph is symmetric with respect to the line $\theta = \frac{\pi }{2}$.
See the graph below:
Work Step by Step
We look for symmetry by making the following substitutions:
(a) $\theta \to - \theta$ :$$r=4\sin 3(- \theta ) \quad \Rightarrow \quad r=-4\sin 3 \theta$$Thus, the graph does not necessarily have symmetry with respect to the polar axis.
(b) $r \to -r, \quad \theta \to -\theta$ :$$-r =4\sin 3 (-\theta ) \quad \Rightarrow \quad r=4\sin 3 \theta$$Thus, the graph is symmetric with respect to the line $\theta=\frac{\pi}{2}$.
(c) $r \to -r$ :$$-r =4\sin 3 \theta \quad \Rightarrow \quad r=-4\sin 3 \theta$$Thus, the graph does not necessarily have symmetry with respect to the pole.
