Answer
Symmetric about the y-axis.
Symmetric about the x-axis.
Symmetric about the origin.
.
Work Step by Step
Testing for symmetry:
- about the x-axis: $(r,\theta)$ on the graph $\Rightarrow (r, -\theta)$ or $(-r, \pi-\theta)$ on the graph.
- about the y-axis: $(r,\theta)$ on the graph $\Rightarrow (r, \pi-\theta)$ or $(-r, -\theta)$ on the graph.
- about the origin: $(r,\theta)$ on the graph $\Rightarrow (-r, \theta)$ or $(r, \theta+\pi)$ on the graph.
- about the x-axis:
$\sin(\pi-\theta)=\sin(\theta)=r^{2},\quad(r, \pi-\theta)$ is on the graph
Symmetric about the x-axis.
- about the y-axis:
$-\sin(\pi-\theta)=-\sin(\theta)=r^{2}=(-r)^{2},\quad(-r, \pi-\theta)$ is on the graph.
Symmetric about the y-axis.
So, the graph is also symmetric about the origin.
To graph, select a few values for $\theta \in[\pi,3\pi/2]$ and calculate $r=\sqrt{-\sin\theta}.$
Use the symmetries.
See the resulting image.
