Answer
Graph:
Work Step by Step
Plotting the points $(r,\theta)$:
$r$ is the directed distance of the point from the pole.
$\theta$ defines the angle of the ray on which the point lies,
- remains $\theta$ when $r$ is positive
- becomes $\theta\pm\pi$ when $r$ is negative
The $r= -1$ indicates that this region is a part of the circle around the pole, with radius 1, and points that are represented terminate in opposite quadrants of $\theta's$ terminal sides.
The angle ranges form $0$ to $\pi$, which covers the upper part of the circle, but because r is negative, we take the points in the opposite quadrants, that is, the lower semicircle is the graph.
