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 condition $-1 \leq r \leq 1$ implies that the region is inside or on the circle of radius 1 about the pole.
The condition on $\theta$ implies a sector between the angles $-\pi/4$ and $\pi/4$, including the borders.
Since r can be negative and positive, the symmetric points are also part of the region.
So, we have two sectors that make up the region.
