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 on r implies that the region is between or on the circles of radius 1 and radius 2 about the pole.
The condition on $\theta$ implies a sector between the angles $-\pi/2$ and $\pi/2$, including the borders (the right half of the area between the circles).
Since r can be only positive, the symmetric points are not part of the region.
So, only the right side of the area between circles makes up the region.
