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 (a ring, the area between two concentric circles).
It also implies that r can take negative and positive values.
The condition on $\theta$ implies a sector between the angles $0$ and $\pi/2$, including the borders (the upper right quarter of the ring).
Since r can also be negative,, the symmetric points are also part of the region. So, the lower left quarter of ring is a part of the region as well.
