Answer
See image:
Work Step by Step
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.