Answer
See image:
Work Step by Step
Conversion formulas: $\left\{\begin{array}{ll}
(x,y)=(r\cos\theta,r\sin\theta) & \\
r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x}
\end{array}\right.$
$r$ is the distance of the point from the pole.
$r=1$ defines all points at a distance of 1 unit from the pole.
$r=2$ defines all points at a distance of 2 units from the pole.
So, $1 \leq r \leq 2$ describes all points on or between these circles.
In Cartesian coordinates, the region is between the circles
$x^{2}+y^{2} = 1$ and $x^{2}+y^{2} = 4$
