Answer
See image:
Work Step by Step
Conversion formulas: $\left\{\begin{array}{ll}
(x,y)=(r\cos\theta,r\sin\theta) & \\
r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x}
\end{array}\right.$
The points $(r,\theta)$ of the region are such that:
The angle $\pi/3$ terminates in the 1st quadrant, and
defines a line through the pole (the origin) with slope $\tan( \pi/3) =\sqrt{3}$
(In cartesian coordinates, $y=\sqrt{3}x$ ).
The directed distance r is partly negative, from -1 to 0,
so some points in the opposite (3rd) quadrant are involved. These are points on the line that are at a distance 1 or less from the pole.
For the rest of the values of r, the points represented lie on the line segment from the pole to the point that is at a distance of 3 units from the pole.
