Answer
Graph:
Work Step by Step
Plotting 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 points $(r,\theta)$ of the region are such that:
The angle $2\pi/3$ defines a line through the pole (the origin) with slope $\tan( 2\pi/3) =-\sqrt{3}.$
$2\pi/3$ terminates in the 2nd quadrant, but the directed distance r is negative, so only points in the opposite (4th) quadrant are involved.
Also, $r \leq -2$ means that these points (on the ray are at least two units away from the pole).
The graph is the ray with initial point on the circle of radius 2, quadrant IV.
