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 $ 0 \leq r \leq 1$ implies that the region is inside or on the circle of radius 1 about the pole.
The condition $ \pi/4 \leq \theta \leq 3\pi/4 $ implies a sector between the angles $\pi/4$ and $3\pi/4$, including the borders. Since r is positive, the symmetric points are not part of the region.
