Answer
Graph:
Work Step by Step
$\left\{\begin{array}{ll}
(x,y)=(r\cos\theta,r\sin\theta) & \\
r^{2}=x^{2}+y^{2}, & \tan\theta=\frac{y}{x}
\end{array}\right.$
$r$ is the 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 of the region are such that
- the directed distance r is positive or zero,
- the angle is any angle between $0$ and $\pi/6$ (1st quadrant)
$\theta=0$ is the +x axis ray,
$\theta=\pi/6$ is the ray on the line $y=(\displaystyle \tan\frac{\pi}{6})x$, from the origin into the 1st quadrant.
