Answer
The point has coordinates $(1, -\sqrt 3)$ in the rectangular coordinate system.
Work Step by Step
The point $(x,y)$ in the rectangular coordinate system can be expressed as:
$x=r \ \cos(\theta)$, $y=r \ \sin(\theta) ...(1)$
Here, we have $r=-2$ and $ \theta= \dfrac{2\pi}{3}$
Plug these values in equation (1) to obtain:
$x=(-2) \cos(\dfrac{2\pi}{3})=(-2)(\dfrac{-1}{2})=1 \\
y=(-2) \sin(\dfrac{2\pi}{3})=(-2)(\dfrac{\sqrt 3}{2})=- \sqrt 3$
Therefore, the point has coordinates $(1, -\sqrt 3)$ in the rectangular coordinate system.
