Answer
$(1,-\sqrt3)$
Work Step by Step
By definition: $x=r\cdot \cos(\theta)$ and $y=r\cdot \sin(\theta)$.
Here $r=-2, \theta=\frac{2\pi}{3}$.
Hence, after plugging these in:
$x=-2\cdot \cos(\frac{2\pi}{3})=-2\cdot(-0.5)=1$
$y=-2\cdot \sin(\frac{2\pi}{3})=-2\cdot\frac{\sqrt3}{2}=-\sqrt3$
The point has coordinates $(1,-\sqrt3)$ in the rectangular coordinate system.