Answer
$(-3\sqrt 3, 3)$
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 $r=6$ and $ \theta= 150^{\circ}$
Plug these values in equation (1) to obtain:
$x=(6) \cos(150^{\circ})=(6)(-\dfrac{\sqrt 3}{2})=-3\sqrt 3 \\
y=(6) \sin(150^{\circ})=(6)(\dfrac{1}{2})=3$
Therefore, the point has coordinates $(-3\sqrt 3, 3)$ in the rectangular coordinate system.
