Answer
$(\dfrac{5}{2}, \dfrac{-5 \sqrt 3}{2})$
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 $r=5$ and $ \theta= 300^{\circ}$
Plug these values in equation (1) to obtain:
$x=(5) \cos(300^{\circ})=(5)(\dfrac{\sqrt 1}{2})=\dfrac{5}{2} \\
y=(5) \sin(300^{\circ})=(5)(\dfrac{-\sqrt 3}{2})=\dfrac{-5 \sqrt 3}{2}$
Therefore, the point has coordinates $(\dfrac{5}{2}, \dfrac{-5 \sqrt 3}{2})$ in the rectangular coordinate system.
