Answer
The point in rectangular coordinates is $\Big(\dfrac{\sqrt{3}}{2},\dfrac{3}{2}\Big)$
Work Step by Step
$(\sqrt{3},-5\pi/3)$
The point has $r=\sqrt{3}$ and $\theta=-\dfrac{5\pi}{3}$. The formulas for converting polar to rectangular coordinates are $x=r\cos\theta$ and $y=r\sin\theta$
Substitute the known values into the formulas to obtain $x$ and $y$:
$x=r\cos\theta$
$x=(\sqrt{3})\cos\Big(-\dfrac{5\pi}{3}\Big)=(\sqrt{3})\Big(\dfrac{1}{2}\Big)=\dfrac{\sqrt{3}}{2}$
$y=r\sin\theta$
$y=(\sqrt{3})\sin\Big(-\dfrac{5\pi}{3}\Big)=(\sqrt{3})\Big(\dfrac{\sqrt{3}}{2}\Big)=\dfrac{(\sqrt{3})^{2}}{2}=\dfrac{3}{2}$
The point in rectangular coordinates is $\Big(\dfrac{\sqrt{3}}{2},\dfrac{3}{2}\Big)$
