Answer
The point in rectangular coordinates is $(-3,3\sqrt{3})$
Work Step by Step
$(6,2\pi/3)$
The point has $r=6$ and $\theta=\dfrac{2\pi}{3}$. 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 $y$:
$x=r\cos\theta$
$x=(6)\cos\Big(\dfrac{2\pi}{3}\Big)=(6)\Big(-\dfrac{1}{2}\Big)=-3$
$y=r\sin\theta$
$y=(6)\sin\Big(\dfrac{2\pi}{3}\Big)=(6)\Big(\dfrac{\sqrt{3}}{2}\Big)=3\sqrt{3}$
The point in rectangular coordinates is $(-3,3\sqrt{3})$
