Answer
The point in rectangular coordinates is $(3\sqrt{6},-3\sqrt{2})$
Work Step by Step
$(6\sqrt{2}, 11\pi/6)$
The point has $r=6\sqrt{2}$ and $\theta=\dfrac{11\pi}{6}$. 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 $y$:
$x=r\cos\theta$
$x=(6\sqrt{2})\cos\Big(\dfrac{11\pi}{6}\Big)=(6\sqrt{2})\Big(\dfrac{\sqrt{3}}{2}\Big)=3\sqrt{6}$
$y=r\sin\theta$
$y=(6\sqrt{2})\sin\Big(\dfrac{11\pi}{6}\Big)=(6\sqrt{2})\Big(-\dfrac{1}{2}\Big)=-3\sqrt{2}$
The point in rectangular coordinates is $(3\sqrt{6},-3\sqrt{2})$
