Answer
The point in rectangular coordinates is $\Big(2\sqrt{3},2\Big)$
Work Step by Step
$(4,\pi/6)$
The point has $r=4$ and $\theta=\dfrac{\pi}{6}$. The formulas for converting polar to rectangular coordinates are $x=r\cos\theta$ and $y=r\sin\theta$.
Substitute the known values into the formula to obtain $x$ and $y$:
$x=r\cos\theta$
$x=(4)\cos\Big(\dfrac{\pi}{6}\Big)=(4)\Big(\dfrac{\sqrt{3}}{2}\Big)=2\sqrt{3}$
$y=r\sin\theta$
$y=(4)\sin\Big(\dfrac{\pi}{6}\Big)=(4)\Big(\dfrac{1}{2}\Big)=2$
The point in rectangular coordinates is $\Big(2\sqrt{3},2\Big)$
