Find the rectangular coordinates of the point whose polar coordinates are given.

Question

Quizplus · Accepted Answer

To convert from polar coordinates to rectangular coordinates, use the formulas:
$x=r\cos(	heta)$
$y=r\sin(	heta)$
In this case, $r=11$, and $	heta=\frac{5\pi}{6}$. Plugging in these values, we get:
$x=11\cos\left(\frac{5\pi}{6}ight)=11\left(-\frac{\sqrt{3}}{2}ight)=-\frac{11\sqrt{3}}{2}$
$y=11\sin\left(\frac{5\pi}{6}ight)=11\left(\frac{1}{2}ight)=\frac{11}{2}$
Therefore, the rectangular coordinates are $\left(-\frac{11\sqrt{3}}{2},\frac{11}{2}ight)$, which corresponds to choice D.

Find the Rectangular Coordinates of the Point Whose Polar Coordinates