Find the rectangular representation of the given polar point.

Question

Quizplus · Accepted Answer

The rectangular representation of a polar point is given by $x=r\cos	heta$ and $y=r\sin	heta$ where $r$ is the distance from the origin and $	heta$ is the angle measured counterclockwise from the positive $x-$axis. Converting the given polar point to rectangular form gives:

$x=11\cos\left(\frac{\pi}{2}+\frac{\pi}{4}ight)=-11\sin\frac{\pi}{4}=-\frac{11}{\sqrt{2}}$
$y=11\sin\left(\frac{\pi}{2}+\frac{\pi}{4}ight)=11\cos\frac{\pi}{4}=\frac{11}{\sqrt{2}}$

Therefore, the rectangular form is $-\frac{11}{\sqrt{2}}+ \frac{11i}{\sqrt{2}}$, which corresponds to choice C.

Find the Rectangular Representation of the Given Polar Point