Convert the polar equation to rectangular form.

Question

Convert the polar equation to rectangular form. ​  ​

Quizplus · Accepted Answer

To convert a polar equation to rectangular form, we use the following formulas:
$x=r\cos	heta$
$y=r\sin	heta$
where $r$ and $	heta$ are given in the polar equation. 
In this case, $r=11$ and $	heta= \frac{\pi}{4}$. Substituting these values into the formulas, we get:
$x=11\cos\left(\frac{\pi}{4}ight)=11\cdot\frac{\sqrt{2}}{2}=\frac{11\sqrt{2}}{2}$
$y=11\sin\left(\frac{\pi}{4}ight)=11\cdot\frac{\sqrt{2}}{2}=\frac{11\sqrt{2}}{2}$
Therefore, the rectangular form is $(x,y)=\left(\frac{11\sqrt{2}}{2},\frac{11\sqrt{2}}{2}ight)$ or $(x,y)=\left(-\frac{11\sqrt{2}}{2},-\frac{11\sqrt{2}}{2}ight)$, depending on which quadrant the point is in. Simplifying the choices, we can see that only option D matches these values, so the answer is D.

Convert the Polar Equation to Rectangular Form