# What is the Cartesian form of (-4,(11pi)/4))?

May 26, 2017

In Cartesian coordinates, $\left(- 4 , \frac{11 \pi}{4}\right)$ = $\left(2 \sqrt{2} , - 2 \sqrt{2}\right)$

#### Explanation:

If you consider that $x = r \cos \Theta$ and $y = r \sin \Theta$, you can plug in those values from that polar coordinate to find $\left(x , y\right)$.

On the unit circle, $\theta = \frac{11 \pi}{4}$ is equal to $\frac{3 \pi}{4}$.

When you plug it in, $x = - 4 \cos \left(\frac{3 \pi}{4}\right)$ and $y = - 4 \sin \left(\frac{3 \pi}{4}\right)$.

More simplified, $x = - 4 \cdot - \frac{\sqrt{2}}{2}$ and $y = - 4 \cdot \frac{\sqrt{2}}{2}$.

Once everything is finally simplified, you will get $x = 2 \sqrt{2}$ and $y = - 2 \sqrt{2}$