# What is the Cartesian form of (2,(3pi)/4)?

Jan 5, 2017

$\left(- \sqrt{2} , \sqrt{2}\right)$

#### Explanation:

The Cartesian equivalent of the polar coordinate $\left(r , \theta\right)$ is $\left(r \cos \theta , r \sin \theta\right)$

So, $\left(2 , \frac{3 \pi}{4}\right)$ is equivalent to:

$\left(2 , \frac{3 \pi}{4}\right) \rightarrow \left(2 \cos \left(\frac{3 \pi}{4}\right) , 2 \sin \left(\frac{3 \pi}{4}\right)\right)$
$\text{ } = \left(2 \left(- \frac{\sqrt{2}}{2}\right) , 2 \left(\frac{\sqrt{2}}{2}\right)\right)$
$\text{ } = \left(- \sqrt{2} , \sqrt{2}\right)$