# What is the Cartesian form of ( 3 , (-9pi)/4 ) ?

Nov 20, 2016

The cartesian coordinates are $\left(\frac{3 \sqrt{2}}{2} , \frac{- 3 \sqrt{2}}{2}\right)$

#### Explanation:

To convert from polar coordinates $\left(r , \theta\right)$ to cartesian coordinates $\left(x , y\right)$, we use the following equations

$x = r \cos \theta$

and $y = r \sin \theta$

Here $\left(r , \theta\right) = \left(3 , - 9 \frac{\pi}{4}\right)$

Therefore,

$x = 3 \cos \left(\frac{- 9 \pi}{4}\right) = 3 \cos \left(- 2 \pi - \frac{\pi}{4}\right) = 3 \cos \left(- \frac{\pi}{4}\right)$

$x = 3 \cos \left(\frac{\pi}{4}\right) = \frac{3 \sqrt{2}}{2}$

$y = 3 \sin \left(\frac{- 9 \pi}{4}\right) = 3 \sin \left(- 2 \pi - \frac{\pi}{4}\right) = 3 \sin \left(- \frac{\pi}{4}\right)$

$y = 3 \cdot - \frac{\sqrt{2}}{2} = \frac{- 3 \sqrt{2}}{2}$

The cartesian coordinates are $\left(\frac{3 \sqrt{2}}{2} , \frac{- 3 \sqrt{2}}{2}\right)$