# What is the Cartesian form of (-13,(9pi)/8)?

Jan 10, 2018

$\left\langle- 13 , \frac{9 \pi}{8}\right\rangle = \left(\frac{13 \sqrt{2 + \sqrt{2}}}{2} , \frac{13 \sqrt{2 - \sqrt{2}}}{2}\right)$

#### Explanation:

We use the following formulae to convert the polar point $\left\langler , \varphi\right\rangle$ to a Cartesian point $x , y$:

$x = r \cos \varphi$

$y = r \sin \varphi$

$\therefore x = - 13 \cos \left(\frac{9 \pi}{8}\right) = \frac{13 \sqrt{2 + \sqrt{2}}}{2}$

$y = - 13 \sin \left(\frac{9 \pi}{8}\right) = \frac{13 \sqrt{2 - \sqrt{2}}}{2}$

So, $\left\langle- 13 , \frac{9 \pi}{8}\right\rangle = \left(\frac{13 \sqrt{2 + \sqrt{2}}}{2} , \frac{13 \sqrt{2 - \sqrt{2}}}{2}\right)$