# What is the Cartesian form of (33,(-pi)/8)?

May 3, 2018

$\left(\frac{33 \sqrt{2 + \sqrt{2}}}{2} , \frac{33 \sqrt{2 - \sqrt{2}}}{2}\right) \approx \left(30.5 , - 12 , 6\right)$

#### Explanation:

(r,theta)->(x,y);(x,y)-=(rcostheta,rsintheta)

$r = 33$
$\theta = - \frac{\pi}{8}$

$\left(x , y\right) = \left(33 \cos \left(- \frac{\pi}{8}\right) , 33 \sin \left(- \frac{\pi}{8}\right)\right) = \left(\frac{33 \sqrt{2 + \sqrt{2}}}{2} , \frac{33 \sqrt{2 - \sqrt{2}}}{2}\right) \approx \left(30.5 , - 12 , 6\right)$