# What is the Cartesian form of (18,(-34pi)/8)?

Nov 16, 2016

The cartesian coordinates are $= \left(9 \sqrt{2} , - 9 \sqrt{2}\right)$

#### Explanation:

We use the following equations to transform polar coordinates to cartesian coordinates.

$x = r \cos \theta$

$y = r \sin \theta$

The polar coordinates are $\left(18 , \frac{- 34 \pi}{8}\right)$

therefore,

#x=18cos ((-34pi)/8)=18cos ((-2pi)/8)=18*cos(-pi/4)

$x = 18 \cdot \frac{\sqrt{2}}{2} = 9 \sqrt{2}$

$y = 18 \cdot \sin \left(\frac{- 34 \pi}{8}\right) = 18 \cdot \sin \left(\frac{- 2 \pi}{8}\right) = 18 \cdot \sin \left(- \frac{\pi}{4}\right)$

$y = - 18 \cdot \frac{\sqrt{2}}{2} = - 9 \sqrt{2}$

$\left(x , y\right) = \left(9 \sqrt{2} , - 9 \sqrt{2}\right)$