# What is the Cartesian form of (49,(-7pi)/4)?

Feb 24, 2017

$\left(49 , \frac{- 7 \pi}{4}\right)$ in Cartesian coordinates is $\left(\frac{49}{\sqrt{2}} , \frac{49}{\sqrt{2}}\right)$ or $\left(34.65 , 34.65\right)$

#### Explanation:

Polar coordinates $\left(r , \theta\right)$ in Cartesian form is $\left(r \cos \theta , r \sin \theta\right)$

Hence, $\left(49 , \frac{- 7 \pi}{4}\right)$ in Cartesian coordinates is

$\left(49 \cos \left(\frac{- 7 \pi}{4}\right) , 49 \sin \left(\frac{- 7 \pi}{4}\right)\right)$

or $\left(49 \cos \left(\frac{- 7 \pi}{4} + 2 \pi\right) , 49 \sin \left(\frac{- 7 \pi}{4} + 2 \pi\right)\right)$

or $\left(49 \cos \left(\frac{\pi}{4}\right) , 49 \sin \left(\frac{\pi}{4}\right)\right)$

i.e. $\left(49 \times \frac{1}{\sqrt{2}} , 49 \times \frac{1}{\sqrt{2}}\right)$

or $\left(\frac{49}{\sqrt{2}} , \frac{49}{\sqrt{2}}\right)$

i.e. $\left(34.65 , 34.65\right)$