# What is the Cartesian form of ( 6,-pi/6 )?

Oct 8, 2016

Cartesian form of $\left(6 , - \frac{\pi}{6}\right)$ is $\left(3 \sqrt{3} , - 3\right)$

#### Explanation:

Polar coordinates $\left(r , \theta\right)$ are equivalent to Cartesian Coordinates $\left(r \cos \theta , r \sin \theta\right)$

Hence polar coordinates $\left(6 , - \frac{\pi}{6}\right)$ are equivalent to Cartesian Coordinates $\left(6 \times \cos \left(- \frac{\pi}{6}\right) , 6 \times \sin \left(- \frac{\pi}{6}\right)\right)$

i.e. $\left(6 \times \cos \left(\frac{\pi}{6}\right) , 6 \times - \sin \left(\frac{\pi}{6}\right)\right)$

or $\left(6 \times \frac{\sqrt{3}}{2} , - 6 \times \frac{1}{2}\right)$

or $\left(3 \sqrt{3} , - 3\right)$