# What is the Cartesian form of ( 6 , ( - 16pi)/3 ) ?

Apr 10, 2017

$\left(x , y\right) = \left(- 3 , 3 \sqrt{3}\right)$

#### Explanation:

$\left(r , \theta\right) = \left(6 , - \frac{16 \pi}{3}\right)$

$x = r \cos \theta = 6 \cos \left(- \frac{16 \pi}{3}\right) = 6 \cdot \left(- \frac{1}{2}\right) = - 3$

$y = r \sin \theta = 6 \sin \left(- \frac{16 \pi}{3}\right) = 6 \cdot \frac{\sqrt{3}}{2} = 3 \sqrt{3}$

Hence, $\left(x , y\right) = \left(- 3 , 3 \sqrt{3}\right)$

I hope that this was clear.