# How do you write the rectangular coordinates for the point: (6, 3/2 pi)?

Mar 20, 2018

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

#### Explanation:

For given coordinates $\left(r , \theta\right)$, $\left(r , \theta\right) \to \left(x , y\right) \implies \left(r \cos \theta , r \sin \theta\right)$

$r = 6$
$\theta = \frac{2 \pi}{3}$

$\left(6 , \frac{2 \pi}{3}\right) \to \left(x , y\right) \implies \left(6 \cos \left(\frac{2 \pi}{3}\right) , 6 \sin \left(\frac{2 \pi}{3}\right)\right) \equiv \left(- 3 , 3 \sqrt{3}\right)$