# What is the Cartesian form of ( 9 , (16pi)/6 ) ?

Cartesian form $\left(x , y\right) = \left(- \frac{9}{2} , \frac{9 \sqrt{3}}{2}\right)$

#### Explanation:

We start from the given $\left(9 , \frac{16 \pi}{6}\right)$

$r = 9$ and $\theta = \frac{16 \pi}{6} = \frac{8 \pi}{3}$

solve for x

$x = r \cdot \cos \theta$
$x = 9 \cdot \cos \left(\frac{8 \pi}{3}\right) = 9 \cdot \cos \left(\frac{2 \pi}{3}\right) = 9 \cdot \left(- \frac{1}{2}\right) = - \frac{9}{2}$

solve for y

$y = r \cdot \sin \theta$
$y = 9 \cdot \sin \left(\frac{8 \pi}{3}\right) = 9 \cdot \sin \left(\frac{2 \pi}{3}\right) = 9 \cdot \left(\frac{\sqrt{3}}{2}\right) = \frac{9 \sqrt{3}}{2}$

God bless....I hope the explanation is useful.