# What is the Cartesian form of (-23,(5pi)/16))?

Apr 8, 2017

(x,y)
($23 \frac{\sqrt{3}}{2}$, $- \frac{23}{2}$ )

#### Explanation:

Polar and cartesian points are related through:

$x = r \cos \left(\theta\right)$
$y = r \sin \theta$

$x = r \cos \left(\theta\right)$
$x = - 23 \left(\cos \left(\frac{5 \pi}{6}\right)\right)$
$\cos \left(\frac{5 \pi}{6}\right) = - \frac{\sqrt{3}}{2}$

$- \frac{\sqrt{3}}{2} \left(- 23\right) = 23 \frac{\sqrt{3}}{2}$
$x = 23 \frac{\sqrt{3}}{2}$

$y = r \sin \theta$
$x = 23 \frac{\sqrt{3}}{2}$

$\sin \left(\frac{5 \pi}{6}\right) = \frac{1}{2}$

$y = - \frac{23}{2}$

(x,y)
($23 \frac{\sqrt{3}}{2}$, $- \frac{23}{2}$ )