# What is the Cartesian form of ( 2 , ( 15pi)/2 ) ?

Nov 19, 2016

$\left(0 , - 2\right)$

#### Explanation:

Whereas Cartesian coordinates follow the form $\left(x , y\right)$, polar coordinates follow the form $\left(r , \theta\right)$, where $r$ is the radius and $\theta$ is the angle. To convert from polar to Cartesian form given both $r$ and $\theta$, use $x = r \cos \left(\theta\right)$ and $y = r \sin \left(\theta\right)$.

$x = r \cos \left(\theta\right)$
$x = 2 \cos \left(\frac{15 \pi}{2}\right)$
$x = 0$

$y = r \sin \left(\theta\right)$
$y = 2 \sin \left(\frac{15 \pi}{2}\right)$
$y = - 2$

Thus, the Cartesian form of $\left(2 , \frac{15 \pi}{2}\right)$ is $\left(0 , - 2\right)$.