# What is the Cartesian form of ( 5 , ( - 15pi)/4 ) ?

Mar 19, 2016

$\left(0 , 5\right)$

#### Explanation:

If Cartesian or rectangular coordinate of a point be (x,y)
and its polar polar coordinate be $\left(r , \theta\right)$

then $x = r \cos \theta \mathmr{and} y = r \sin \theta$
here $r = 5 \mathmr{and} \theta = - 15 \frac{\pi}{2}$
$x = 5 \cdot \cos \left(- 15 \frac{\pi}{2}\right) = 5 \cos \left(15 \frac{\pi}{2}\right) = 5 \cos \left(8 \pi - \frac{\pi}{2}\right) = 5 \cdot \cos \left(\frac{\pi}{2}\right) = 0$
$y = 5 \cdot \sin \left(- 15 \frac{\pi}{2}\right) = - 5 \sin \left(15 \frac{\pi}{2}\right) = - 5 \sin \left(8 \pi - \frac{\pi}{2}\right) = 5 \cdot \sin \left(\frac{\pi}{2}\right) = 5$
So Cartesian coordinate=$\left(0 , 5\right)$