# What is the Cartesian form of ( 12, (-7pi)/2 ) ?

Mar 22, 2016

So Cartesian coordinate=$\left(0 , 12\right)$

#### 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 $r = 12 \mathmr{and} \theta = - 7 \frac{\pi}{2}$
$x = 12 \cdot \cos \left(- 7 \frac{\pi}{2}\right) = 12 \cdot \cos \left(7 \frac{\pi}{2}\right) = 12 \cdot \sin \left(4 \pi - \frac{\pi}{2}\right)$
$= 12 \cos \left(\frac{\pi}{2}\right) = 0$
$y = 12 \cdot \sin \left(- 7 \frac{\pi}{2}\right) = - 12 \cdot \cos \left(7 \frac{\pi}{2}\right)$
= -12*sin(4pi-pi/2)=12sin(pi/2=12

So Cartesian coordinate=$\left(0 , 12\right)$