# What is the Cartesian form of ( 4, (5pi)/2 ) ?

Jul 17, 2016

The point is $\left(0 , 4\right)$.

#### Explanation:

The standard conversion between polar and cartesian coordinates is:
$x = r \cos \left(\theta\right)$
$y = r \sin \left(\theta\right)$

The given coordinates are of the form $\left(r , \theta\right)$. And one will also note that:
$\frac{5 \pi}{2} = \frac{\pi}{2} + 2 \pi$

Meaning that we can simply reduce the angle to $\frac{\pi}{2}$ since we can always subtract full revolutions of the unit circle from angles in polar coordinates, so the result is:
$x = 4 \cos \left(\frac{\pi}{2}\right) = 0$
$y = 4 \sin \left(\frac{\pi}{2}\right) = 4$

The point, then, is $\left(0 , 4\right)$