# What is the Cartesian form of ( 3, (-5pi)/2 ) ?

Feb 14, 2018

Using the formulas:
$x = r \cdot \cos \left(\theta\right)$
$y = r \cdot \sin \left(\theta\right)$

our answer is $\left(0 , - 3\right)$ in Cartesian

#### Explanation:

To convert from Polar coordinates to Cartesian, we must apply the following formulas:

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

where polar form is $\left(r , \theta\right)$
and Cartesian form is $\left(x , y\right)$

for x:
$x = 3 \cdot \cos \left(- 5 \frac{\pi}{2}\right) = 3 \cdot 0 = 0$

$y = 3 \cdot \sin \left(- 5 \frac{\pi}{2}\right) = 3 \cdot - 1 = - 3$

thus converting from polar to Cartesian:

Cartesian = $\left(0 , - 3\right)$