# How do you find the rectangular form of (4, -pi/2)?

May 25, 2018

$\left(0 , - 4\right)$

#### Explanation:

Polar coordinates are represented as:

$\left(r , \theta\right)$

Since we're given:

$\left(4 , - \frac{\pi}{2}\right)$

$4$ is $r$ and $- \frac{\pi}{2}$ is $\theta$

Use the formula:

$\left(r \cos \theta , r \sin \theta\right)$

The rest is plugging and solving:

$r \cos \theta$
$4 \cos \left(- \frac{\pi}{2}\right)$
$4 \left(0\right)$ $\textcolor{b l u e}{\text{ The "cos " value of "-pi/2" is 0}}$
$0$
$x = 0$

$r \sin \theta$
$4 \sin \left(- \frac{\pi}{2}\right)$
$4 \left(- 1\right)$ $\textcolor{b l u e}{\text{ The "sin " value of "-pi/2" is -1}}$
$- 4$
$y = - 4$

color(red)((0, -4)