# What are the components of the vector between the origin and the polar coordinate (-1, (3pi)/4)?

Jan 17, 2018

$\left[\frac{\sqrt{2}}{2} , - \frac{\sqrt{2}}{2}\right]$

#### Explanation:

We can use $x = r \cos \left(\theta\right)$ and $y = r \sin \left(\theta\right)$ to convert:

$x = - 1 \cos \left(\frac{3 \pi}{4}\right) = - 1 \left(- \frac{\sqrt{2}}{2}\right) = \frac{\sqrt{2}}{2}$
$y = - 1 \sin \left(\frac{3 \pi}{4}\right) = - 1 \left(\frac{\sqrt{2}}{2}\right) = - \frac{\sqrt{2}}{2}$

So the vector is $\left[\frac{\sqrt{2}}{2} , - \frac{\sqrt{2}}{2}\right]$.