# How can (-pi, -3pi/4) be converted into rectangular coordinates?

Feb 12, 2018

color(blue)((-pi-sqrt(2)/2,-pi-sqrt(2)/2)

#### Explanation:

From the diagram we can see that point P has polar coordinates
$\left(r , \theta\right)$ and Cartesian coordinates $\left(x , y\right)$.

And $\textcolor{w h i t e}{88} x = r \cos \left(\theta\right)$ , $y = r \sin \left(\theta\right)$

$\left(x , y\right) \to \left(r \cos \left(\theta\right) , r \sin \left(\theta\right)\right)$

We can use this to convert polar coordinates to Cartesian coordinates.

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

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

$\therefore$

color(blue)((-pi-sqrt(2)/2,-pi-sqrt(2)/2)