# What is the Cartesian form of (12,(-7pi)/3))?

Oct 25, 2017

$\left(5 , - 10.39\right)$

#### Explanation:

It can be seen from the diagram that the x coordinate of P is $r \cos \left(\theta\right)$ and the y coordinate of P is $r \sin \left(\theta\right)$

So:

$x = r \cos \left(\theta\right)$

$y = r \sin \left(\theta\right)$

From example:

$x = 12 \cos \left(\frac{- 7 \pi}{3}\right) = - 6$

$y = 12 \sin \left(\frac{- 7 \pi}{3}\right) = - 10.39$ (2 .d.p.)

Cartesian coordinate:

$\left(5 , - 10.39\right)$