# What is the Cartesian form of (10,(-7pi)/3))?

$x = 5$
$y = - 5 \sqrt{3}$

#### Explanation:

The given data $\left(r , \theta\right) = \left(10 , \frac{- 7 \pi}{3}\right)$

$x = r \cos \theta = 10 \cdot \cos \left(\frac{- 7 \pi}{3}\right) = 10 \cdot \cos \left(- \frac{\pi}{3}\right) = 10 \cdot \left(\frac{1}{2}\right)$
$x = 5$
$y = r \sin \theta + 10 \cdot \sin \left(\frac{- 7 \pi}{3}\right) = 10 \cdot \sin \left(- \frac{\pi}{3}\right) = 10 \left(\frac{- \sqrt{3}}{2}\right)$
$y = - 5 \sqrt{3}$

God bless....I hope the explanation is useful.