What is the Cartesian form of ( 5, (-7pi)/3 ) ?

Dec 9, 2017

$\left(\frac{5}{2} , - \frac{5 \sqrt{3}}{2}\right)$

Explanation:

We converting from polar to cartesian:

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

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

Hence the cartesian will be:

$\left(5 \cos \left(\frac{- 7 \pi}{3}\right) , 5 \sin \left(\frac{- 7 \pi}{3}\right)\right)$

Hence evaluating on a calculator or using your trig values yields:

$\left(\frac{5}{2} , - \frac{5 \sqrt{3}}{2}\right)$