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

Jul 5, 2017

In order to convert this polar coordinate into a Cartesian one, use the following formulas:

$x = r \cos \theta$
$y = r \sin \theta$

A polar coordinate is written in the form $\left(r , \theta\right)$, so in this case $r = - 5$ and theta=(7π)/3, which can be written also as π/3.

Thus,
x = -5 cos ((π)/3) = -5/2
y = -5 sin ((π)/3) = -(5sqrt3)/2

The Cartesian coordinate would be $\left(- \frac{5}{2} , - \frac{5 \sqrt{3}}{2}\right)$.