# What is the Cartesian form of ( 2 , (13pi)/3 ) ?

Oct 13, 2016

$\text{Polar:" (r,theta)=(2,(13pi)/3)color(white)("X")harr"Cartesian:} \left(x , y\right) = \left(1 , \sqrt{3}\right)$

#### Explanation:

$\theta = \frac{13 \pi}{3} = 2 \times \left(2 \pi\right) + \frac{\pi}{3}$

Since $2 \pi$ represents a complete circle
$\frac{13 \pi}{3}$ is equivalent (in terms of location) to $\frac{\pi}{3}$

Here is the standard $\frac{\pi}{3}$ triangle (with $r = 2$)

from which we can see $x = 1$ and $y = \sqrt{3}$