# How do you convert (4, 4pi/3) into rectangular forms?

Dec 6, 2015

$x = - 2$
$y = - 2 \sqrt{3}$

#### Explanation:

If you know the poalr coordinates $\left(\setminus \rho , \setminus \theta\right)$, then the transformation to have the rectangular ones is

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

$x = 4 \cos \left(\frac{4 \pi}{3}\right)$
$y = 4 \sin \left(\frac{4 \pi}{3}\right)$
since $\cos \left(\frac{4 \pi}{3}\right) = - \frac{1}{2}$, and $\sin \left(\frac{4 \pi}{3}\right) = - \frac{\sqrt{3}}{2}$, we have
$x = 4 \cdot \left(- \frac{1}{2}\right) = - 2$
$y = 4 \cdot \left(- \frac{\sqrt{3}}{2}\right) = - 2 \sqrt{3}$