# How do you convert (3, 2pi/3) into rectangular forms?

polar form: $\left(3 , \frac{2 \pi}{3}\right) \rightarrow$ rectangular form: $\left(- \frac{3}{2} , \frac{3 \sqrt{3}}{2}\right)$
Given $\left(r , \theta\right) = \left(3 , \frac{2 \pi}{3}\right)$
$x = r \cdot \cos \left(\theta\right) = 3 \cdot \cos \left(\frac{2 \pi}{3}\right) = 3 \cdot \left(- \frac{1}{2}\right) = - \frac{3}{2}$
$y = r \cdot \sin \left(\theta\right) = 3 \cdot \sin \left(\frac{2 \pi}{3}\right) = 3 \cdot \left(\frac{\sqrt{3}}{2}\right) = \frac{3 \sqrt{3}}{2}$