# How do you find the rectangular coordinate of  (-4, pi/3)?

Nov 11, 2015

$\frac{\pi}{3}$ is in quadrant I. However, the negative value for the magnitude places the coordinate into quadrant III
$x = - 4 \cos \left(\frac{\pi}{3}\right) = - 4 \left(\frac{1}{2}\right) = - 2$
$y = - 4 \sin \left(\frac{\pi}{3}\right) = - 4 \left(\frac{\sqrt{3}}{2}\right) = - 2 \sqrt{3}$
rectangular coordinate $= \left(- 2 , - 2 \sqrt{3}\right)$