# What are the components of the vector between the origin and the polar coordinate (-2, pi/3)?

color(brown)((x,y) = (-1, - sqrt3), " III Quadrant"
$\left(r , \theta\right) = \left(- 2 , \frac{\pi}{3}\right)$
$x = r \cos \theta = - 2 \cdot \cos \left(\frac{\pi}{3}\right) = - 1$
$y = r \sin \theta = - 2 \cdot \sin \left(\frac{\pi}{3}\right) \approx - \sqrt{3}$