How do you convert (-4,pi/6) into rectangular coordinates?

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

Explanation:

To convert the polar coordinate $\left(- 4 , \frac{\pi}{6}\right)$ to rectangular coordinates, you have to use the following

$x = r \cos \theta$ and $y = r \sin \theta$

given $r = - 4$ and $\theta = \frac{\pi}{6}$

$x = r \cos \theta = - 4 \cdot \cos \left(\frac{\pi}{6}\right) = - 4 \cdot \frac{\sqrt{3}}{2} = - 2 \sqrt{3}$

$y = r \sin \theta = - 4 \cdot \sin \left(\frac{\pi}{6}\right) = - 4 \cdot \left(\frac{1}{2}\right) = - 2$

God bless you...I hope my explanation helps...