cylindrical and rectangular coordinates

Question

Hi! I am currently working on some online homework and I don't understand what I am doing wrong when solving this problem. I know that the first and third coordinates are correct, but I seem to be having some issues finding the correct second coordinate. I understand that, when converting from rectangular to spherical coordinates, theta is equal to arctan(y/x). So to solve for the second coordinate i set theta equal to arctan((-15sqrt3)/-15) and received an answer of 60 which is equivalent to pi/3 but apparently that is incorrect according to the homework site. If someone can help me understand how to correctly solve for the second coordinate in the problem i would greatly appreciate it.

Answer 1

Because $x$ and $y$ are negative, the point is in the 3rd quadrant of the $xy$ plane, so that $\pi \leq \theta \leq \frac{3\pi}{2}$.

So here, $\theta = \pi + \frac{\pi}{3} = \frac{4\pi}{3}$.