I am a math tutor at the local university and encountered a trigonometric problem which stumped me. (Of course, I'm certain that this material was covered in my students class, but they still didn't know how to solve it, either.) Basically, the problem boils down to solving the following system of equations for $x$ and $y$ with $-\pi \leq x, y \leq \pi$:
$c_1\cos x + c_2 \cos y = 0$
$c_1\sin x + c_2 \sin y = 0$
How to solve a system of trigonometric equations is a similar question, but I am having difficulty following the answer and applying them to this particular problem. Any tips would be appreciated.