Question

find the exact value of:
arctan(-square root of 3)

Answer 1

you are looking for a number ( or angle if you prefer) whose tangent is
\[-\sqrt{3}\]

Answer 2

since a familiar triangle has one side
\[\frac{\sqrt{3}}{2}\] and other side
\[\frac{1}{2}\] and since
\[\tan(x)=\frac{\sin(x)}{\cos(x)}\] this should be easy to find. make sure you are in the right quadrant