Question

tan^-1 -root3

Answer 1

\(\large tan^{-1}(-\sqrt3)=\theta \) is equivalent to \(\large tan\theta = -\sqrt3 \).
if you can answer the second question, you'll have answered the first.

Answer 2

This is asking you "What angle will give you a tangent of -root3? Since the tangent is sin/cos or y/x, tangent is negative in the second and fourth quadrants. Since you are told that y = -root3 and it is understood that x = 1, our angle is in the fourth quadrant where y is negative and x is positive. The side across from the angle is -root3, so which of our special angles has a tangent of root 3/1?