Question

Solve: x=Arctan(-sqrt3).

Answer 1

You should be able to do this without a calculator, if you recognize the special triangle with angles 30,60 and 90 degrees.

It has sides 1,√3 and 2 correspondingly.

So what the question really says is, find x if tan x = -√3

from that special triangle, we know tan 60º=√3
so the angle in standard position is 60º

but x must be in the II or IV quadrants, so x = 120 or x = 300 degrees
or

x = 2pi/3 or 5pi/3 radians