Question

How do you find the exact value of `Arctan (-sqrt3/3)`?

Answer 1

`"arctan"(-sqrt(3)/3)=color(green)(-pi/6)=color(green)(-30^@)`

Explanation:

Note that `sqrt(3)/3 = 1/sqrt(3)`
which is a ratio of the opposite side to the adjacent side (the "tan") for one of the standard triangles.

Assuming the standard restriction of `"arctan" in [-pi/2,+pi/2]`
gives the answer above.