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

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Answer 1 · 2016-09-22T12:13:20

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

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