How do you find the exact value of $arc tan(-sqrt3)$ ?

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Answer 1 · 2015-05-14T21:10:13

$sin(pi/3) = sqrt(3)/2$ and $cos(pi/3) = 1/2$

Since $sin(-theta) = -sin theta$ and $cos(-theta) = cos theta$ for any $theta$ , we have

$tan(-pi/3) = sin(-pi/3)/cos(-pi/3) = (-sin(pi/3))/cos(pi/3)$

$= -(sqrt(3)/2)/(1/2) = -sqrt(3)/1 = -sqrt(3)$

So $arctan(-sqrt(3)) = -pi/3$

How do you find the exact value of arc tan(-sqrt3)arc tan(-sqrt3)?