How do you calculate $arctan (- \frac{\sqrt{3}}{3})$ $Arctan( - sqrt 3/3)$ ?

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Answer 1 · 2018-03-21T10:10:08

$color(blue)(theta = npi - (pi/6) color(white)(aaa) n in ZZ$

Let $theta = arctan (-sqrt3/3) = tan^-1 (-sqrt3/3)$

$tan theta = -sqrt3 / 3 = - (cancelsqrt3) /cancel( (sqrt3)^2 )^color(red)(1/sqrt3)= -1/sqrt3$

We know, $tan (pi - pi/6) = tan((5pi)/6) = - 1/sqrt3$

Further, $tantheta$ is negative in II & IV quadrant#

General solutions is

$theta = npi - (pi/6) color(white)(aaa) n in ZZ$

How do you calculate Arctan( - sqrt 3/3)arctan(−√33)Arctan( - sqrt 3/3)?