How do you calculate #Arctan( - sqrt 3/3)#?

1 Answer
sankarankalyanam
Mar 21, 2018

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

Explanation:

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#

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