Question

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

Answer 1

`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`