Question

What is the inverse tan of tan((4*pi)/3)? Show your steps. I would have answered (4*pi)/3 but I wonder why the answer is just pi/3? Where did the four go?

Answer 1

\[\tan^{-1} (\tan (4*\pi)/3)\]

Answer 2

the reason it is not
\[\frac{4\pi}{3}\] is that
\[\frac{4\pi}{3}\] is larger than
\[\frac{\pi}{2}\] and thefore not in the range of arctangent

Answer 3

tangent is periodic with period pi, so subtract pi from
\[\frac{4\pi}{3}\] so get
\[\frac{\pi}{3}\]