Question

What is the exact value of:
tan^-1(tan(4pi/5))
I put 4pi/5 as the answer, why is that wrong?

Answer 1

\[\tan (\frac{4 \pi}{5})=-0.726542528\]
\[\tan^{-1} -0.726542528=-0.6283185307\ radians=-36\ degrees\]

Answer 2

it is wrong because \(\frac{4\pi}{5}>\frac{\pi}{2}\)

Answer 3

you want the same angle (number) that will give you the same tangent, only it must be between \(-\frac{\pi}{2}\) and \(\frac{\pi}{2}\) because that is the range of arctangent

Answer 4

that is why the obvious answer is not correct