# How do you simplify the expression arctan(tan(( -7pi)/6))?

Oct 16, 2016

arctan and tan are two opposite functions. They cancel out.

#### Explanation:

Just like ${\sqrt{x}}^{2} = x$ or $5 \times x \div 5$
$\arctan \left(\tan x\right) = x$

In this case: $= - \frac{7 \pi}{6} = - \frac{7}{6} \pi$

But since tan is a periodic function (period$= \pi$) the right answer would be $- \frac{7}{6} \pi + k \cdot \pi$ which can be made simpler by moving the whole $\pi$'s:
Answer $= \frac{5}{6} \pi + k \pi$ or Answer$= - \frac{1}{6} \pi + k \pi$

Usually the answer (without the $k \pi$) is given in the range $\left(0 , \pi\right)$:
Answer$= \frac{5}{6} \pi$