Question

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

Answer 1

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

Explanation:

Just like `sqrtx^2=x` or `5xx xdiv5`
`arctan(tanx)=x`

In this case: `=-(7pi)/6=-7/6pi`

But since tan is a periodic function (period`=pi`) the right answer would be `-7/6pi+k*pi` which can be made simpler by moving the whole `pi`'s:
Answer `=5/6pi+kpi` or Answer`=-1/6pi+kpi`

Usually the answer (without the `kpi`) is given in the range `(0,pi)`:
Answer`=5/6pi`