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

1 Answer
MeneerNask
Oct 16, 2016

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#

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