How do you find the value for #tan^-1[tan(5pi/7)]#?

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How do you find the value for #tan^-1[tan(5pi/7)]#?

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Answer 1 · 2015-05-28T22:17:35

The formula
#tan^(-1)[tan(a)]=a#
works for #a in (-pi/2;pi/2)#

In our case #(5pi)/7>pi/2# but we can use the periodicity of #tan#:
#tan((5pi)/7)=tan((5pi)/7-pi)=tan(-(2pi)/7)#
#tan^(-1)[tan((5pi)/7)]=tan^(-1)[tan(-(2pi)/7)]=-(2pi)/7#

Btw, a similar formula
#tan[tan^(-1)(a)]=a#
works for all #a in RR#.

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How do you find the value for #tan^-1[tan(5pi/7)]#?

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