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

1 Answer
May 28, 2015

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.