How do you evaluate #sin^-1(sin(pi/6))# without a calculator?

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Answer 1 · 2016-08-26T04:23:30

#pi/6#

Use #f^(-1)f(x) = x # that is valid for any function y = f(x) that is

bijective in an (infinitesimal) #in #- neighborhood #(x-in, x+in)# of x.

Here, it is #sin^(-1)sin(pi/6)=pi/6#.

It is important to note that #sin (pi/6) = sin (13/6pi)=1/2# and, while

#sin^(-1)(1/2)# = the conventional principal value #pi/6#,,

#sin^(-1)sin(pi/6)=pi/6# and

#sin^(-1)sin(13/6pi)=13pi/6#.