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

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

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