Question

How do you find the exact value of `sin^-1(cos(pi/3))`?

Answer 1

Use `sin^(-1)sin x = x`

Here, `sin^(-1)cos(pi/3)=sin^(-1)sin(pi/2-pi/3)=pi/2-pi/3=pi/6`.

This is the conventional principal value.

The general value for the angle whose sine = `cos (pi/3)=sin(pi/6)` is

`npi+(-1)^npi/6, n = 0, +-1, +-2, +-3, ...`