If possible, find the exact value of the expression without the use of a calculator. cos^-1 (sin pi/3)

Question

I really need some help on this. Please walk me through it.

 

If possible, find the exact value of the expression without the use of a calculator. cos^-1 (sin pi/3)

Answer 1

For |x| ≤ π/2 we have: cos^-1 sin x = π/2 - x

 

This follows from the identity sin x = cos(π/2 - x) and the range [0,π] of the function cos^-1 x.

 

cos^-1 sin π/3 = π/2 - π/3 = π/6