Question

How do you evaluate `cos^-1(sin(pi/6))`?

Answer 1

`pi/3.`

Explanation:

`sin(pi/6)=cos(pi/2-pi/6)=cos(pi/3)`

`:. cos^-1(sin(pi/6))=cos^-1(cos(pi/3))=pi/3.`

as `cos^-1` and `cos` are inverses of each other, their composition is the Identity Fun, i.e., `cos^-1(costheta))=theta`, if `theta in [o,pi],` and, `cos(cos^-1x)=x. if |x|<=1.`