Question

How do you evaluate `cos^-1(sin((5pi)/6))` without a calculator?

Answer 1

`cos^(-1)(sin((5pi)/6))=pi/3`

Explanation:

We know that `sin(pi/2+theta)=costheta`

Hence `sin((5pi)/6)=sin((3pi+2pi)/6)=sin((3pi)/6+(2pi)/6)`

= `sin(pi/2+pi/3)=cos(pi/3)=1/2`

Hence `cos^(-1)(sin((5pi)/6))=cos^(-1)(1/2)=pi/3`