Question

How do you evaluate `cos(sin^-1(1/2))`?

Answer 1

`cos(sin^(-1) (1/2))=cos(cos^(-1) sqrt(1-(1/2)^2) )=sqrt(1-(1/2)^2)=sqrt 3/2.`

Explanation:

Use `cos^(-1) x = sin^(-1)(+- sqrt(1-x^2))`.

Here the angle is in Q1. So, + sign is taken.