Question

How do you evaluate `sin^-1(1/2)` without a calculator?

Answer 1

By Defn. of `sin^-1` function, `sin^-1 x=theta, |x| le1 iff sin theta=x, theta in [-pi/2,pi/2]`.

As `sin (pi/6)=1/2, &, pi/6 in [-pi/2,pi/2], sin^-1 (1/2)=pi/6`.