Find the principal values of `sin^(-1)(1/2)`

Options

A. (a) `pi/2`
B. (b) `pi/3`
C. (c) `pi/4`
D. (d) `pi/6`

Answer

(d) `pi/6`

Explanation

Let,

`sin^-1(frac{-1}{2}) = y` then, `sin y =frac{-1}{2}`


Range of principal value for `sin^-1` is `[-pi/2,pi/2]` and `sin(frac{-pi}{6})=frac{-1}{2}`.


Principal value of `sin^-1(frac{-1}{2})=frac{-pi}{6}`.