What is the principal value of `sin^(-1)(-(sqrt(2))/2)?`

Explanation

let `sin^(-1)(-1/sqrt2)=y`
`rArr siny =- 1/sqrt2`
`:'` The principal values of `sin^(-1)" lie in "[-pi/2,pi/2]` and in this interval `sin.(pi/4)=1/sqrt2`
`:. Sin^(-1)(-1/sqrt2)=-pi/4`
`:." The principal value of " sin^(-1)(-1/sqrt2)" is " -pi/4` .