Question

How do you simplify `Sin^-1(-sqrt2/2)`?

Answer 1

`sin^-1(-sqrt2/2)=-pi/4`.

Explanation:

The Defn. of `sin^-1` function is :

`sin^-1x=theta, |x|<=1 iff sin theta=x, theta in [-pi/2,pi/2]`.

Knowing that, `sin(-pi/4)=-sin(pi/4)=-sqrt2/2, &, -pi/4 in [-pi/2,pi/2]`, we have,

`sin^-1(-sqrt2/2)=-pi/4`.