Question

How do you evaluate `sin^-1(-1/sqrt2)`?

Answer 1

`-pi/4`

Explanation:

Let `sin^-1(-1/sqrt2)=theta.`

Then, by defn. of `sin^-1, sintheta=-1/sqrt2`, where, `theta in [-pi/2,pi/2]`

We have, `sin(-pi/4)=-1/sqrt2,` & `-pi/4 in {-pi/2,pi/2]`, `theta=-pi/4`