Question

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

Answer 1

`sin(sin^-1 (-1/sqrt2)) = -1/sqrt2`

Explanation:

`sin(sin^-1 (-1/sqrt2))`.

Let `sin^-1 (-1/sqrt2) = theta :. sin theta = (-1/sqrt(2))`

We know `sin(pi/4)=1/sqrt2 , sin(-pi/4)= -1/sqrt2`

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

`sin(sin^-1 (-1/sqrt2)) = sin (-pi/4) = -1/sqrt2` [Ans]