If you are dealing with the inverse sine FUNCTION, the range is [-π/2, π/2]. So, Sin-1(-√2/2) is the angle in the interval
[-π/2, π/2] whose sine is -√2/2.
So, Sin-1(-√2/2) = -π/4. This is the value (in approximate decimal form) returned by a calculator if Sin-1(-√2/2) is entered and the calculator is in radian mode. In degree mode, -45° would be the calculator's output.