Question

Sin(theta)=-sqrt(2)/2, what is the angle measure?

Answer 1

First you should notice that sqrt(2) / 2 is equal to 1/sqrt(2).
So the sine of the angle theta is equal to -1/sqrt(2)
Ignore the negative sign for now (or rather make it -sin(theta) = 1/sqrt(2)

Answer 2

Next, draw a right angle triangle. You know sin(theta) is equal to opposite/hypotenuse (from SOH-CAH-TOA), so you can see that the length of the side opposite to the angle theta is of length 1, and the hypotenuse is of length sqrt(2).