Answer
Find the Exact value of each expression.
(a). $sin^{-1}(-1)$ = -90 degrees or $-\frac{\pi}{2}$
(b). $sin^{-1}(\frac{\sqrt 2}{2})$ = 45 degrees or $\frac{\pi}{4}$
(c). $sin^{-1}(-2)$ = Not Possible
Work Step by Step
What this problem is saying is that at which angle on the unit circle is sine -1, $\frac{\sqrt 2}{2}$, and -2.
Looking at the unit circle find the angle at which the y coordinate is the values you are solving for.
The angle at which the y-coordinate is -1 is at -90 or $-\frac{\pi}{2}$.
The angle at which the y-coordinate is $\frac{\sqrt 2}{2}$ is 45 degrees or $\frac{\pi}{4}$.
As you can see because there is no y coordinate of -2 that means that the angle doesn't exist.
