Answer
a. $\frac {\pi}{2}$
b. $\frac{\pi}{3}$
c. Does not exist
Work Step by Step
The problem asks to find the exact value of an inverse trigonometric function
a. $\sin^{-1} 1$
b. $\sin^{-1} \frac{\sqrt 3}{2}$
c. $\sin^{-1} 2$
Inverse sine reverses the x and y-values, so basically $\sin x = y$; $sin^{-1} y = x$
Look at the unit circle find the angle of the y coordinate
The angle at which the y-coordinate is 1 is at $\frac {\pi}{2}$
The angle at which the y-coordinate is $\frac{\sqrt 3}{2}$ is at $\frac{\pi}{3}$
There is no y coordinate of 2 so the angle does not exist.
