Answer
a. $\frac{\pi}{4}$
b. $0$
c.$\frac{3\pi}{4}$
Work Step by Step
The problem asks to find the exact value of an inverse trigonometric function
a. $\cos^{-1} \frac{\sqrt 2}{2}$
b. $\cos^{-1} 1$
c. $\cos^{-1} \frac{-\sqrt 2}{2}$
Inverse trigonometric functions reverses the x and y-values; Example: $\sin x = y$; $sin^{-1} y = x$
Look at the unit circle find the angle of the y coordinate
The angle at which the y-coordinate is $\frac{\sqrt 2}{2}$ is at $\frac{\pi}{4}$
The angle at which the y-coordinate is $1$ is at $0$
The angle at which the y-coordinate is $\frac{-\sqrt 2}{2}$ is at $\frac{3\pi}{4}$
