Answer
a. ${\pi}$
b. $\frac{\pi}{3}$
c. $\frac{5\pi}{6}$
Work Step by Step
The problem asks to find the exact value of an inverse trigonometric function
a. $\cos^{-1} -1$
b. $\cos^{-1} \frac{1}{2}$
c. $\cos^{-1} \frac{-\sqrt 3}{2}$
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 -1 is at ${\pi}$
The angle at which the y-coordinate is $\frac{1}{2}$ is at $\frac{\pi}{3}$
The angle at which the y-coordinate is $\frac{-\sqrt 3}{2}$ is at $\frac{5\pi}{6}$
