Answer
a. $[-1, 1] $
b. $[0, \pi]$
c. decreasing
d. because $-\displaystyle \frac{4\pi}{3}\not\in[0, \pi]$
Work Step by Step
See figure 17 on p.701
(or the table on page 703 )
In order to have an inverse, the domain of $\cos x$ is restricted to $[0, \pi]$.
$y=\cos^{-1}x$
($y$ is the number from $[0, \pi]$ for which $\cos y=x$)
Domain:$[-1, 1] $
Range:$ [0, \pi]$
Quadrants (unit circle): I and II
Figure 17: $\cos^{-1}x$ is decreasing.
For part (d),
$y=\displaystyle \frac{2\pi}{3}$ is the number from $[0, \pi]$ for which $\displaystyle \cos y=-\frac{1}{2}$
$-\displaystyle \frac{4\pi}{3}\not\in[0, \pi]$ (not in the range)
