## Precalculus (10th Edition)

$\left\{2.69, 3.59\right\}$.
The domain of $\cos^{-1}{x}$ is the range of $\cos{x}$, which is $[−1, 1]$. The range of $\cos^{-1}{x}$ is a specified domain of $\cos{x}$, i.e. $\left[0,\pi \right]$. After using a calculator in radian mode the solutions for $\cos^{-1}{-0.9}=2.6906\approx2.69$ (given by the calculator) and because the cosine function is symmetric to $x=\pi$ the second solution is: $\pi+(\pi-2.69)\approx3.59$. (for it to be in the right domain).