Answer
$0.93, 5.36$.
Work Step by Step
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 $\cos^{-1}{0.6}$ is $0.93$ (given by the calculator) and because the cosine function is symmetric to $x=0$ the second solution is: $-0.93+2\pi\approx5.36$. (for it to be in the right domain).