Answer
$1.82, 4.46$.
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. $\left[0,\pi \right]$.
We know that $\sec^{-1}(x)=\cos^{-1}{\frac{1}{x}}$.
After using a calculator in radian mode the solutions for $\sec^{-1}{-4}=\cos^{-1}{\frac{1}{4}}$ is $1.82$ (given by the calculator) and because the sec function is symmetric $x=\pi$ the second solution is: $\pi+(\pi-1.82)\approx4.46$.
