Answer
We calculate
$\cos^{-1}(0.1)$ or $\displaystyle \cos^{-1}(\frac{1}{10})$
Work Step by Step
$\sec^{-1}10$ is the angle $\theta$ for which $\sec\theta=10$
But sec and cos are reciprocal , $\displaystyle \sec\theta=\frac{1}{\cos\theta}$
so, if $\sec\theta=10$, then $\displaystyle \quad \cos\theta=\frac{1}{\sec\theta}=\frac{1}{10}=0.1$
So, $\theta$ is the angle for which the secant is 10,
and the cosine is $0.1$.
On our calculator, we have the $\cos^{-1}$ button.
We find $\theta=\sec^{-1}10$ by calculating
$\cos^{-1}(0.1)$ or $\displaystyle \cos^{-1}(\frac{1}{10})$
