# How do you evaluate sec^-1(1) without a calculator?

Dec 1, 2016

$2 k \pi$ such that $k$ is represents all integers

#### Explanation:

We revert the inverse function as follows:

${\sec}^{-} 1 \left(1\right) = x$
$\sec \left(x\right) = 1$
$\frac{1}{\cos} x = 1$
$\cos x = 1$
Thus $x$ must be an integral multiple of $2 \pi$. This is because whenever x is an integral multiple of $2 \pi$, $\cos x = 1$.