# What is the range of sec x?

Sep 26, 2014

The range of $\sec x$ is $\left(- \infty , - 1\right] \cup \left[1 , \infty\right)$.

Let us look at some details.

We know

$| \cos x | \le 1$

by taking the reciprocal,

$R i g h t a r r o w | \sec x | = \frac{1}{|} \cos x | \ge 1$

(Note that we need to switch the direction of inequality.)

Hence, its range is $\left(- \infty , - 1\right] \cup \left[1 , \infty\right)$.