# What is the domain of f(x)=secx?

Oct 17, 2014

By rewriting a bit,

$f \left(x\right) = \sec x = \frac{1}{\cos} x$.

Since the denominator cannot be zero, we need to exclude numbers that make $\cos x$ equal to zero.

Since for all integer $n$,

$\cos \left(\frac{\pi}{2} + n \pi\right) = \cos \left(\frac{2 n + 1}{2} \pi\right) = 0$,

the domain of $f$ is all real numbers except for $x = \frac{2 n + 1}{2} \pi$ for all integer $n$.

I hope that this was helpful.