What are the asymptote(s) and hole(s), if any, of  f(x) = 1/cosx?

Aug 30, 2016

There will be vertical asymptotes at $x = \frac{\pi}{2} + \pi n$, n and integer.

Explanation:

There will be asymptotes.

Whenever the denominator equals $0$, vertical asymptotes occur.

Let's set the denominator to $0$ and solve.

$\cos x = 0$

$x = \frac{\pi}{2} , \frac{3 \pi}{2}$

Since the function $y = \frac{1}{\cos} x$ is periodic, there will be infinite vertical asymptotes, all following the pattern $x = \frac{\pi}{2} + \pi n$, n an integer.

Finally, note that the function $y = \frac{1}{\cos} x$ is equivalent to $y = \sec x$.

Hopefully this helps!