# For what values of x, if any, does f(x) = secx  have a vertical asymptote?

In radians, the value of $x = \frac{\pi}{2} \pm n \cdot \pi \text{ }$for $n = 0 , 1 , 2 , 3 , 4. \ldots .$
or
In degrees, the value of $x = {90}^{\circ} \pm n \cdot 180 \text{ }$for $n = 0 , 1 , 2 , 3 , 4. \ldots .$

#### Explanation:

To solve for these values, we only need to know where sec x is undefined. Those values are quadrantal angles $\frac{\pi}{2} , \frac{3 \pi}{2} , \frac{5 \pi}{2} , \frac{7 \pi}{2} , e t c$

The vertical asymptotes are

$x = \frac{\pi}{2}$
$x = \frac{3 \pi}{2}$
$x = \frac{5 \pi}{2}$
$x = \frac{7 \pi}{2}$
etc

God bless....I hope the explanation is useful.