which of the following is an asymptote of y = sec(x)?\no x=-2π\no x = -π/6\no x = π\no x = 3π/2

Explanation:

Step1: Recall secant - cosine relationship

We know that $\sec(x)=\frac{1}{\cos(x)}$. The vertical asymptotes of $y = \sec(x)$ occur where $\cos(x)=0$.

Step2: Find the values of $x$ for which $\cos(x)=0$

The general solution for $\cos(x) = 0$ is $x=\frac{\pi}{2}+n\pi$, where $n\in\mathbb{Z}$ (the set of integers). When $n = 1$, $x=\frac{\pi}{2}+\pi=\frac{3\pi}{2}$.

Answer:

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