what is the domain of y = sec(x)?\no all real numbers\no all real numbers except (npi+\frac{pi}{2}), where n…

Explanation:

Step1: Recall secant - cosine relationship

Recall that $\sec(x)=\frac{1}{\cos(x)}$.

Step2: Find where cosine is zero

The cosine function $\cos(x) = 0$ when $x=n\pi+\frac{\pi}{2}$, where $n\in\mathbb{Z}$ (set of all integers).

Step3: Determine the domain

Since $\sec(x)=\frac{1}{\cos(x)}$, $\sec(x)$ is undefined when $\cos(x) = 0$. So the domain of $y = \sec(x)$ is all real numbers except $x=n\pi+\frac{\pi}{2}$, where $n$ is any integer.

Answer:

all real numbers except $n\pi+\frac{\pi}{2}$, where $n$ is any integer