# What is the domain and range of  y=secx?

Nov 25, 2017

Domain: $x \in \mathbb{R} | x \ne \left(n \pi + \frac{\pi}{2}\right)$
Range: $y \le - 1 \cup y \ge 1 \mathmr{and} y | \left(- \infty , - 1\right) \cup \left(1 , \infty\right)$

#### Explanation:

$y = \sec x \mathmr{and} y = \frac{1}{\cos} x \therefore \sec x$ is undefined at $\cos x = 0$

$\cos \left(n \pi + \frac{\pi}{2}\right) = 0 \therefore x \ne \left(n \pi + \frac{\pi}{2}\right)$ Thus, the domain of the

secant function is the set of real numbers excluding

$x = \left(n \pi + \frac{\pi}{2}\right)$​ i.e Domain: $x \in \mathbb{R} | x \ne \left(n \pi + \frac{\pi}{2}\right)$

Range: cosine function only takes values that are between −1 and

$+ 1$. So $\sec x$ can only take values that are $\ge 1 \mathmr{and} \le - 1 \therefore$

Range: $y \le - 1 \cup y \ge 1 \mathmr{and} y | \left(- \infty , - 1\right) \cup \left(1 , \infty\right)$

graph{secx [-10, 10, -5, 5]} [Ans]