Domain and range of y sec x

Asked by maham237 @ 22/02/2021 in Mathematics viewed by 318 People

What is the domain of y = sec(x)?

Answered by maham237 @ 22/02/2021

$\bf sec(\theta)=\cfrac{1}{cos(\theta)}$

now, whenever the cosine function, becomes 0, it turns the rational secant function to "undefined". that occurs at $\bf \frac{\pi }{2},\frac{3\pi }{2}$ on the range from [0, 2π]

now, if you keep going around, it will happen at $\bf \frac{\pi }{2}+\pi n\qquad n\in \mathbb{Z}$ , or so long "n" is an integer

so... the domain for secant then, has to be anything BUT those values.

$\bf \{\theta |\qquad \theta =\mathbb{R};\qquad \theta \ne \frac{\pi }{2}+\pi n\qquad n\in \mathbb{Z}\}$

Domain and range of y sec x

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