Question

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

Answer 1

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

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.

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

Answer 2

The domain of the function y = sec(x) is:

D: {x | x ≠ (2m + 1)*pi/2, m ∈ Z}

How to find the domain of a function?

We start by assuming that the domain is the set of all real numbers, and then we remove the "problematic points".

Where the problematic points are the points that cause problems in the equation, for example, zeros in denominators and things like that.

In this case, we have:

y = sec(x) = 1/cos(x).

Then we start by assuming that the domain is the set of all real numbers, and now we need to remove all the values of x such that:

cos(x) = 0

Because in that case, we would have a zero in the denominator.

We know that:

cos(pi/2) = 0

cos(3*pi/2) = 0

Then we need to remove all the points of the form:

n*pi/2

from the domain.

Where n is an odd number.

Then we can replace:

n = (2m + 1) with m an integer.

Now we can write the domain as:

D: {x | x ≠ (2m + 1)*pi/2, m ∈ Z}

If you want to learn more about domains, you can read:

https://brainly.com/question/1770447