# Thread: Determing the Domain of a Trigonometric Function

1. ## Determing the Domain of a Trigonometric Function

Hi,

How do you determine the domain of a trigonometric function?
For example:
y = 4cos3(x+1)-3

Thanks!

2. $\displaystyle x \in \mathbb{R}$ as the function is defined for all x

3. Originally Posted by pickslides
$\displaystyle x \in \mathbb{R}$ as the function is defined for all x
Thank you!
Would the domain equal real numbers for most of these kinds of functions?

4. Most of them. A function such as
$\displaystyle f(x) = \cos\left(\sqrt{x}\right)$
would have a domain of $\displaystyle x \ge 0$, and a function like
$\displaystyle f(x) = \cos\left(\frac{1}{x}\right)$
would have a domain of all reals except at x = 0.

01

5. Originally Posted by stouffie
Thank you!
Would the domain equal real numbers for most of these kinds of functions?

what Yeongil said!

6. Originally Posted by yeongil
Most of them. A function such as
$\displaystyle f(x) = \cos\left(\sqrt{x}\right)$
would have a domain of $\displaystyle x \ge 0$, and a function like
$\displaystyle f(x) = \cos\left(\frac{1}{x}\right)$
would have a domain of all reals except at x = 0.

01