# Thread: Domain of tangent functions?

1. ## Domain of tangent functions?

Hi, how do i find the domains of tangent functions. For instance we were given a practice problem: y = 5*tan(x+(pi/2)) - 3. I know the domain is all numbers not equal to pi*k. But how do I do the math to find that out and how can I do it for different tangent functions as well?

Thank you!

2. ## Re: Domain of tangent functions?

In general the domain of the tangens function is given by $\displaystyle \mathbb{R}$\$\displaystyle \{\frac{\pi}{2}+k\pi\}$. If you solve the equation $\displaystyle x+\frac{\pi}{2}=\frac{\pi}{2}+k \pi$ then you know automatically the values wherefore $\displaystyle x+\frac{\pi}{2}\neq\frac{\pi}{2}+k\pi$ which you need to define the domain.

3. ## Re: Domain of tangent functions?

what is the R you gave for the general domain of tangent functions. And I noticed you used pi/2 as your example, would i always use pi/2 in calculating it?

4. ## Re: Domain of tangent functions?

$\displaystyle \mathbb{R}$ is the set of the real numbers and yes because $\displaystyle \tan\left(\frac{\pi}{2}\right)$ doesn't exist.