# . Quick Math Question .

1. Dec 2, 2004

### xLaser

What is the x-intercept of y=tan(x)?

there are multiple x-intercepts, how should i write it correctly?

and the y-intercept is : y | where y is a set of real numbers right?

2. Dec 2, 2004

### xLaser

ok is it:

n(pi) where n is the set of integers?

3. Dec 2, 2004

### chroot

Staff Emeritus
xLaser: That sounds right to me.

- Warren

4. Dec 2, 2004

### xLaser

lol i have some more questions.

what is the domain and asymptotes of the tan graph?

and btw, is the peroid of tan graph PI?

5. Dec 2, 2004

### xLaser

how do u write the asymptotes, there are so many! is there a general way to write it?

6. Dec 3, 2004

### Galileo

Hi.
Do you have a graph of this function? You can get a lot of information from it.
For example: it's clear there is only one intercept with the x-axis every period.
Since you already know the intercepts occur at $x=n\pi$, the period must be $\pi$.

As for the domain and asymptotes. Use the definition of tanx:
$$\tan x=\frac{\sin x}{\cos x}$$.

Since the period is pi, if you have an asymptote, there's another one pi units to the left and right of it. From the graph it's clear there are only vertical asymptotes and precisely one every period.
So you can write $x=a+n\pi$, where $x=a$ is an asymptote.