How can i find the period of y=tanx without graphing it?
I know the answer but is there a way to find it without all the graphing?

Question

How can i find the period of y=tanx without graphing it? 
I know the answer but is there a way to find it without all the graphing?

anonymous · Answer

For the general form of tangent, $y=a\tan b(x-c)+d$, the period is given by $p=\dfrac{\pi}{b}$.

avanti · Answer

oh i thought the period is always 2pi/b ? its different for tangent?

anonymous · Answer

$\dfrac{2\pi}{b}$ is the period for sine/cosine. Easy to mix up.

anonymous · Answer

The difference has to do with the singularities of tangent.

avanti · Answer

oh okay that makes sense now, thanks!

anonymous · Answer

You're welcome!

avanti · Answer

@SithsAndGiggles I have another question. How come the period for y=tan(x/3) is 3pi? How to i get rid of the 3 in (x/3) ?

anonymous · Answer

In this case, $b=\dfrac{1}{3}$.

The period is then $p=\dfrac{\pi}{\frac{1}{3}}=\dfrac{\pi}{\frac{1}{3}}\cdot\dfrac{3}{3}=\dfrac{3\pi}{1}=3\pi$

avanti · Answer

okay got it! thanks so much for all your help!

anonymous · Answer

You're welcome again!