# How do you graph y=1/3 tanx and include two full periods?

Aug 13, 2018

See double-cycle graph.

#### Explanation:

$y = \frac{1}{3} \tan x = \frac{1}{3} \left(\sin \frac{x}{\cos} x\right) ,$

$x \ne$ ( zero of denominator ) $k \pi , k = 0 , 1 , \pm 2 , \pm 3 , \ldots$.

Tthe period of $\infty$-arm tan wave $= \pi$.

Amplitude of a wave of infinite length, about the axis y = 0 is pi/2.

x-intercepts ( zeros of the numerator )#

$x = \left(2 k + 1\right) \frac{\pi}{2} , k = 0 , \pm 1 , \pm 2 , \pm 3 , \ldots$

See $\infty$-arm tan waves, for two cycles, between ( asymptotic )

$x = \pm \pi$. , .
graph{(3ysin x - cos x )(x+pi+0.0001y)(x-pi+0.0001y)=0[-5 5 -2.5 2.5]}