# How do you graph two cycles of y=3tantheta?

Jul 16, 2018

I Inroduce a method for two-cycle graph, from any x.

#### Explanation:

The cycle period is $\pi$.

One-cycle graph, from x = a rad is given by the piecewise-inverse

$x = a + \frac{\pi}{2} + \arctan \left(\frac{y}{3}\right) , x \in \left(a , a + \pi\right)$

The forward neighbor is given by

$x = a + \left(\frac{3}{2}\right) \pi + \arctan \left(\frac{y}{3}\right)$,

$x \in \left(a + \pi , a + 2 \pi\right)$

A 2-cycle graph,

with $a = \frac{\pi}{2} , x \in \left(\frac{\pi}{2} , \left(\frac{5}{2}\right) \pi\right) = \left(1.5708 , 7.854\right)$ : :

graph{(x-arctan(y/3)-pi)(x-arctan(y/3)-2pi)((x-pi/2)^2+y^2-0.01)((x-5pi/2)^2+y^2-0.01)(x-pi/2+0y)(x-5/2pi+0y)=0}

See dot plots on the x-axis,

for the double cycle domain $x \in \left(1.5708 , 7.854\right)$.

Also, this is in-between two asymptotes, with another in the middle..