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

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Answer 1 · 2018-07-16T03:49:43

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

The cycle period is #pi#.

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

#x = a + pi/2 + arctan(y /3), x in ( a , a + pi )#

The forward neighbor is given by

#x = a + (3/2)pi + arctan (y/3)#,

#x in ( a + pi , a + 2 pi )#

A 2-cycle graph,

with # a = pi/2, x in ( pi/2, (5/2)pi ) = (1.5708, 7.854 )# : :

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 (1.5708, 7.854 )#.

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