How do you graph two cycles of $y = 3 tan θ$ $y=3tantheta$ ?

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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 $π$ $pi$ .

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

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

The forward neighbor is given by

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

$x \in (a + π, a + 2 π)$ $x in ( a + pi , a + 2 pi )$

A 2-cycle graph,

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

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 $x \in (1.5708, 7.854)$ $x in (1.5708, 7.854 )$ .

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

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