How do you graph #y=tan2pix#?

1 Answer
Nov 17, 2016

Answer:

Using the Socratic facility, I have managed to insert the graph for x of small magnitude. Of course, as #x to (1/4)_ . y to oo # and as# x to (-1/4)_ + , y to -oo#

Explanation:

The period of y=tan kx is #pi/k#. Here, #k=2pi# and the period is 1/2.

So, choose one period, and a good choice is # in (-1/4, 1/4)#.

Using the Socratic facility, I have managed to insert the graph for x

of small magnitude (near 0 ). Of course, as #x to (1/4)_ . y to oo # and as# x

to (-1/4)_ + , y to -oo#

The source for the approximation formula

#y=tan 2pix=2pix+(2pix)^3/3#, nearly, when x is small, is the Maclaurin series

#tan x =x+x^3/3+...#

graph{y= 6.28x+82.7x^3 [-10, 10, -5, 5]}