# How do you graph y=tan2pix?

Nov 17, 2016

Using the Socratic facility, I have managed to insert the graph for x of small magnitude. Of course, as $x \to {\left(\frac{1}{4}\right)}_{.} y \to \infty$ and as$x \to {\left(- \frac{1}{4}\right)}_{+} , y \to - \infty$

#### Explanation:

The period of y=tan kx is $\frac{\pi}{k}$. Here, $k = 2 \pi$ and the period is 1/2.

So, choose one period, and a good choice is $\in \left(- \frac{1}{4} , \frac{1}{4}\right)$.

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

of small magnitude (near 0 ). Of course, as $x \to {\left(\frac{1}{4}\right)}_{.} y \to \infty$ and as x

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

The source for the approximation formula

$y = \tan 2 \pi x = 2 \pi x + {\left(2 \pi x\right)}^{3} / 3$, nearly, when x is small, is the Maclaurin series

$\tan x = x + {x}^{3} / 3 + \ldots$

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