# How do you graph  tan(x/2)?

Mar 19, 2018

Assuming you know what a tan function looks like, then we know that $y = f \left(x\right)$, $f \left(x\right) = \tan x$

When $y = f \left(\frac{x}{a}\right)$, the function is squished along the $x$-axis by $a$. So, $a =$ represents all the $x$-values being doubled. So if for a function $f \left(x\right)$, $f \left(2\right) = 5$ and $f \left(4\right) = 12 , w i t h$f(x/2)$-$f(4)=5#

So, $y = \tan \left(\frac{x}{2}\right)$ would be $y = \tan x$ but each value of $x$ would be doubled.

$y = \tan x$:
graph{tanx [-10, 10, -5, 5]}

$y = \tan \left(\frac{x}{2}\right)$:
graph{tan(x/2) [-10, 10, -5, 5]}