# How do you graph y=4tan(pi/2t) over the interval [-2,2]?

Feb 18, 2017

(see below)

#### Explanation:

If we let $\theta = \frac{\pi}{2} t$
then $t \in \left[- 2 , 2\right]$
is equivalent to $\theta \in \left[- \pi , + \pi\right]$
and we know $y = \tan \left(\theta\right) , \theta \in \left[- \pi , + \pi\right]$ looks like:

Replacing the horizontal axis with the $t$ variable based scale:

Replacing $y = \tan \left(\frac{\pi}{2} t\right)$ with $y = 4 \tan \left(\frac{\pi}{2} t\right)$
simply pushes every $y$ coordinate value $4$ further away from the horizontal axis;
the easiest way to show this is to modify the scale along the vertical axis to $4$ times their previous values: