# How do you graph y=-tan2x and include two full periods?

Mar 20, 2017

Create a normal tan graph:
graph{tan(x) [-0.5, 6.29, -4, 4]}
(If you don't know how, then either think of how tan changes as the angle of the triangle increases from zero, or remember this chart:

$0$ : $0$
$\frac{\pi}{4}$ : $1$
$\frac{\pi}{2}$ : undefined (goes off to infinity)
$\frac{3 \pi}{4}$ : $- 1$
$\pi$ : $0$
Repeat this at least twice.)

Then compress it in the horizontal by a factor of two (because of the $2 x$ in the tan:
graph{tan(2x) [-0.5, 6.29, -4, 4]}
Then flip it on the vertical (because of the negative sign):
graph{-tan(2x) [-0.5, 6.29, -4, 4]}

The graph must show at least $\pi$, since the period of $\tan \left(x\right)$ is pi, which was divided in two by the 2x inside the tan, then multiplied because you need to show two periods