This animation plots sin, cos, and tan. Tan is cool because it has asymptotes (loosely: straight lines that the equation approaches but never reaches – kind of like the Cooper situation). This is because for angle a, tan a = opposite/adjacent = sin a / cos a … but WAIT! cos a sometimes comes out to 0! We see that in the graph whenever the cosine line touches the x-axis. Well, as you probably recall from algebra, you can’t divide by 0. The answer is just undefined. So when cos a hits 0, you’ll see the tan line jump to a remote y coordinate – in other words, it appears again at the edge.
Tan is sexy like that. Just wait til we get to secant, cosecant, cotangent, arcsine, arccosine, and arctangent!!!!