I just became an online supplementary teacher. For my friends at least.
I was explaining the graphs of $\sin x$ and $\cos x$. I got a useful image or rather GIF at https://math.stackexchange.com/a/734790/719444
For tangent I managed to construct a line equal to the tangent of the angle. It explained the shape of the curve by referencing fast and slow changes to the length of the line with change in the angle $\theta$.
In this case the required line is $CD$
For negative tangent all I could say was the line segment $C'D'$ is negative because the positive one is mapped to it by reflection. Is that the only way to do it or is there a better explanation?
