BQ#4: Unit T Concepts 1-3-Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill?

Photocredits: desmos.com

Yes, tangent and cotangent are inverses of each other but, that does not fully explain why exactly a tangent graph is uphill and a cotangent graph is downhill. Let's start off with tangent first and why it's uphill. Tan=sin/cos in order for tan to be undefined and have asymptotes cos must be zero in certain points of the unit circle: pi/2 (90degrees) and 3pi/2 (270degrees). Co-tan, unlike tan, has asymptotes in other points on the unit circle, it's asymptotes are on: 0pi, pi (180 degrees), 2pi (360 degrees). And that completely answers our question. Tangent graphs and cotangent graphs go in two different directions because of the different asymptotes, they are undefined in different areas, so, therefore, they go in different directions.

Photocredits: desmos.com