BQ#4 Unit T Concepts 1-3 Tangent & Cotangent graphs

Why is a “normal tangent graph uphill but a “normal” cotangent graph downhill?

The graphs for tangent and cotangent are in every single way bit for some reason they end up looking weird at the end. This is because of the way their asymptotes are formed. We know that tangent and cotangent are (+) in quadrants 1 & 3, and (-) 2 & 4. To understand this more, remember that to get an asymptote the trig ration must be undefined to have an undefined ratio you need to divide by zero.

For tangent, we know the ratio is Y/X so... to get an asymptote X must equal to zero. This means to will have asymptotes at pi/2 & 3pi/2. So the graph of tangent cannot touch these lines, but somehow it must be are in quadrants 1 & 3, and (-) 2 & 4. The only way to draw this is making it look like it is going “uphill”

Cotangent, we know the ratio is X/Y so… it will have asymptotes wherever cos=0 or y=0. This means the graph will have asymptotes at 0, pi, 2pi. The only way to graph this is how we did it above, giving it a “downhill” looking graph.