BQ #4: Unit T Concepts 3: Tangent and Cotangent Graphs

BQ #4

1) Why is a "normal" tangent graph uphill but a "normal" cotangent graph is downhill?

They have different ratios, and that is why they go uphill and downhill. For example, the ratio for tangent is sine/cosine, this also means that whenever cosine is 0 on a graph that's where tangent will have an asymptote. Cotangent, has the inverse of that ratio, it's cosine/sine and that means that it will have an asymptote when cosine is equal to 0.The difference in the asymptote location causes for the differences in shape. Since cotangent and tangent follow the same ASTC pattern, they both are positive is quadrants I and III and negative in II and IV. In order for cotangent to follow this pattern, it must be downhill.