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

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

For a Tangent graph we know that it is positive only in quadrant I and III based off the Unit Circle. A tangent graph has the ratio of sine/cosine, and for an asymptote to appear the denominator must be zero; meaning that the value of cosine must equal 0.To complete a full period, an asymptote must go from a negative to a positive, creating an uphill graph.

A cotangent graph is bit similar to that of a tangent graph, but a few things differ. For instance the ratio is cosine/sine; meaning that the sine must equal 0 to give it an asymptote. so in order for the cotangent to complete a full period with an asymptote, the graph has to start from a positive and move to a negative, creating a downhill graph.