ASYMPTOTES. They are the reasons why tangent goes uphill and cotangent goes downhill. As we previously learned, tangent is sine/cosine and the only way to make an asymptote is for it to be undefined. This means cosine must be zero. We know that cosine equals zero at 90º (0,1) and 270º (0,-1). So, on a graph, the asymptote starts at π/2 and ends at 3π/2. Remember, these aren't all the asymptotes, they are just one period. In the picture below, you can see that the asymptotes are the dotted lines. Quadrants two and three consists of one whole period and quadrants one and four are just the halves because it's a snapshot.