BQ#4 - Unit T Concept 3

Why is a "normal" tangent graph uphill, but a "normal" tangent graph downhill? Use unit circle ratios to explain.

To start off, the ratio for tangent is sine/cosine. So whenever cosine equals 0, we have an asymptote because anything with a denominator of 0 is undefined which is where asymptotes come from. Therefore, the asymptotes for tangent are pi/2 and 3pi/2 which is also at (0,1) and (0,-1). From here, looking at the unit circle, it says that tangent is only positive in the first and third quadrant and negative in the second and fourth quadrant. Therefore, when we graph tangent with its asymptotes, the only possible way to draw tangent and follow its rules is with an uphill line. For cotangent, the ratio is cosine/sine, so whenever sine is equal to 0, there will be an asymptote which is 0 and pi. On the unit circle the asymptotes would be (1,0) and (-1,0). Also on the unit circle, cotangent is only positive on the first and third quadrant. So when plotting the cotangent on the trig graph with its asymptotes, it can only be in an downhill line within its period because of the rules it has to follow.