BQ 4: Unit T Concept 3

Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill? Use unit circle ratios to explain.
The tangent graph is uphill while the cotangent graph is downhill due to their asymptotes, and this is because of their different trig ratios. Tangent's is y/x, while cotangent's is x/y. As we have learned in the previous concepts, asymptotes exist where the trig function of the graph is undefined, or when its denominator is equal to zero. Therefore, tangent would be undefined whenever x=0 (pi/2 and 3pi/2), while cotangent would be undefined whenever y=0 (0 and pi).

Even though the signs may be the same for the two graphs--positive-positive-negative-negative--tangent and cotangent graphs are different because their asymptotes are in different places. Thus, their whole graphs are "shifted" and this results in tangent going uphill and cotangent going downhill according to the signs.