BQ #4: Unit T Concept 3

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

The tangent graph is uphill and the cotangent graph is downhill because of the asymptotes and they are different because of the trig ratios. Tangent has a ration of y/x and cotangent is x/y. Asymptotes exist when the trig function is undefined and the denominator equals zero. Tangent is undefined when it is at pi/2 and 3pi/2 which is where x=0. Cotangent is undefined when y=0 and on the unit circle it would be at 0 and pi.
The signs are the same for both graphs in the quadrants which is positive, positive, negative, negative. The graphs are different because the asymptotes are in different places and the graphs are shifted and that makes tangent go uphill and cotangent go downhill because of the signs.