BQ#4: Unit T Concept 3: Difference Between a Tangent and Cotangent Graph

4. Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill? Use unit circle ratios to explain.
Asymptotes are based on the Unit Circle, so since tangent is sin/cos and cotangent is cos/sin, their denominators differs and so do their asymptotes. For tangent, cosine is its denominator, so we have to see where cosine is zero (0,1) (0,-1) and that leads to undefined which is an asymptote. For cotangent, sine is its denominator, so we have to see where sine is zero (1,0) (-1,0) and that will lead for your answer to be undefines which is an asymptote. Both tangent and cotangent are positive in the first and third quadrant, and negative in the second and fourth quadrant. Because we know this, we understand that in a "normal" tangent graph it goes uphill because of its asymptotes, at pi/2 or 90 degrees, and 3pi/2 or 270 degrees. On the other hand, a "normal" cotangent graph goes downhill because of its asymptotes at zero and pi or 180 degrees.