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.
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• A cotangent and tangent have goes different ways because of their ratios. Cotangent with x/y and tangent with y/x. These affect the graphs because it determines where the asymptotes will be. In a tangent graph when sine is 0 there will be an asymptote and when cosine is 0 there will be an asymptote for the cotangent graph. In the unit circle the quadrants are exactly the same but the ratio changes the graph. In quadrant 1 they are both positive but since sine is 0 at 90 degrees the tangent graph needs to go uphill in order to follow the unit circle of being positive and get near the asymptote. For the cotangent graph the asymptote is at 0 so the graph needs to start up near the asymptote to be positive then go downhill to be negative in the next quadrant.