Big Question Blog Posts Unit T Question 3

Question 3:
Why is a "normal" tangent graph uphill, but a "normal" cotangent graph downhill?

Explanation:
This question can be explained by basically telling that the asymptotes of cotangent and tangent graphs differ in movement. They are divided separately because the signs of tangent don't start repeating their pattern until they go through each quadrant while cotangent just goes through the first two quadrants and its pattern repeats. By these two picture it is easily shown the difference, there are more asymptotes for a tangent graph than a cotangent graph due to the ratios use and their solutions of getting undefined. The ratios such as sin/cos=tan and cos/sin=cot are what seem to determine these asymptotes because the denominator cannot equal zero. The asymptotes and where they are drawn are basically what determines the difference in the movement of these two graphs. As seen in the picture for the cotangent graph there is an asymptote starting at 0 and another one at pi while tangent has its first asymptote starting at pi/2 which means that the curve lands in the first quadrant which is positive meaning  that the line is going uphill but then when it goes into the second quadrant tangent is negative in the second quadrant which makes sense that the graph go downward but upward again in the third quadrant.

Asymptote for cotangent graph

Asymptotes for tangent graph 

Citations:
Picture 1:
http://aventalearning.com/content168staging/2008Trigonometry/unit4/images/MTH08-68.20159.jpg
Picture Cot:
http://www.drdelmath.com/slu_precalculus/trig_images/trig_graph_cotangent.gif