Why is the "normal" tangent graph uphill, but a "normal" cotangent graph downhill? Use unit circle ratios to explain.
The reason that a tangent graph is uphill and yet a cotangent graph is downhill is due to the fact that they are different ratios and different of which then creates different asymptotes. We know that tan=sin/cos and cot=cos/sin, or in other words, tan is equaled to y/x and cot is equaled to x/y. See how the denominators are different, tangent has a denominator of cosine while cotangent has a denominator of sine and therefore for tangent we would get our asymptotes wherever cosine is equaled to zero which would be at the 90 degree (pi/2) and at the 270 degree (3pi/2). Furthermore, for cotangent we would get asymptotes wherever sine is equaled to zero which would be at the 0 degree (0) and at the 180 degree (pi). We do know that the pattern for both is positive, negative, positive, negative, yet the asymptotes are located in distinct places and so creates a different looking graph.
References:
-http://www.mathamazement.com/images/Pre-Calculus/04_Trigonometric-Functions/04_06_Graphs-of-Other-Trig-Functions/cotangent-graph.JPG
-http://www.regentsprep.org/Regents/math/algtrig/ATT7/otherg91.gif
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