Why do sine and cosine NOT have asymptotes, but the other four trig graphs do?
The ratio for sine is y/r and the ratio for cosine is x/r. We know that in order for there to be an asymptote that the value has to be zero, or undefined. We also know that r equals 1 so sine is y/1 and cosine is x/1. The value of r is not zero, so we do not end up with an asymptote. The other four trig functions have asymptotes because their x or y value in the denominator is not 0, it can vary depending on the values of x and y.
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| (http://ramanujan.math.trinity.edu/rdaileda/teach/m1312f08/invtrig/7.jpg) |
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| (http://www.analyzemath.com/trigonometry/graph_cosecant.gif) |
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(http://www.mathipedia.com/GraphingSecant,Cosecant,andCotangent_files/image033.jpg)
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(http://www.mathamazement.com/images/Pre-Calculus/04_Trigonometric-Functions/04_06_Graphs-of-Other-Trig-Functions/secant-graph.JPG)
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