BQ#5: Unit T Concepts1-3-Why do sine and cosine NOT have asymptotes, but the other four trig graphs do?

First question that should be answered is: how can you get an asymptote? When a trig function is undefined is where an asymptote would appear on a graph. (Okay, got that cleared.) We must know that in the Unit Circle r=1. So therefore, sine and cosine can never be undefined because they would always have a one underneath in their ratio. Unlike sine and cosine, co-secant, secant, tangent and cotangent CAN have asymptotes. Why? Well for one, they do not have "r" underneath as their denominator in their ratio. Meaning, they can possibly have one of their values on the bottom as 0. For instance with secant, its ratio is r/x, we know that "r" is 1 and possibly if "x" is 0, our answer would be undefined. For co-secant, secant, tangent, and cotangent there are many possibilities that an answer can be undefined and that is why these trig functions have asymptotes and, sine and cosine do not. Sine and cosine will never be undefined nor have an asymptote. 

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