Why DON’T sine and cosine have asymptotes, but the other four
trig graphs do?
As you can see, sine and cosine have ratios with "r" in the denominator. We know that from the Unit Circle, "r" IS ALWAYS ONE! Therefore, we can never have "r" being zero and we can never have sine or cosine being undefined. For the other graphs, however, we have either y or x as the denominator. This means that we have possibilities of having a denominator being zero (at the four quadrant angles) and having undefined answers. And we know that undefined= asymptotes. On the other hand, since "r" is always 1 we know that sine and cosine can't be undefined and will not have asymptotes restricting the graph.
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