Sin's ratio in the Unit Circle is "y" over "r". Cos's ratio in the Unit Circle is "x" over "r". Because the trig graphs are directly related to the Unit Circle, sin and cos do not have asymptotes because their ratios do not allow them to. "R" in the Unit Circle, is always 1. Asymptotes exist when there is a zero in the denominator, making it undefined. This cannot be possible for sin and cos because their ratios will never have zero in the denominator. Csc, sec, tan, and cot, however, have asymptotes because their ratios do not have "r" as the denominator so therefore they can have a zero in the denominator.
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