Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.

First of all, we should be familiar that asymptotes happen whenever we get undefined. The only way to get undefined is to be divided by zero. If we refer to the circle ratios of sine and cosine the ratios would be sin=y/r and cos=x/r. We know that r will always equal one so there is no way that sine and cosine will randomly appear with a zero on the bottom. However, every other trig ratio have some value in which the bottom can equal zero, making it possible for them to have an asymptote.

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