Unit T Big Question #4

 

 The Fourth Big Question:

Why do sine and cosine don't have asymptotes, but the other four graphs do?

Sine and cosine do not have asymptotes because of their ratios. Cosine is x over r or x over 1. So when a number is input as X, then the value of the ratio will be that number (because the denominator is 1) even if zero was inputted. The same rule applies for sine, which is y/1. So when a value is inputted for Y, the value of the whole thing will be that number.
So what does all this mean?

Sine and Cosine cannot be undefined in these situations. 

Notice all the other trig functions involve cosine or sine being the denominator, and if they end up equaling to zero, then it makes that certain function undefined and creates an asymptote.