1). Why are sine and cosine the only trig graphs that have asymptotes?
- As we can see from the above picture, sine and cosine have unique ratios when compared with all the other trig values. They both have a denominator of r. In the Unit Circle, r is always equal to 1. Now, the question is why don't sine and cosine have asymptotes whereas all the other ratios do?
- We get an asymptote whenever we divide by zero (in other words, whenever we have a denominator of zero.) This results in undefined answers, in which an asymptote accounts for.
- Sine and cosine have denominators of r which is always equal to one in this case. Therefore when using sine and cosine we will never be dividing by zero and never be getting asymptotes.
- The rest of the trig functions, however, have denominators of x and y. These denominators can be any number, and when that number is zero, then you will get undefined and therefore an asymptote.