BQ#5: Unit T Concepts 1-3: What's Different About Sine and Cosine?

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

Let's start by recapping what the Unit Circle ratios actually are, shall we?



If you will recall, x is the side adjacent to the angle, y is the side opposite to the angle, and r is the hypotenuse of the triangle. In the Unit Circle, r is always equal to 1. 

Now notice how sine and cosine are the only trig functions with a denominator of r. Since r always equals 1, sine and cosine will always be real numbers. For the other trig functions, there are places where the denominator in their ratio will equal 0. This makes the value of the trig function in question undefined, and this is where you get an asymptote. Since r will never equal 0, sine and cosine are never going to be undefined and therefore will also never have asymptotes.

Resources:

http://3.bp.blogspot.com/-_3Jx3hiWnd8/U1HcV67sX9I/AAAAAAAAAQw/U0rSp0q1sSM/s1600/trigratios.png