BQ#5: Unit T Concepts 1-3

Why do sine and cosine NOT have asymptopes, but the other four trig graphs do? Use Unit Circle ratios to explain. 

First, let's find out how to get an asymptote in the first place. We get an asymptote when the equation's answer becomes undefined. Now, let's look at the equations for the trig functions. Now, below are the equations. We know that r will always be 1 because we are referring to the unit circle. Sine and Cosine have a denominator of r so it will be impossible to obtain an undefined answer when the denominator is 1. Cosecant and Cotangent have a denominator of y so if y is 0, then the answer would be undefined and would result in an asymptote. Actually, this would only work for degrees of 90 and 270.  For Secant and Tangent, the denominator is x so if x is 0, that will lead to an answer of undefined and an asymptote. This would only work for degrees of 0 and 180. 

©Kelsea DC

©Kelsea DC

References:

Mrs. Kirch's SSS Packet

Desmos Packet