BQ #5: Unit T Concepts 1-3: Asymptotes

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

• To answer this question, we must first look at the unit circle ratios to better understand how we are getting these asymptotes.

(http://htmartin.myweb.uga.edu/6190/resources/trigfunctions.gif)

           

              Lets break this question up into two parts and answer the sine and cosine part first. If we remember correctly, an asymptote is a result of an undefined value or a value where something is divided by zero. If we look at the ratios for sine and cosine, their denominators have a very specific value called r. R will always equal one value on a unit circle which is the value of 1, and if this is the case,  we will never get asymptotes with sine and cosine. 

             Now if we look at the other four trig graphs we see that their denominators are not constant values, they may change depending on what x or y is. So these trig graphs can have asymptotes as opposed to sine and cosine. 

References

http://htmartin.myweb.uga.edu/6190/resources/trigfunctions.gif