BQ #5: Unit T Concept 1-3 - Why do sine and cosine NOT have asymptotes, but the other four trig graphs do?

(http://literacy.purduecal.edu/STUDENT/mrrieste/trigratios.png)

     First of all, in order for a trig function to have an asymptote, the DENOMINATOR MUST BE 0, or undefined. Looking at the trig ratios from the Unit Circle (as seen on the picture above), sine and cosine have denominators of r, or the hypotenuse. On the unit circle. r will always be 1; r is not 0 and therefore these two trig functions won't have asymptotes. Even outside the Unit Circle, r will never be 0 since it represents the hypotenuse of a right triangle. 

     Cosecant and cotangent relate since both ratios have denominators of y. In order for cosecant and cotangent to have asymptotes, y would need to equal to 0. Same goes for secant and tangent;  both share a denominator of x and x needs to be 0 in order to have an asymptote.