BQ #5: Unit T Concept 1-3: Why do cosine and sine not have asympototes, but the other four trig functions do?

According to the Unit Circle, Sine and Cosine were the only trig functions that were not able to equal zero with their ratio. Sine being y/r and Cosine being x/r, the r representing 1, NEVER can the ratios equal zero. An asympototes only appear when the ratio of a trig function is equal to zero, which is why every other trig function ( CSC, SEC, TAN, COT) do have asymptotes.

(http://www.sosmath.com/trig/Trig2/trig2/img6.gif)