BQ#5: Unit T Concepts 1-3: Graphing Sine, Cosine, Secant, Cosecant, Tangent, and Cotangent

5. Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use the unit circle ratios to explain.
Sine (y/r) and Cosine (x/r) do not have asymptotes, because their denominators will never equal to zero, since their denominator is "r", which equals to one. Since Cosecant (r/y), Secant (r/x), Tangent (y/x), and Cotangent (x/y) don't have "r" as their denominator, they are able to get zero as their denominator which will be undefined which turns into an asymptote. Since Secant and Tangent both have the asymptote in the same location; the points they share is (0,1) and (0,-1). Cosecant and Cotangent both have the asymptote in the same location; the points they share is (1,0) and (-1,0).