BQ #5-Unit T Concepts 1-3

Why do sine and cosine not have asymptotes, but the other four trig functions do? Use unit circle to explain.
Sine and cosine do not have asymptotes due to their ratios on the unit circle. To have asymptotes, you must have an undefined value. Therefore, to obtain an undefined value, a denominator of 0 must be held because you can not divide a number by 0 and not have it be undefined. Sine's ratio is y/r, while cosine'sis x/r. r can not equal 0 because on the unit circle it always equals 1. Therefore, sine and cosine can not have asymptotes. Csc and sec can have asymptotes because their ratios are inverse of sine and cosine. Their rarios are r/y and r/x. In this case, x and y can equal zero, representative of the points (0,1) and (1,0), if y and x can equal zero, and they are the denominators of the ratio, then those values would be undefined, thus constituting the prevalence of asymptotes. It is the same thing with cotangent and tangent. Their respective ratios are x/y and y/x. Since y and x can equal zero on the unit circle and are the denominators of the ratios, then there is a possibility for them to have asymptotes when graphed. An asymptote is, for these trig fuctions, a vertical dashed line that can not be passed on the graph because the graph can not have a value that sits on an undefined line. As a result, we have the other four trig functions besides sine and cosine to have parabolas because the lines we draw must approach the asymptotes but not pass them, while in sine and cosine that is not the case.