Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.
Sine and cosine do not have asymptotes because they are never undefined. Remember, sine means y/r and cosine means x/r. R stands for the hypotenuse, and in the unit circle the radius is always 1, which is the hypotenuse. The other four trig graphs do have asmpytotes because they do not have 1 (r) as their denominator. Instead, their denominators can be any numbers, according to their trig ratio. For example, tangent's ratio y/x. X can be any number; there are no restrictions.
The denominator, however, can be 0 (from the coordinates (0,1) or (-1,0), which makes the ratio undefined once in the according trig function. In cotangent, the ratio x/y also can assume asymptotes. If the coordinate is at (-1,0) or (1,0), when plugged into the ratio, it will be either positive or negative 1 over 0, which is undefined. Also, this applies to secant. Secant is r/y. Y is 0 at (1,0) or (-1,0). This results to be 1 over 0, which makes it undefined. In cosecant, the ratio is r/x. X is 0 as (0,1) and (0,-1). Thus, when plugged in, the ratio is 1/0, making is undefined as well. An asymptote is basically when the ratio is divided by 0, meaning its undefined.