Big Post Blog Questions Unit T Question 4

Question 4:
Why do sine and cosine NOT have asymptotes, but the other four trig functions do?

Explanation:
Sine and cosine do not have asymptotes because as we know from previous units sine is equal to the ratio y over r and we know that r is always equal to 1 so with this knowledge it is easy to see how each ordered pair from each unit does not end up equalling undefined. From the points on the unit circle at each reference angle: (1,0), (0,1), (-1,0), (0,-1) if we plug in each of the y values into the ratio that is equal to sine we get real numbers such as 1, -1, and zero. When we plug in each of these values there are no equations that leave us with an answer as undefined such as tangent and cotangent do. As for cosine, it follows the same process when proving that there are no asymptotes but instead now the ratio we use is x over r where r still has the value of 1. When plugging in each of the ordered pairs x values it is evident that there are no undefined answers and just like sine your answers are either: 1,-1, or 0. There aren't any instances where the denominator is zero in when using these two ratios for sine and cosine. By noticing this we know that there will be no undefined answers meaning there will also be no asymptotes. As for the other four trig functions such as cotangent and tangent it is clear to see how there ratios (x/y and y/x) allow them to have an asymptote. They have an asymptote when the denominator of their ratio is equal to zero. Same goes for cosecant and secant graphs.