Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use the unit circle ratios to explain.

Sin and cosine don't have asymptotes simply by the reason of that their circle ratios are composed of having a denominator of r which is equal to one. Sin has a circle ratio is y/r and cosine has a value of x/r. Referring back to our unit circle, r has a value of one, so therefore whatever the value of x and y will be that value because the denominator is automatically one. In order to obtain an asymptote, the value must be undefined in which leads to having zero on the bottom which creates our asymptote. Other trig functions are able to have asymptotes because of their natural unit circle ratios. Csc is r/y in which y can equal to 0 with the 90 degree angle which leads to 1/0 and is an asymptote. Secant is r/x in which you can use 270 to get the value of 1/0 which results in undefined. Tangent and cotangent are the same in that you can mix up the values, as long as you have 0 on the bottom you can achieve an asymptote since dividing by 0 is undefined.

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