Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use Unit Circle ratios to explain.
The reason that sine and cosine do not have asymptotes is because their ratios are (y/r) for sine and (x/r) for cosine. As we know from the Unit Circle, the letter "r" is the hypotenuse, which is equal to . This means that we will never divide by zero (or any other number, actually), so we will never have an undefined answer, which, as we know, is the only time we have an asymptote. On the other hand, we have Cosecant, Secant, Tangent, and Cotangent. The ratios for these functions are (respectively): (r/y), (r/x), (y/x), and (x/y) since we can have values of x=0 as well as y=0, we would divide by zero in these four trig functions. This would give un an undefined answer, meaning we have asymptotes.
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