Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.
Asymptotes appear on graphs where the values are undefined, or when a ratio is divided by zero. The reason that the sine and cosine graphs do not have any asymptotes is because, according to their unit circle ratios, none of their values will ever turn out undefined. For example, y/r and x/r are the sine and cosine ratios, respectively, and we know that r always equals one. Thus, these ratios cannot possibly be divided by zero, so they will never be undefined.
However, the cosecant, secant, tangent and cotangent graphs will have asymptotes. This is because their ratios have either x or y as denominators, and there is a possibility of a denominator of zero. Secant and tangent are undefined at pi/2 or 3pi/2 (when x=0), and cotangent and cosecant are undefined at 0 and pi (when y=0).
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