Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.
Asymptotes are found when a ratio is divided by zero, or it is undefined. Sine y/r and cosine x/r are never undefined because they are both divided by 'r', where on the Unit Circle 'r' equals 1. However, cosecant r/y, secant r/x, tangent y/x, and cotangent x/y would have asymptotes. The fact that they have y or x as their denominator has a possibility of the denominator being zero. According to the Unit Circle, secant and tangent are undefined at pi/2 or 3pi/2 when x=0. Cotangent and cosecant are undefined at 0 and pi when y=0.
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