Sine and cosine do not have asymptotes because their ratios: y/r and x/r. This means that the radius (r) will always be equal 1, and will never have a 0 as the denominator. Sine and cosine will not encounter asymptotes because we will never have an undefined answer (0 divided by any number).
Unlike sine and cosine, the other four trig graphs do include asymptotes. Cosecant has a ratio of r/y. The "y" value can be 0 in :(1,0) or (-1,0). Secant has a ratio of r/x and x can be 0 in : (0,1) and (0, -1). Cotangent and tangent have the ratios of x/y and y/x, which means either numerator can have the value of 0.
A crucial thing to remember is that cotangent and and cosecant have the same denominator in their ratios (y), which means they will have the same asymptotes. Tangent and secant will have the same asymptotes because their denominators in their ratios (x).
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