Sine & Cosine
These two trig graphs will never have asymptotes because the ratio for sin is y/r and the ratio for cosine is x/r. "r" will always equal 1 therefore this function will never be undefined.
Cosecant, Secant, Tangent & Cotangent
These functions may have asymptotes because of their ratios. csc=r/y, sec=r/x, tan=y/x & cot=x/y. We know that the "x" or "y" value could be 0 which will make anything divided by it an undefined graph. secant and tangent will have the same asymptotes because of the "x" value on the bottom of their rations. The same goes for cosecant and cotangent because the "y" value is in the denominator of both of them.
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