To answer this question, we first need to look at the ratios of the trig functions we are dealing with! These ratio include: sine, cosine, cosecant, secant, tangent, and cotangent.
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| Kirch Math Analysis
When looking at the ratios, we see that sine and cosine are the only two trig functions that have "r" as the denominator. From our previous work with the unit circle, we know that "r" is equal to "1" as that is it is the variable for the radius of the circle. Knowing that this denominator will always be "1," we can conclude that there will never be an undefined value. {to receive and undefined value, we must have a "0" in the denominator; however, as there is a "1," the chance of this happening is eliminated.}The remaining four trigonometric functions contains "x" and "y" values in the denominator. These values could possible have a "0" in the denominator which would lead to the creation of asymptotes.
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