Why do sine and cosine NOT have asymptotes, but the other four trig graphs do? Use unit circle ratios to explain.
The reason that sine and cosine cannot have asymptotes is due to the fact that they will never be undefined. Now, let's recall that in order for there to any asymptotes then we have to have an answer as undefined. Okay, with that in mind we can now prove that sine and cosine do NOT have any asymptotes. We know that the ratio for sine is y over r and as for cosine, we know that it is x over r. "R" is always equaled to one right? And since we will never have a zero be on the denominator, then that means that no asymptotes will be present and created.
The other four trig graphs do have asymptotes and that is because they will not ever have r or a 1 as the denominator. For example, if we did tangent, then we know the ratio is sine (y) over cosine (x) and we know that x can be a zero at the 90 degrees and at the 270 degrees, or pi and 3pi over 2. Also for secant, it would be the same thing since the ratio is r over x and x can be a zero like stated before. Lastly, cosecant (r/y) and cotangent (x/y), they have a denominator of y and we know that y can be equaled to zero at 0 degrees and 180 degrees, or in other words, 0 and pi.
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