BQ #5: Unit T: Concepts 1-3: Why do sine and cosine NOT have asymptotes, but the other four trig graphs do?

So in order to figure out why sine and cosine do not have asymptotoes, we need to understand what an asymptote is. It is basically an undefined ratio, or a ratio that is divided by 0. Keeping that in mind, let's look at the trig ratios once again:

https://precalculusnwr7.wikispaces.com/file/view/Data_table_for_math_wikispaces.JPG/317767144/384x311/Data_table_for_math_wikispaces.JPG

http://staff.argyll.epsb.ca/jreed/math30p/trigonometry/unitCircle.htm

Notice how the only trig ratios to not have "r" are sine and cosine and "r" represent 1 on the unit circle. So whatever you divide sine and cosine by, the denominator will be 1 and therefore, it will not be undefined (asymptote). An asymptote can only exist when the denominator is 0 in order to reach the undefined value. Meanwhile, the other four trig graphs do not have a 1 as a denominator, meaning that they could have a 0 as a denominator to make it undefined and thus an asymptote. In order words, cosecant and cotangent can have asymptotes if the "y" (denominator) is equal to 0. This would apply to secant and tangent is the x is  also equal to 0.

Reference:
https://precalculusnwr7.wikispaces.com/file/view/Data_table_for_math_wikispaces.JPG/317767144/384x311/Data_table_for_math_wikispaces.JPG

http://staff.argyll.epsb.ca/jreed/math30p/trigonometry/unitCircle.htm

SSS Packet Unit T