Asymptoes of Rational Trigonometric Functions Example

Suppose we want to find the asymptotes of  
We can some asymptotes by setting the denominator equal to zero.
\[sin(2x)+1=0 \rightarrow sin(2x)=-1 \rightarrow 2x=(2n+ \frac{3}{2}) \pi \rightarrow x=(n+ \frac{3}{4}) \pi\]

We cannot make  
  the subject, so cannot perform the same analysis to find asymptotes for  
. The function  
  contains only trigonometric functions - no terms or factors such as  
\[e^x, \: x^3\]
  for example. This means that the function is periodic, in this case the function repeats every  
  radians. Because of this there can be no  
  asymptotes, or any other asymptotes of any kind. There only asymptotes are parallel to the  
  axis, given above.

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