\[y=\frac{tanx}{sin(2x)+1}\]
.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
\[x\]
the subject, so cannot perform the same analysis to find asymptotes for \[y\]
. The function \[\frac{tanx}{sin(2x)+1}\]
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 \[\pi\]
radians. Because of this there can be no \[x\]
asymptotes, or any other asymptotes of any kind. There only asymptotes are parallel to the \[y\]
axis, given above.