# How do you find the vertical, horizontal or slant asymptotes for y= cot (x/2)?

Aug 28, 2017

You know that $\cot \left(\theta\right) = \frac{1}{\tan} \left(\theta\right) = \cos \frac{\theta}{\sin} \left(\theta\right)$

and you know that this will be undefined wherever the value of the denominator is zero - because you can't divide by zero.

$\sin \left(\theta\right) = 0$ when $\theta = 0 , \pi , 2 \pi , 3 \pi \ldots$

so, if $\frac{x}{2} = \theta$, then, we have a vertical asymptote when

$\frac{x}{2} = 0 , \pi , 2 \pi , 3 \pi \ldots$

multiply the left side (and every item in the sequence on the right side) by 2 gives us:

$x = 0 , 2 \pi , 4 \pi , 6 \pi \ldots$