Where are the vertical asymptotes of #f(x) = cot x#?
Although it's quite unproperly written, indeed, it has a sense to write that
The point is that you cannot divide by zero, so you must interpret the "division by zero" as a limit process, in which you divide by smaller and smaller quantity; and you'll find out that (if the denominator is fixed) as the denominator gets smaller, the absolute value of the fraction gets bigger and bigger.
This process is visually shown with vertical asymptotes, since you cannot evaluate the function in the fobidden point, but you can evaluate the function in points which lay as near as you want to the exlcluded one. And for what we just said, the value of the function will get bigger and bigger (positively or negatively) as you approach the zero of the denominator.
In your case, the function
So, your vertical asymptotes are vertical lines of equations