Question

How to find vertical asymptotes of cotangent function?

Answer 1

Vertical asypmtotes are line of the form
`x = k`, where k is a point not in the domain of the function.

Since the definition of the cotangent function is

`\cot(x) = (\cos(x))/(\sin(x))`

The function is not defined where the denominator is zero, i.e.

`\sin(x) = 0 \iff x = k\pi,\ k \in \mathbb{Z}`

So, every line with equation
`x = k\pi` is a vertical asymptote for the cotangent function. Some examples may be

`x = 0,\ x = \pi,\ x = -3\pi,\ x = 152\pi,\ x = -234\pi,\ldots`