Find the Asymptotes y=cot(x)

For any ${\displaystyle y=\cot \left(x\right)}$, vertical asymptotes occur at ${\displaystyle x=n\pi }$, where ${\displaystyle n}$ is an integer. Use the basic period for ${\displaystyle y=\cot \left(x\right)}$, ${\displaystyle (0,\pi )}$, to find the vertical asymptotes for ${\displaystyle y=\cot \left(x\right)}$. Set the inside of the cotangent function, ${\displaystyle bx+c}$, for ${\displaystyle y=a\cot (bx+c)+d}$ equal to ${\displaystyle 0}$ to find where the vertical asymptote occurs for ${\displaystyle y=\cot \left(x\right)}$.

Set the inside of the cotangent function ${\displaystyle x}$ equal to ${\displaystyle \pi }$.

The basic period for ${\displaystyle y=\cot \left(x\right)}$ will occur at ${\displaystyle (0,\pi )}$, where ${\displaystyle 0}$ and ${\displaystyle \pi }$ are vertical asymptotes.

The vertical asymptotes for ${\displaystyle y=\cot \left(x\right)}$ occur at ${\displaystyle 0}$, ${\displaystyle \pi }$ , and every ${\displaystyle \pi n}$, where ${\displaystyle n}$ is an integer.

There are only vertical asymptotes for tangent and cotangent functions.

Vertical Asymptotes: ${\displaystyle x=\pi n}$ for any integer ${\displaystyle n}$

No Horizontal Asymptotes

No Oblique Asymptotes