Question

What are the vertical asymptotes of cot(2x)?

Answer 1

Vertical asymptotes of
`cot(2x)` occur where the function is undefined, at

`x = π/4 + nπ/2` for any integer n.

Step-by-step explanation:

The vertical asymptotes of a function are values of x where the function tends towards infinity or negative infinity. For the cotangent function,
`cot(2x)`, vertical asymptotes occur where the function is undefined, which is where
`2x` is an integer multiple of π, because the tangent function, which is the reciprocal of cotangent, is zero at these points.

Thus to find the vertical asymptotes of
`cot(2x)` we look for values of
`x`such that
`2x` is an odd multiple of
`π/2`, since the tangent function has zeros at odd multiples of
`π/2`. The general solution for the vertical asymptotes of ,

`cot(2x) is x = π/4 + nπ/2` where n is an integer. This expression comes from setting
`2x = (2n+1)π/2` which gives the locations were the cotangent function will be undefined and thus have a vertical asymptote.