Final answer:
The vertical asymptotes of cot(x) occur at x = (nπ) where n is an integer. The values of x where sin(x) equals zero cause the function to be undefined.
Step-by-step explanation:
The vertical asymptotes of cot(x) can be found by examining the behavior of the function as x approaches certain values. In this case, cot(x) is equal to cos(x)/sin(x). Since sin(x) approaches zero when x is a multiple of π, and cos(x) is never zero, the vertical asymptotes occur at x = (nπ) where n is an integer.
For example, the first few vertical asymptotes of cot(x) are x = π, 2π, -π, -2π, and so on. These are the values of x where sin(x) equals zero, causing the function to be undefined.
Keep in mind that the function cot(x) repeats every π radians, so the vertical asymptotes occur at regular intervals.