The cotangent function is a trigonometric function defined as the ratio of the adjacent side to the opposite side in a right triangle. It is often abbreviated as cot and is the reciprocal of the tangent function. In mathematical terms, cot(x) = 1/tan(x) or cot(x) = cos(x)/sin(x). The cotangent function is periodic, with a period of π, meaning it repeats its values every π radians. Its graph features vertical asymptotes where the sine function equals zero, resulting in undefined values. The cotangent function is commonly used in various fields, including geometry, engineering, and physics.