Trigonometric functions - Wikipedia
The prefix "co-" (in "cosine", "cotangent", "cosecant") is found in Edmund Gunter's Canon triangulorum (1620), which defines the cosinus as an abbreviation for the sinus complementi (sine of the complementary angle) and proceeds to define the cotangens similarly.

Cotangent | Definition, Formulas, & Facts | Britannica
cotangent, one of the six trigonometric functions, which, in a right triangle ABC, for an angle A, is cot A = length of side adjacent to angle A / length of side opposite angle A. The other five trigonometric functions are sine (sin), cosine (cos), secant (sec), cosecant (csc), and tangent (tan).

Cotangent - Formula, Graph, Domain, Range | Cot x Formula
Cotangent is one of the 6 trigonometric functions. It is usually referred to as "cot". Just like other trigonometric ratios, the cotangent formula is also defined as the ratio of the sides of a right-angled triangle. The cot x formula is equal to the ratio of the base and perpendicular of a right-angled triangle.

Cotangent - Math Open Reference
Cotangent. In a right triangle, the cotangent of an angle is the length of the adjacent side divided by the length of the opposite side. In a formula, it is abbreviated to just 'cot'.

Cotangent Definition (Illustrated Mathematics Dictionary)
Illustrated definition of Cotangent: In a right angled triangle, the cotangent of an angle is: The length of the adjacent side divided by the length...

Introduction to the Cotangent Function - Wolfram
The classical definition of the cotangent function for real arguments is: "the cotangent of an angle in a right‐angle triangle is the ratio of the length of the adjacent leg to the length to the opposite leg."

Cotangent -- from Wolfram MathWorld
The cotangent function cotz is the function defined by cotz = 1/(tanz) (1) = (i(e^(iz)+e^(-iz)))/(e^(iz)-e^(-iz)) (2) = (i(e^(2iz)+1))/(e^(2iz)-1), (3) where tanz is the tangent. The cotangent is implemented in the Wolfram Language as Cot[z].