Which trigonometric function is defined as the ratio of adjacent to opposite?

The function defined as the ratio of the length of the adjacent side to the length of the opposite side in a right triangle is the cotangent function. This function is expressed mathematically as:

[ \text{cotangent}(\theta) = \frac{\text{adjacent}}{\text{opposite}} ]

This definition highlights the relationship between the sides of the triangle with respect to an angle θ, specifically emphasizing the ratio rather than the length of any specific side.

In contrast, the tangent function is actually defined as the ratio of the opposite side to the adjacent side, while secant and cosecant relate to the hypotenuse and either the adjacent or opposite side respectively. Thus, cotangent is accurately represented as the ratio mentioned in the question.