What is the expression for cotangent (cot)?

The cotangent function, often abbreviated as cot, is defined as the ratio of the adjacent side to the opposite side in a right triangle or, in terms of sine and cosine, cotangent is the reciprocal of the tangent function.

Tangent itself is defined as the ratio of the sine of an angle to the cosine of that angle, or tan(θ) = sin(θ)/cos(θ). Consequently, if we take the reciprocal of this relationship, we can express cotangent as follows:

cot(θ) = 1/tan(θ) = cos(θ)/sin(θ).

Thus, the relationship that identifies cotangent as the reciprocal of tangent accurately captures why the expression for cotangent is 1 divided by tangent, confirming that the correct answer is indeed aligned with this definition.