What is the formula for cotangent in terms of tangent?

The correct formula for cotangent in terms of tangent is determined by understanding the relationships between the trigonometric functions. The cotangent of an angle, represented as cot(θ), is defined as the ratio of the cosine of that angle to the sine of that angle, which is given by cot(θ) = cos(θ) / sin(θ).

To relate cotangent to tangent, we recall that the tangent function is the ratio of sine to cosine: tan(θ) = sin(θ) / cos(θ). From this definition, if we take the inverse of tangent, we can see that cotangent, being the reciprocal of tangent, can be expressed as cot(θ) = 1/tan(θ). However, the form cot(θ) = cos(θ) / sin(θ) directly represents its definition and aligns with the traditional definitions of trigonometric functions.

Thus, recognizing cotangent as a ratio of cosine to sine not only aligns with its fundamental definition but also helps to understand its relationship with other trigonometric functions, making it a key concept in trigonometry.