Understanding the Cotangent Function | Definition, Formula, and Evaluating Methods

cotx

In mathematics, the cotangent function, denoted as cot(x), is a trigonometric function that represents the ratio of the adjacent side to the opposite side in a right triangle

In mathematics, the cotangent function, denoted as cot(x), is a trigonometric function that represents the ratio of the adjacent side to the opposite side in a right triangle. Specifically, cot(x) is defined as the reciprocal of the tangent function (tan(x)).

The formula for cot(x) can be derived from the basic trigonometric identities. Given a right triangle with an angle x, where the side adjacent to x is represented by a and the side opposite to x is represented by b, we can define:

cot(x) = a / b

Alternatively, we can express cot(x) in terms of the tangent function:

cot(x) = 1 / tan(x)

It’s important to note that cot(x) is undefined when the tangent function is equal to zero, which occurs at x = (n * π), where n is an integer. This is because the cotangent is the reciprocal of the tangent, and division by zero is undefined.

To evaluate cot(x) for a specific angle x, you can use a scientific calculator or consult a trigonometric table.

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