Cotangent

Cotangent($\cot$) is a trigonometric ratio. In a right triangle with an angle $\theta$ ,

$\cot(\theta)=\frac{\text{adjacent}}{\text{opposite}}$

$\text{Opposite}$ is the side of the triangle not part of angle $\theta$ , and $\text{adjacent}$ is the side of the triangle that is part of angle $\theta$ .

Properties

The reciprocal of cotangent is tangent (abbreviated as $\tan$), while its inverse is $\operatorname{arccot}$ or $\cot^{-1}$ . Note that cotangent is not being raised to the power of -1; this is an inverse function, not a reciprocal.

The derivative of $\cot(x)$ is $-\csc^2(x)$ , while its antiderivative is $\ln\bigl(|\sin(x)|\bigr)$ .

It should also be noted that $\cot(\theta)=\frac{\cos(\theta)}{\sin(\theta)}$ .