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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 \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)} .

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