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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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