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# Cotangent

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## Trigonometry

In trigonometry, the cotangent is a function (see trigonometric function) defined as:

$\,\cot x = \frac{\cos x}{\sin x}$

or

$\,\cot x = \frac{1}{\tan x}$

An interpretation of the cotangent of an angle x is as follows. In a right triangle with one angle equal to x, cot x is the ratio of the length of the leg adjacent to the angle x to the leg opposite the angle x.

### Derivative

The derivative of the cotangent is:

$\,\frac{\mathrm{d} (\cot x)}{\mathrm{d} x} = \frac{-1}{\sin^2 x} = -\csc^2 x$

where csc is the cosecant.