Cosecant (\csc) is a trigonometric ratio. In a right triangle with an angle \theta ,


\text{Opposite} is the side of the triangle not part of angle \theta , and \text{hypotenuse} is the side opposite the right angle.


The reciprocal of cosecant is sine (abbreviated as \sin), while its inverse is \arccsc or \csc^{-1} . Note that cosecant is not being raised to the power of -1; this is an inverse function, not a reciprocal.

The derivative of \csc(x) is -\csc(x)\cot(x) , while its antiderivative is \ln\bigl(\left|\tan(\tfrac{x}{2})\right|\bigr) .

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