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The hyperbolic cosecant function $\mathrm{csch} \colon \mathbb{R} \setminus \{0\} \rightarrow \mathbb{R} \setminus \{0\}$ is defined by $$\mathrm{csch}(z)=\dfrac{1}{\sinh(z)},$$ where $\sinh$ denotes the hyperbolic sine. Since this function is one-to-one, its inverse function, the inverse hyperbolic cosecant function is clear.


Derivative of hyperbolic cosecant
Antiderivative of hyperbolic cosecant
Relationship between csch and csc
Relationship between cot, Gudermannian, and csch
Relationship between csch, inverse Gudermannian, and cot

See Also[edit]



Hyperbolic trigonometric functions