Csch

From specialfunctionswiki
(Redirected from Hyperbolic cosecant)
Jump to: navigation, search

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.

Properties

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
Pythagorean identity for coth and csch

See Also

Arccsch

References

Hyperbolic trigonometric functions