Sech

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The hyperbolic secant function $\mathrm{sech} \colon \mathbb{R} \rightarrow (0,1]$ is defined by $$\mathrm{sech}(z)=\dfrac{1}{\cosh(z)},$$ where $\cosh(z)$ denotes the hyperbolic cosine. Since this function is not one-to-one, we define the inverse hyperbolic secant function as the inverse function of $\mathrm{sech}$ restricted to $[0,\infty)$.

Properties

Derivative of sech
Antiderivative of sech
Relationship between cosine, Gudermannian, and sech
Relationship between sech, inverse Gudermannian, and cos
Pythagorean identity for tanh and sech

See Also

Arcsech

References

Hyperbolic trigonometric functions