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sech

sech(x)

Try it yourself:

See also:
coth csch cosh

Calculate hyperbolic secant with sech

sech(x) is the reciprocal of hyperbolic cosine: 1 / cosh(x). For real x it is even, equals 1 at zero, and approaches zero as |x| grows.

Relationships

Use cosh for its denominator and tanh for the identity sech(x)^2 + tanh(x)^2 = 1. It appears in localized pulse and probability-shaped models.

Caveats

Unlike sec, sech is hyperbolic rather than circular. Complex inputs can encounter poles where cosh is zero. For exponential expressions, compare exp and take care with extreme values.

Try Sech in Calcul.io

Start with one of the editable examples above, then replace its arguments with your own values. Keeping the function on a separate calculator line makes the input and result easy to compare. For a longer workflow, assign the result to a variable or reference that line in the next expression.

Check the shown signature before adding optional arguments, and use the related-function links to compare operations with similar purposes.

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