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Hyperbolic functions

Calculation of hyperbolic functions

This online calculator shows values of hyperbolic functions of given argument. The definitions of functions are below

PLANETCALC, Hyperbolic Functions

Hyperbolic Functions

Digits after the decimal point: 2
Hyperbolic Functions



Hyperbolic sine
\operatorname{sh}x=\frac{e^x-e^{-x}}{2}

Hyperbolic cosine
\operatorname{ch}x=\frac{e^x+e^{-x}}{2}

Hyperbolic tangent
\operatorname{th}x=\frac{\operatorname{sh}x}{\operatorname{ch}x} = \frac {e^x - e^{-x}} {e^x + e^{-x}} = \frac{e^{2x} - 1} {e^{2x} + 1}

Hyperbolic cotangent
\operatorname{cth}x=\frac{1}{\operatorname{th}x}

Hyperbolic secant
\operatorname{sech}x=\frac{1}{\operatorname{ch}x}

Hyperbolic cosecant
\operatorname{csch}x=\frac{1}{\operatorname{sh}x}

Functions sh, ch, th, sech are continuous functions. Functions cth, csch are not defined for x=0.

Hyperbolic sine is increasing function passing through zero - \operatorname{sh}0=0.
Hyperbolic cosine is even function where \operatorname{ch}0=1 is the minimum.

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