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Hyperbolic functions

Calculation of hyperbolic functions

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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
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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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