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# Hyperbolic functions

##### Calculation of hyperbolic functions
Timur2011-06-17 22:08:52

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

##### Hyperbolic Functions
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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