# Free Mathematics Tutorials # Hyperbolic Functions Calculator

An online calculator to calculate hyperbolic functions is presented.
The six hyperbolic functions are defined by:
$\sinh(x) = \dfrac{e^x - e^{-x}}{2}$  ,   $\cosh(x) = \dfrac{e^x + e^{-x}}{2}$  ,   $\tanh(x) = \dfrac{e^x - e^{-x}}{e^x + e^{-x}}$  ,   $\coth(x) = \dfrac{e^x + e^{-x}}{e^x - e^{-x}}$  ,   $\text{sech}(x) = \dfrac{2}{e^x + e^{-x}}$  ,   $\text{csch}(x) = \dfrac{2}{e^x - e^{-x}}$

## How to use the calculator

1 - Enter the variable $x$ as a real number and the number of decimal places desired then press "Enter".

 $x$ = 1 Decimal Places = 5

## Activities

Use the values of the six hyperbolic functions and your own calculator to verify ( approximately ) the following identities
$\cosh^2(x) - \sinh^2(x) = 1$
$1 - \tanh^2(x) = \text{sech}^2(x)$
$\tan(x) = \dfrac{\sinh(x)}{\cosh(x)}$
$\coth(x) = \dfrac{1}{\tanh(x)}$
$\text{sech}(x) = \dfrac{1}{\text{cosh}(x)}$
$\text{csch}(x) = \dfrac{1}{\sinh(x)}$

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