Introduction to hyperbolic functions and learn hyperbolic functions from basics to advanced level.

A function that expressed in terms of exponential form functions is called a hyperbolic function.

Hyperbolic functions are six types and here is the list of six hyperbolic functions in exponential functions form for beginners.

01

$\sinh{x} \,=\, \dfrac{e^x-e^{-x}}{2}$

02

$\cosh{x} \,=\, \dfrac{e^x+e^{-x}}{2}$

03

$\tanh{x} \,=\, \dfrac{e^x-e^{-x}}{e^x+e^{-x}}$

04

$\coth{x} \,=\, \dfrac{e^x+e^{-x}}{e^x-e^{-x}}$

05

${\mathop{\rm sech}\nolimits}{x} \,=\, \dfrac{2}{e^x+e^{-x}}$

06

${\mathop{\rm csch}\nolimits}{x} \,=\, \dfrac{2}{e^x-e^{-x}}$

The six hyperbolic functions also have inverse functions. Learn the mathematical form of inverse hyperbolic functions with proofs in mathematics.

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