Hyperbolic functions

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

List of functions

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

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

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

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

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

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

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

Inverse Hyperbolic functions

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

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.