Hyperbolic functions
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.
List of functions
Hyperbolic functions are six types and here is the list of six hyperbolic functions in exponential functions form for beginners.
Hyperbolic Sine Function
$\sinh{x} \,=\, \dfrac{e^x-e^{-x}}{2}$
Hyperbolic Cosine Function
$\cosh{x} \,=\, \dfrac{e^x+e^{-x}}{2}$
Hyperbolic Tangent Function
$\tanh{x} \,=\, \dfrac{e^x-e^{-x}}{e^x+e^{-x}}$
Hyperbolic Cotangent Function
$\coth{x} \,=\, \dfrac{e^x+e^{-x}}{e^x-e^{-x}}$
Hyperbolic Secant Function
${\mathop{\rm sech}\nolimits}{x} \,=\, \dfrac{2}{e^x+e^{-x}}$
Hyperbolic Cosecant Function
${\mathop{\rm csch}\nolimits}{x} \,=\, \dfrac{2}{e^x-e^{-x}}$
Inverse Hyperbolic functions
The six hyperbolic functions also have inverse functions. Learn the mathematical form of inverse hyperbolic functions with proofs in mathematics.