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

${\mathop{\rm sech}\nolimits}^{-1}{x} \,=\, \dfrac{2}{e^x+e^{-x}}$

06

${\mathop{\rm csch}\nolimits}^{-1}{x} \,=\, \dfrac{2}{e^x-e^{-x}}$

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

Latest Math Topics

Latest Math Problems

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved