How we Define Hyperbolic Functions and their Simple Formulas

Define Hyperbolic Function in Simple Way

  • Sin Hyperbolic Function
  • Cos Hyperbolic Function

Simply Define sinh x hyperbolic function

Sinh x = \frac12\left(e^x-\;e^{-x}\right) is called hyperbolic sine function. Its domain and range are the set of all real numbers.

Define sinh x hyperbolic function

Formula for Cosine hyperbolic function in Math with Detail

Cosh x = \frac12\left(e^x+\;e^{-x}\right) is called hyperbolic cosine function. its domain is the set of all real numbers and the range is the set of all numbers in the interval.

[1, +∞)

Formula for Cosine hyperbolic function

Four Hyperbolic Functions and Formulas and Their Details

The remaining four hyperbolic functions are defined in the terms of the hyperbolic sine and the hyperbolic cosine function as follows:

Four Hyperbolic Function Formulas are

Functionsis equal toFormulas
tanh x\frac{\sin h\;x}{\cos h\;x}\frac{e^x\;-\;e^{-x}}{e^x\;+\;e^{-x}}
sech x\frac1{\cos h\;x}\frac2{e^x\;+\;e^{-x}}
coth x\frac{\cos h\;x}{\sin h\;x}\frac{e^x\;+\;e^{-x}}{e^x\;+\;e^{-x}}
csch x\frac1{\sin h\;x}\frac2{e^x\;-\;e^{-x}}

The hyperbolic functions have the same properties that resemble to those of trigonometric functions.

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