# 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.

### 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, +∞)

### 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

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