Hyperbolic functions

Hyperbolic functions are different versions of trigonometric functions. They are defined using a hyperbola instead of a circle. Also, as the derivatives of  and  are  and , the derivatives of  and  are  and .

The basic hyperbolic functions are:

 hyperbolic sine "" (),(1999) Collins Concise Dictionary, 4th edition, HarperCollins, Glasgow, , p. 1386
 hyperbolic cosine "" (),

Using these, you can get:

 hyperbolic tangent "" (),
 hyperbolic cotangent "" (),
 hyperbolic secant "" (),
 hyperbolic cosecant "" or "" ()

and these have similar logic to the normal trigonometric functions.

The inverse hyperbolic functions are:

 inverse hyperbolic sine "" (also "", "" or sometimes "")
 inverse hyperbolic cosine "" (also "", "" or sometimes "")
 inverse hyperbolic tangent "" (also "", "" or sometimes "")
 inverse hyperbolic cotangent "" (also "", "" or sometimes "")
 inverse hyperbolic secant "" (also "", "" or sometimes "")
 inverse hyperbolic cosecant "" (also "", "", "","", "", or sometimes "" or "")

 Definitions 
With hyperbolic angle u, the hyperbolic functions sinh and cosh can be defined using the exponential function eu.Weisstein, Eric W. "Hyperbolic Functions". mathworld.wolfram.com. Retrieved 2020-08-29."Hyperbolic Functions". www.mathsisfun.com. Retrieved 2020-08-29. In the figure
 .

 Exponential definitions 

 Hyperbolic sine: the odd part of the exponential function, that is, 
 Hyperbolic cosine: the even part of the exponential function, that is, 


 Hyperbolic tangent: 
 Hyperbolic cotangent: for , 
 Hyperbolic secant: 
 Hyperbolic cosecant: for , 

 Related pages 
 e (mathematical constant)
 Trigonometric functions

 References 

Category:Trigonometry
Category:Functions and mappings