Client Account:   Login
Home Site Statistics   Contact   About Us   Sunday, March 26, 2017

users on-line: 2 | Forum entries: 6   
Pj0182295- Back to Home
   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Complex Numbers and Functions › ~ Hyperbolic Functions

      Skip Navigation Links

Hyperbolic Functions

This page contains various complex hyperbolic functions, including Sinh, Cosh, Tanh functions.

Hyperbolic Sine Function

It is known that a complex Sinh function can be calculated using complex exponential functions:

sinh z = 1/2 (ez - e-z)
= 1/2 [ex (cos y + i siny) - e-x (cos y - i sin y)]
= sinh x cos y + i cosh x sin y

Using this relationship, we wrote the following method:

           public static Complex Sinh(Complex c)
           return new Complex(Math.Sinh(c.Real) * Math.Cos(c.Imaginary) +
                                        (Math.Cosh(c.Real) * Math.Sin(c.Imaginary));

Hyperbolic Cosine Function

Similar to the case of the complex Sinh function, a complex Cosh function can also be represented by:

cosh z = 1/2 (ez + e-z)
= 1/2 [ex (cos y + i siny) + e-x (cos y - i sin y)]
= cosh x cos y + i sinh x sin y

Using the above equation we added this method to the "Complex class". (Note - Complex class is part of our mathematical algorithms library and is not shown in these examples):

           public static Complex Cosh(Complex c)
           return new Complex(Math.Cosh(c.Real) * Math.Cos(c.Imaginary) +
                                        (Math.Sinh(c.Real) * Math.Sin(c.Imaginary));

Hyperbolic Tangent Function

A complex tanh can be computed using Sinh and Cosh functions:

tanh z = sinh z / cosh z

Adding a complex Tanh method to the Complex class:

           public static Complex Tanh(Complex c)
             return Sinh(c) / Cosh(c);

Skip Navigation Links.

Home Skip Navigation Links
   Algorithms, Graphics, Vectors,
            implementation techniques.
   Mineral Transactions info,
            sales, agreements...
   Numerical Modeling services
            mineral environment.
   Want to know about Mining?
            basic knowledge here...
   What are Mineral Commodities?
            our elementary charts.
   Math, Analysis and More...
            our expertise in the matter.


Platform Implementation

Home Algorithm Implementation
We design applications for different environments and platforms...
        Home Graphics and Animation
The graphics classes in Smalltalk were designed...
        Home Optimization Algorithms
An optimization problem is a numerical problem...
        Home Vectors and Matrices
The concise notation introduced in linear algebra for vector...

2017 © Keystone Mining Post  |   2461 E. Orangethorpe Av., Fullerton, CA 92631 USA  |