TeXipedia

ch

Represents the hyperbolic cosine function in mathematical expressions and equations.

Overview

Essential in mathematical analysis and physics, particularly when dealing with hyperbolic functions and their applications.

  • Commonly used in differential equations and complex analysis
  • Appears frequently in physics problems involving wave equations and oscillations
  • Important in engineering calculations, especially in structural analysis and electrical circuit theory
  • Often paired with other hyperbolic functions like sinh and tanh
  • Fundamental in the study of catenaries and certain geometric curves

Examples

Hyperbolic cosine function in a mathematical expression

ch⁡(x)=ex+e−x2\ch(x) = \frac{e^x + e^{-x}}{2} 
\ch(x) = \frac{e^x + e^{-x}}{2}

Relationship between hyperbolic functions

ch⁡2(x)−sinh⁡2(x)=1\ch^2(x) - \sinh^2(x) = 1 
\ch^2(x) - \sinh^2(x) = 1

Solution to a differential equation involving hyperbolic cosine

y=Ach⁡(kx)+Bsinh⁡(kx)y = A\ch(kx) + B\sinh(kx) 
y = A\ch(kx) + B\sinh(kx)