How to Use LaTeX Hyperbolic Cosine (cosh) Symbol

To write the Hyperbolic cosine (cosh) in LaTeX, use the LaTeX command \cosh. It will add cosh symbol in the text.

In this article, we will discuss how to use Hyperbolic cosine (cosh) in the LaTeX document and its applications in calculus, differential equations, physics etc..

Symbol Overview

Symbol: Hyperbolic Cosine

Unicode: U+221C

Type: Trigonometric

Package Requirement: None (built-in symbol)

Argument: None (no additional arguments needed)

LaTeX Command: \cosh

Example: cosh

Description

The Hyperbolic Cosine is a built-in symbol available in LaTeX, and one of the fundamental trigonometric functions used in mathematics to relate exponential growth and properties of hyperbolas.

In LaTeX, it is commonly used to represent hyperbolic cosine functions which is widely used in calculus, differential equations, physics etc..

Syntax

The LaTeX command \cosh is used to display the Hyperbolic Cosine symbol.

\cosh

Let’s understand using Hyperbolic cosine symbol in various domains like mathematics, trigonometry with the help of examples.

Using the Hyperbolic Cosine Symbol to Calculate the Hyperbolic Cosine of a Value

\documentclass{article}
\begin{document}
$\cosh (1) = \frac{e + e^{-1}}{2}$
\end{document}

Output: 👇️

cosh(1) = (e + e ^-1 )/2

In the above example, the hyperbolic cosine symbol is used to calculate the hyperbolic cosine of the value 1, which is equal to (e1 + e ^-1)/2.

Using the Hyperbolic Cosine Symbol in Mathematical Expression

\documentclass{article}
\begin{document}
$\frac{\text{d}}{\text{d}x}{\cosh(x)} = \sinh(x)$
\end{document}

Output 👇️

d/dx (cosh(x)) = sinh(x)

In the above example, the hyperbolic cosine symbol appears in a derivative expression, where the derivative of cosh(x) is equal to sinh(x).

Applications

The hyperbolic cosine symbol has numerous applications in LaTeX documents such as:

• Solve differential equations involving exponential functions.
• Analyze the properties of hyperbolic functions in calculus and trigonometry.

Conclusion

I hope the above article on how to use hyperbolic cosine symbol help you. The hyperbolic cosine symbol (cosh) is a fundamental trigonometric functions used extensively in mathematics and widely used in LaTeX documents.

By effiectively use the the hyperbolic cosine symbol in LaTeX documents to convey accurate and precise trigionometric calculations and mathematical concepts.