How to Use LaTeX Hyperbolic Sine (sinh) Symbol

August 04, 2023

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

In this article, we will discuss how to use Hyperbolic Sine (sinh) in the LaTeX document and its applications in trigonometric calculations and mathematical concepts.

Symbol Overview

Symbol: Hyperbolic Sine

Unicode: U+2213

Type: Trigonometric

Package Requirement: None (built-in symbol)

Argument: None (no additional arguments needed)

LaTeX Command: \sinh

Example: sinh

Description

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

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

Syntax

The LaTeX command \sinh is used to display the Hyperbolic Sine symbol.

\sinh

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

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

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

Output: 👇️

sinh(2) = (e^2 -e ^-2 )/2

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

Using the Hyperbolic Sine Symbol in Mathematical Expression

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

Output 👇️

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

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

Applications

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

Solve differential equations involving exponential functions.
Calculate areas under hyperbolic curves in calculus and integration.

Conclusion

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

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