How to Use LaTeX Hyperbolic Tangent (tanh) Symbol

August 04, 2023

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

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

Symbol Overview

Symbol: Hyperbolic Tangent

Unicode: U+2208

Type: Trigonometric

Package Requirement: None (built-in symbol)

Argument: None (no additional arguments needed)

LaTeX Command: \tanh

Example: tanh

Description

The Hyperbolic Tangent 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 tangent functions which is widely used in calculus, differential equations, physics and scientific fields etc..

Syntax

The LaTeX command \tanh is used to display the Hyperbolic Tangent symbol.

\tanh

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

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

\documentclass{article}
\begin{document}
$\tanh (0) = 0$
\end{document}

Output: 👇️

tanh(0) = 0

In the above example, the hyperbolic tangent symbol is used to calculate the hyperbolic tangent of the value 0, which is equal to 0.

Using the Hyperbolic Tangent Symbol in Mathematical Expression

\documentclass{article}
\begin{document}
\[ \int \tanh(x) \, dx = \ln(\cosh(x)) + C \]
\end{document}

Output 👇️

∫tanh(x)dx = ln(cosh(x))+C

In the above example, the hyperbolic tangent symbol is used in an integral expression. The integral of tanh(x) with respect to x is equal to the natural logarithm of the hyperbolic cosine function (cosh(x)), plus a constant of integration (C).

Applications

The hyperbolic tangent 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 tangent symbol help you. The hyperbolic tangent symbol (tanh) is a fundamental trigonometric functions used extensively in mathematics and widely used in LaTeX documents.

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