# How to Use LaTeX Hyperbolic Cotangent (coth) Symbol

To write the Hyperbolic Cotangent (coth) in LaTeX, use the LaTeX command `\coth`

. It will add `coth`

symbol in the text.

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

## Symbol Overview

**Symbol:** Hyperbolic Cotangent

**Unicode:** U+2210

**Type:** Trigonometric

**Package Requirement:** None (built-in symbol)

**Argument:** None (no additional arguments needed)

**LaTeX Command:** \coth

**Example:** coth

## Description

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

## Syntax

The LaTeX command `\coth`

is used to display the **Hyperbolic Cotangent** symbol.

```
\coth
```

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

## Using the Hyperbolic Cotangent Symbol to Calculate the Hyperbolic Cotangent of a Value

```
\documentclass{article}
\begin{document}
$\coth (1) = \frac{\cosh(1)}{\sinh(1)}$
\end{document}
```

Output: 👇️

coth(1) = cosh(1) / sinh(1)

In the above example, the Hyperbolic cotangent symbol is used to calculate the Hyperbolic cotangent of the value 1, which is equal to cosine of 1 divided by hyperbolic sine of 1

## Using the Hyperbolic Cotangent Symbol in Mathematical Expression

```
\documentclass{article}
\begin{document}
$\frac{\text{d}}{\text{d}x}{\coth(x)} = - \frac{1}{\sinh ^ 2(x)}$
\end{document}
```

Output 👇️

coth(x) = - (1 / sinh^2(x))

In the above example, the Hyperbolic cotangent symbol is used in an derivative expression, where the derivative of coth(x) is equal to -1 divided by the hyperbolic sine squared of x.

## Applications

The `Hyperbolic Cotangent`

symbol has numerous applications in LaTeX documents such as:

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

## Conclusion

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

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