# COTH

The `COTH` function returns the hyperbolic cotangent of any real number. The hyperbolic cotangent is defined as the ratio of the hyperbolic cosine to the hyperbolic sine of a given angle or value. This function can be used in various mathematical calculations such as in calculus and in solving problems related to physics and engineering.

## Usage

Use the `COTH` formula with the syntax shown below, it has 1 required parameter:

Parameters:
1. value (required):
The real number for which to calculate the hyperbolic cotangent. This can be entered as a number or a reference to the cell containing the number.

## Examples

Here are a few example use cases that explain how to use the `COTH` formula in Google Sheets.

### Calculate the hyperbolic cotangent of a number

Use `COTH` to calculate the hyperbolic cotangent of a given number. This can be useful in many different mathematical calculations.

### Calculate the inverse hyperbolic cotangent of a number

Use `ACOTH(1/x)` to calculate the inverse hyperbolic cotangent of a given number. This can be useful in many different mathematical calculations.

### Calculate the area of a hyperbolic sector

Use `COTH(x) * y` to calculate the area of a hyperbolic sector. This can be useful in geometry and trigonometry problems.

## Common Mistakes

`COTH` not working? Here are some common mistakes people make when using the `COTH` Google Sheets Formula:

### Incorrect argument type

The value provided to COTH() must be a numeric value. If a non-numeric value is used, this error will occur. To fix this, ensure that the argument provided is a number.

### Divide by zero error

If the argument provided to COTH() is zero, this error will occur. To fix this, provide a non-zero argument.

The following functions are similar to `COTH` or are often used with it in a formula:

• `SINH`

The `SINH` function returns the hyperbolic sine of any real number. The hyperbolic sine is a mathematical function that describes the shape of a hanging cable supported at its ends and acted upon by a uniform gravitational force. In Google Sheets, it is most commonly used in mathematical and statistical formulas.

• `COS`

The `COS` function in Google Sheets returns the cosine of an angle provided in radians. It is commonly used in trigonometry to calculate the cosine of an angle. The function takes one parameter, the angle in radians.

• `TAN`

The `TAN` function returns the tangent of an angle specified in radians. Tangent is the ratio of the length of the opposite side to the length of the adjacent side of a right-angled triangle. This function is commonly used in trigonometry and geometry calculations.

• `ACOTH`

The `ACOTH` function returns the hyperbolic arccotangent of a number. It is the inverse function of the hyperbolic cotangent. This function is useful in trigonometry and calculus.

You can learn more about the `COTH` Google Sheets function on Google Support.