# COSH

The `COSH` function returns the hyperbolic cosine of a given value. The hyperbolic cosine is defined as (ex + e-x) / 2, where x is the given value. This function is most commonly used in mathematical calculations and modeling.

## Usage

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

Parameters:
1. value (required):
The value for which to calculate the hyperbolic cosine. Must be a number or a reference to a cell containing a number.

## Examples

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

### Calculate the hyperbolic cosine of a value

To calculate the hyperbolic cosine of a value in a cell, use the formula `=COSH(A1)`, where A1 is the cell containing the value.

### Calculate the distance between two points in a hyperbolic space

To calculate the distance between two points in a hyperbolic space, use the formula `=ACOSH(COSH(x1)*COSH(x2)-SINH(x1)*SINH(x2)*COS(y1-y2))`, where x1, x2, y1, and y2 are the coordinates of the two points in the hyperbolic space.

### Calculate the rate of growth of a population

To calculate the rate of growth of a population, use the formula `=LN(COSH(r*t))`, where r is the growth rate and t is the time period.

## Common Mistakes

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

### Incorrect argument type

The value provided must be a numeric value such as a number or a cell reference that contains a number. If a non-numeric value is provided, an error will occur.

### Incorrect argument format

The value provided must be in radians. If the value is in degrees, it must be converted to radians first. To convert degrees to radians, multiply the value by PI()/180 or use the RADIANS function.

### Using COS instead of COSH

COS and COSH are different functions. Make sure to use COSH when you want to calculate the hyperbolic cosine.

The following functions are similar to `COSH` 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.

• `TANH`

The `TANH` function returns the hyperbolic tangent of a value. It is commonly used in mathematical modeling, such as in statistics, physics, and engineering.

• `ACOSH`

The `ACOSH` function returns the inverse hyperbolic cosine of a number. In other words, it calculates the value whose hyperbolic cosine is the specified number. This function is useful for solving mathematical problems involving hyperbolic functions.

• `ATANH`

The `ATANH` function returns the inverse hyperbolic tangent of a value. It is commonly used in mathematical calculations involving hyperbolic functions.

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