# COS Function in☝️ Google Sheets Explained (Definition, Syntax, How to Use It, Examples)

This guide covers everything you need to know about the Google Sheets COS function, including its definition, syntax, use cases, and how to use it.

Quick Jump

## What is the COS Function? How Does It Work?

The COS function in Google Sheets returns the cosine of a given angle provided in radians. This function is pivotal in trigonometry and other mathematical fields, enabling users to calculate the cosine without resorting to manual computation or external resources.

To understand how the COS function works, it’s important to familiarize yourself with the concept of cosine in trigonometry. In a right-angled triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. So, if you’ve got the angle in radians, the COS function can expediently calculate this ratio for you.

Note that the angle must be in radians, not in degrees. If your angle is in degrees, you will have to convert it to radians before using it in the COS function. The RADIANS function can be used for this conversion.

The COS function works with a single argument – the angle in radians. You can input this angle directly, like COS(1), or reference a cell containing the angle, like COS(A2). Alternatively, you can use other functions to calculate the angle, such as the PI function, and use that as your argument, like COS(PI()).

The COS function can be used in a wide variety of applications, such as calculating the coordinates of points in a circle or modeling periodic phenomena in physics and engineering. It’s an invaluable function for anyone who regularly works with mathematical calculations in Google Sheets.

## COS Syntax

The syntax and arguments for the function are as follows:

COS(angle)

The COS function in Google Sheets accepts one argument:

• angle: This is the angle for which you want to find the cosine, expressed in radians. The argument must be a numeric value, and it can be a direct number, a cell reference containing the number, or the result of another function that yields a numeric result.

Usage notes related to the syntax and arguments:

• The COS function in Google Sheets expects the angle to be provided in radians. If you have an angle in degrees, you need to convert it to radians before using it in the COS function. Google Sheets provides a RADIANS function for this purpose.
• The COS function will return a #VALUE! error if the angle argument is non-numeric.
• The result of the COS function will be a numeric value between -1 and 1, inclusive.
• The COS function is case-insensitive, meaning you can use it as COS, cos, Cos, etc.
• The COS function can be used as a part of a larger formula or function in Google Sheets as long as the argument provided to it adheres to the rules mentioned above.
• The COS function in Google Sheets is a mathematical function and follows the standard mathematical rules for the cosine function.

## Examples of How to Use the COS Function

Here are some practical examples to help you understand how to use the COS function in Google Sheets.

### Example #1: Basic COS Function

Let’s start with a simple example. Suppose you want to find the cosine of 45 degrees.

In cell A1, type 45. Then in cell B1, type the formula =COS(RADIANS(A1)).

The RADIANS function is used to convert degrees to radians because the COS function in Google Sheets uses radians. Press Enter, and you will get the result 0.707106781, which is the cosine of 45 degrees.

### Example #2: Using COS Function in a Formula

The COS function can also be used in a formula. Let’s say you want to find the length of the adjacent side of a right-angled triangle, given the hypotenuse length and the angle.

In cell A1, type the hypotenuse length, let’s say 10. In cell B1, type the angle in degrees, let’s say 60. Then in cell C1, type the formula =A1*COS(RADIANS(B1)). Press Enter, and you will get the length of the adjacent side, which is 5.

### Example #3: Using COS Function with PI Function

You can use the COS function with the PI function to find the cosine of multiples of π.

For example, if you want to find the cosine of π/4, in cell A1, type the formula =COS(PI()/4). Press Enter, and you will get the result 0.707106781, which is the cosine of π/4.

### Example #4: Using COS Function with Other Trigonometric Functions

The COS function can be used with other trigonometric functions.

For example, if you want to prove the Pythagorean identity sin²θ + cos²θ = 1 for a certain angle, you can do so in Google Sheets. In cell A1, type the angle in degrees, let’s say 30. Then in cell B1, type the formula =SIN(RADIANS(A1))^2+COS(RADIANS(A1))^2.

Press Enter to get the result 1, proving the Pythagorean identity.

## Why Is COS Not Working? Troubleshooting Common Errors

If you are having trouble with the COS function in Google Sheets, there are several common errors you might encounter. Knowing how to identify these errors, understanding their causes, and learning how to fix them can help you use the COS function more effectively.

### #VALUE! Error

Cause: This error generally occurs when the function’s input argument is non-numeric. Since the COS function only works with numeric values, any text or string value will cause the function to return the #VALUE! error.

Solution: Check the cell reference or the argument that you are using in the COS function. Make sure that it is a numeric value. If it’s a cell reference, ensure it contains a number. If you’re directly inputting the value, confirm that you’re entering a number, not text.

### #DIV/0! Error

Cause: While this error is less common with the COS function, it can still occur in certain situations. The #DIV/0! error typically happens when a formula tries to divide a number by zero.

Solution: Since the COS function does not involve division, this error is likely due to an issue with other parts of your formula. Review the entire formula to identify any divisions by zero and correct them.

### #NUM! Error

Cause: This error happens when the function’s input argument is outside the function’s acceptable range. For the COS function, the argument should be a real number.

Solution: Check the argument you are using in the COS function to ensure it is a real number. If it is a cell reference, ensure the cell contains a real number.

### #N/A Error

Cause: This error typically appears when Google Sheets cannot find the input or value you referenced in your formula.

Solution: Check your formula to ensure all references point to the correct cells and ranges. If you’re using a direct input, verify that the value is valid for the COS function.

### #REF! Error

Cause: The #REF! error usually occurs when a formula references a cell that does not exist. This can happen if you delete a row, column, or cell that your formula is referencing.

Solution: Review your formula to ensure all cell references are correct. If you have deleted a row, column, or cell, you may need to adjust your formula or undo the deletion.

These are some of the most common errors you might encounter while using the COS function in Google Sheets. By understanding their causes and knowing how to solve them, you can ensure that your COS function works correctly.

## Using COS With Other Google Sheets Functions

Combining the COS function with other Google Sheets functions can help you perform more complex calculations and analysis. Here are a few examples:

### With SUM

Usage: The SUM function adds all the numbers in a range of cells. You can use it with the COS function to find the sum of the cosine values of a range of numbers.

Example: Suppose you want to find the sum of the cosine values of the numbers from 1 to 3. You can use the following formula:

=SUM(COS(1), COS(2), COS(3))

This will return the sum of the cosine values of 1, 2, and 3.

### With AVERAGE

Usage: The AVERAGE function calculates the average of a range of numbers. You can use it with the COS function to find the average of the cosine values of a range of numbers.

Example: Suppose you want to find the average of the cosine values of the numbers from 1 to 3. You can use the following formula:

=AVERAGE(COS(1), COS(2), COS(3))

This will return the average of the cosine values of 1, 2, and 3.

### With PI

Usage: The PI function returns the value of Pi. You can use it with the COS function to find the cosine of Pi.

Example: Suppose you want to find the cosine of Pi. You can use the following formula:

=COS(PI())

This will return the cosine of Pi, which is -1.

Usage: The RADIANS function converts degrees to radians. You can use it with the COS function to find the cosine of an angle given in degrees.

Example: Suppose you want to find the cosine of 45 degrees. You can use the following formula:

This will return the cosine of 45 degrees, which is approximately 0.7071.

For more details on the COS function, check out the official documentation at the Google Docs Editors Help Center.

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