What Is COSH Function in Google Sheets?
COSH is a powerful function in Google Sheets that allows you to calculate the hyperbolic cosine of a given value. It is a useful tool for mathematical calculations and data analysis. COSH stands for hyperbolic cosine, which is a mathematical function that finds the hyperbolic cosine of a given number. One of the common uses of COSH is in the calculation of interest rates to model the growth of an investment. The hyperbolic cosine function mathematically is the average of the exponential function e^x and e^(-x). Let us look at a simple example of how to apply the cosh function.
Here, we have applied the formula =COSH(value) for 0 and 1. Press Enter and view the results, as shown below. This function is useful in various scientific applications, and we present it in this article.
Key Takeaways
- The COSH function in Google Sheets calculates the hyperbolic cosine of a value. The hyperbolic functions are similar to trigonometric functions, but these are used for hyperbolic calculations rather than circles.
- The syntax of the COSH function is as follows: =COSH(value)
- value: The numeric input for which you want to find the hyperbolic cosine.
- The COSH function is used in finance, engineering, physics, and other fields that involve hyperbolic functions.
- The result of the COSH function will always be greater than or equal to 1 since it increases exponentially for both positive and negative inputs.
COSH() Google Sheets Formula
Here is the syntax of the COSH Function in Google Sheets.
=COSH(value)
- COSH takes a single argument, the value for which you calculate the hyperbolic cosine.
This function takes a single argument, which is the value for which you want to calculate the hyperbolic cosine. This argument can be a numeric value, a reference to a cell containing a numeric value, or another function or formula that returns a numeric value. The COSH function then calculates the hyperbolic cosine of this value and returns the result.
How to Use COSH Function In Google Sheets?
There are two ways you can enter the COT function in Google Sheets.
- Manually enter the COSH function
- Through the Google Menubar
#1 – Manually Enter The COSH Function
Now that we have a clear understanding of what COSH is and its formula, let’s explore how to use it in Google Sheets. Follow the step-by-step process below:
Step 1: Open a new sheet in Google Sheets and enter the values for which you must find the COSH result.
Step 2: Select cell B2, where you want to display the COSH function’s result first.
Enter the formula =COSH(A2) and press Enter.
Step 3: Drag the Autofill handle, which is similar to the Excel Autofill handle, all the way to cell C6.
By following these simple steps, you can easily use the COSH function in Google Sheets to perform hyperbolic cosine calculations.
The most common physical applications of hyperbolic functions are calculations involving catenaries.
#2 – Using The Google Menubar
- Choose the cell where you want to enter the COSH formula.
- Go to the menu bar and click on “Insert” ➝ “Function” ➝ “Math” ➝ “COSH.”
- Enter the required argument. Close the bracket and press the “Enter” key.
Examples
Let us look at some examples of using the COSH function in Google Sheets and its application.
Example #1 – Using the COSH Function with Cell References
Let us look at an interesting example of using the COSH function. It is known that according to maths, COSH(x) = COSH(-x). Let us prove it using Google Sheets.
Step 1: Open a new Google Sheet and enter some values as shown.
Step 2: Now, let’s apply the formula COSH(A2) to cell B2. Press Enter.
Step 3: Now, drag the formula to cell B3. Check the results.
Step 4: To prove the equation COSH(x) = COSH(-x), let’s apply the following formula to cell C2.
=COSH(-A2). Press Enter and drag the formula.
As seen above, the formula COSH(x) = COSH(-x) is proved.
Example #2 – Calculate the Hyperbolic Cosine of a Single Number
In this example, let’s find the COSH value of some commonly used angles in trigonometry. We have to apply the values directly.
Step 1: Use the RADIANS function to convert the angles into radians. First, find the COSH of 0 degrees. Hence, enter the following formula in cell A1.
=COSH(RADIANS(90)).
Step 2: Press Enter. You get the COSH result for the degree converted to radians.
Step 3: Let us apply a few more numbers in degrees, convert them to RADIANS and apply the COSH function in Google Sheets.
Look at the image below.
Example #3 – Using the COSH Function with Negative Numbers
One of the applications of hyperbolic functions involves hanging cables. Suppose you have a cable of uniform density suspended between two supports. There is no load apart from its own weight. The curve formed by the cable is called a catenary. Examples include high-voltage power lines, strands of a spider’s web, etc. The COSH function can be used in such scenarios to find the cable length needed. You can also apply the COSH for negative values. Let us check how the function works with negative numbers.
Step 1: Enter the required numbers in a Google sheet as shown below.
Step 2: Enter the following function in cell B1.
=COSH(A1). Press Enter.
As observed, the COSH function does not give any errors and can be used with negative numbers as well. Any real number can be given as an argument.
Step 3: Drag the Autofill handle up to cell B5. You get the COSH values for all the negative numbers.
We can also check what happens when we give a very large negative number. Let us enter -1000 in cell B6 and apply the function to it. Copy the formula =COSH(A6) into cell B6.
We get the #NUM error. Use the IFERROR function to manage errors gracefully. We can use it can provide a custom message if COSH results in an error. Enter the formula as follows in cell A6.
=IFERROR(COSH(A6), “Too big result to be displayed”). Press Enter.
You can also use ISNUMBER to validate if an input value is a valid real number. Enter the following formula in cell A7.
=IF(ISNUMBER(A7), COSH(A7), “Invalid input”)
The error message is displayed accurately. Thus, the COSH function can effectively calculate the hyperbolic cosine value.
Important Things to Note
- The hyperbolic cosine function is an even function, where COSH(−x)=COSH(x), as shown in our example above.
- The result of the COSH function grows exponentially for both positive and negative values of x in COSH(x). It is because it is a hyperbolic function.
- Many times, the COSH function is used to handle complex numbers and returns complex results. However, you can give complex numbers in Google Sheets using the function IMCOSH.
- If the numbers given are outside the acceptable range, you may have to handle the #NUM error.
Frequently Asked Questions (FAQs)
In geometry, the distance between two points on a hyperbolic plane can be calculated using the COSH function. It can also be helpful in solving equations involving hyperbolic functions. The COSH function in Google Sheets can be used to model certain data types, such as stock prices or interest rates in finance. You can perform complex mathematical calculations like modeling exponential growth or decay phenomena. In Physics, it can be used to find values such as the charging and discharging of capacitors, population growth, etc. Overall, the COSH function is handy, and Google Sheets helps find the value in no time.
There are a few limitations when using the COSH function in Google Sheets:
● The COSH function accepts a single argument, so it cannot be used to calculate the hyperbolic cosine of multiple values.
● The COSH function works only with numeric real values. It will return an error for any other value.
● In some cases, the COSH function may be unable to model or analyze certain types of data. Use it only when working with appropriate data, such as hyperbolic functions.
For COSH in Google Sheets, note that the input value should be a real number. The output is also always a real number, usually increasing exponentially as the input value increases. The COSH function can also handle negative input values and returns the hyperbolic cosine, providing accurate results for both positive and negative real values.
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