How to Use the ASINH Function in Google Sheets

This guide will explain how to use the ASINH function in Google Sheets.

Hyperbolic functions are a class of mathematical functions that are analogous to trigonometric functions. However, instead of using the unit circle as a reference, hyperbolic functions base their calculations on a unit hyperbola. 

Similar to how trigonometric functions have their equivalent inverse functions, hyperbolic functions also have their respective inverse functions. One of these inverse functions is the inverse hyperbolic sine (sinh-1) which is the inverse of the hyperbolic sine (sinh).

The ASINH function in Google Sheets allows users to find the inverse hyperbolic sine of any real number. In this guide, we will provide a step-by-step tutorial on how to use the ASINH function.

The Anatomy of the ASINH Function

The syntax of the ASINH function is as follows:

=ASINH(value)

Let’s look at each argument to understand how to use the ASINH function.

• the ASINH function takes an input value and computes an output x where SINH(x) is equal to the input value.
• the value argument refers to the value for which to calculate the inverse hyperbolic sine
• Do note that Google Sheets does not support imaginary or complex numbers as input or output for hyperbolic functions.

A Real Example of the ASINH Function in Google Sheets

Let’s explore a simple example where we’ll need to calculate the inverse hyperbolic sine of one or more values.

In the table above, we have a set of values in column A that we want to find the inverse hyperbolic sine of.

We can use the ASINH function to find the inverse hyperbolic sine of all the values in the first column. 

We can calculate for column B using the following formula:

=ASINH(A2)

By using the ASINH function, our final data would be like this:

Using ASINH and ARRAYFORMULA

If you plan on using the ASINH function on a large dataset, we recommend using the function with ARRAYFORMULA. With the ARRAYFORMULA function, we can provide an entire range of numbers as input to a single ASINH function. This change will also help improve the performance of your sheet.

We’ll use the following formula to achieve our desired result:

=ARRAYFORMULA(ASINH(A2:A11))

The table above shows our final dataset, in which we applied  the ASINH function to the array A2:A11 using the ARRAYFORMULA method.

Click on the link below to create your own copy of our examples.

Head to the next section to read our step-by-step tutorial on how to use the ASINH function in Google Sheets.

How to Use the ASINH Function in Google Sheets

1. Select the cell where you want to output the inverse hyperbolic sine.
   In our example above, we’ll start by placing our ASINH formula in cell B2.
   
   
   
2. Type the ASINH function and input the value you want to calculate as the sole argument. In our example, we’ll find the inverse hyperbolic sine of the value in cell A2 using the formula ASINH(A2).
   
3. Hit the Enter key to evaluate the ASINH function.
   
4. We can use the AutoFill feature to find the inverse hyperbolic sine of the remaining values in our dataset. To do this, use your cursor to drag the fill handle of the first cell downward.
   
5. We can use the ASINH function with the ARRAYFORMULA function to find the inverse hyperbolic sine of multiple values at once. Start by typing the ARRAYFORMULA.
   Ensure that there is enough space below the cell to accommodate the array output.
   
   
   
6. Enter the ASINH function as an argument of the ARRAYFORMULA. Now that ASINH is wrapped with an ARRAYFORMULA, we can now input an array reference as our ASINH argument.
   In this example, we’ll add the array A2:A11 as an argument.
   
   
   
7. Hit the Enter key to evaluate the formula. The result of the formula should also be an array with the same size as the input array.
   

These are all the steps you need to know to start using the ASINH function in Google Sheets.

FAQs

1. Why is the ASINH function returning an error?
   The ASINH function requires the value argument to be a valid number. Entering non-numeric values or cell references containing non-numeric values will result in a #NUM! error.
   
2. How do I retrieve the hyperbolic sine of a number or other inverse hyperbolic functions?
   The ASINH function returns the inverse hyperbolic sine rather than the hyperbolic sine of a given input. Use SINH instead if you wish to compute for the hyperbolic sine.
   If you wish to find the inverse hyperbolic cosine or tangent, you may use the ACOSH and ATANH functions, respectively.

To learn more about using hyperbolic functions in Google Sheets, you can read our post on how to use the IMCOSH function.

That’s all for this guide! Be sure to check out our library of spreadsheet resources, tips, and tricks!