SinH in Google Sheets

What Is SinH in Google Sheets?

The SINH function is a built-in function in Google sheets. SINH in Google Sheets is the hyperbolic sine of an input given in radians. The hyperbolic sine is a mathematical function that relates to hyperbolic trigonometry. There are many hyperbolic functions in Google Sheets, such as SINH, COSH, and TANH. These functions, especially SINH, are used in a wide range of calculations involving hyperbolic geometry. When using SINH in Google Sheets, we must understand that the hyperbolic sine function is represented as (e^x – e^(-x))/2. Here, e is the base of the natural logarithm. It is beneficial in scenarios involving exponential growth and decay, as well as in complex analysis.

For example, we have a SINH function calculation, which helps us understand its use. Let us apply the following equation to cell B1 to find the hyperbolic sine of the value in radians. =SINH(A1). Here, the value in cell A1 is in RADIANS. Instead of a cell reference, you can also give a direct value to the function like =SINH(2).

The SINH function calculates the hyperbolic sine of a number. It belongs to the type – hyperbolic function. These functions are based on hyperbolas rather than circles.
The syntax for the SINH function is:
SINH(number)
number: The value in radians for which you must calculate the hyperbolic sine. It can be a direct number or a cell reference containing a number.
The result of SINH can be positive or negative.
The SIN function differs from SINH in that it calculates the trigonometric sine of an angle, whereas SINH is used for hyperbolic calculations.
The SINH function is used for modeling exponential growth or decay and in various fields such as physics, engineering, and statistics.

Syntax

The syntax for SINH in Google Sheets is:

SINH(value)

The “value” argument is the angle in radians for which you want to calculate the hyperbolic sine.
It is either a number or a cell reference. It can also be a formula whose result evaluates to a number.

How to use SINH in Google Sheets?

The SINH function in Google Sheets can be used in two ways.

Manually Enter the Function

To use the SINH function in Google Sheets, follow these steps:

Step 1: First. select the cell where you want the result to be displayed. We have some values, as shown below.

Step 2: Type “=” to start the formula. Enter the SINH function, followed by an open parenthesis.

=SINH(

Step 3: Enter the reference to the cell containing the value. Close the parenthesis and press Enter.

Step 4: Drag the formula to cell B2 to apply it to the value in cell A2.

Through the Google menu bar

Place the cursor where you want the formula to be entered. Then, in the menu bar, go to the Insert tab and click on the Functions. From here, go to “Math” and “COSH.”

Upon completing these steps, the cell will display the calculated value of the hyperbolic sine for the specified input.

Examples

When using the SINH function in Google Sheets, it is important to note that the input value can be a real number, a cell reference, or even another formula. Let us look at the different ways in which the SINH function can be used in Google sheets with suitable SINH Google Sheets example.

Example #1 – Calculating the Hyperbolic Sine of a Value

Given below are some values whose SINH in Google Sheets value has to be found. Instead of using the cell reference, we enter the values directly.

Step 1: Enter the values whose SINH is to be found directly.

Step 2: Let us plot a graph for SINH(x) for the given values.

The graph of SINH(x) is always between the graphs of e^x/2and e^−x/2.

Example #2 – Calculating growth rates in investment

The SINH value can be used to calculate the growth rate of investments. Since you initially invested $10,000, let’s assume we use a hyperbolic sine model. Let’s find the growth rate of this investment at the end of three years.

Step 1: Enter the details in a Google sheet.

Step 2: Apply the following formula to know the growth rate in cell B3.

=B1*SINH(B2)

Step 3: Press Enter. You can see the final amount based on the hyperbolic sine growth.

Example #3 – Modeling population growth in demography

Modeling population growth in demography using SINH in Google Sheets is not simple, but growth patterns that exhibit hyperbolic characteristics can be used. Let us look at the example below.

Step 1: Enter all the required data in a sheet.

Initial Population: Enter the initial population size: 10000.

Growth Factor: Enter the growth factor: 0.4

Also, list the years. Here, we list 1,2,3,4,5.

Step 2: In cell D2, enter the formula shown below for population growth.

=initial population * SINH(growth factor * years). Here, we enter the formula: =$A$2* SINH($B$2*C1). Press Enter.

Step 3: Now, drag the formula to calculate the population growth for each year.

The SINH function model starts slowly and then accelerates, as it is a hyperbolic model. It is helpful in calculating the growth in specific demographic scenarios. You can adjust the growth factor and change how the population grows. As the growth factor increases, the rate of growth increases highly.

Example #4 – Using a Cell Reference

Below are a few angles in degrees. We must find the hyperbolic sine of these values. First, we must convert them to radians and then find the hyperbolic sine of the radian values.

To find the radians of the angles, which are specified in degrees, we multiply them by PI()/180. Another alternative is to use the RADIANS function. Here, we will use PI()/180 for a few values and RADIANS for the rest.

Step 1: In cell B2, enter the value =RADIANS(A2) and press Enter. We get a value of zero degrees in radians.

Step 2: Drag the Autofill handle from B2 to B4 and get the radians value for the corresponding angles in degrees.

Step 3: Now, we must find the hyperbolic sine values of these radians. In cell C2, enter the formula =SINH(B2) and Press Enter.

Now, drag the formula till C4.

Step 4: In cell C5, enter the formula as =(PI()/180)*A5.

Step 5: Drag the Autofill handle from C5 to C7 to get the SINH values for all the radians. Thus, the SINH function is easy to calculate for any real number.

Important Things to Note

If the argument supplied to the SINH function is non-numeric, the function returns the #VALUE! Error.
The input number given to the SINH function is the angle in radians.
When using the SINH function in Google Sheets, if the argument provided is in degrees, you must convert it to radians first. Multiply the number in degrees by PI ()/180 or use the RADIANS function to convert it into radians.
If you want the result in degrees, multiply the result by 180/PI().
This function calculates the hyperbolic sine of a number which is useful for mathematical and engineering applications.

Frequently Asked Questions (FAQs)

1. How to approximate a cumulative probability distribution using SINH in Google Sheets?

Suppose you get a test value in a lab that may vary between 0 and 20 seconds. When we analyze the results of various experiments conducted, we notice that the probability of getting a result, x, of less than t seconds, is obtained by:
P(x<t) = 2.868 * SINH(0.0342 * t), where 0<t<20
To calculate the probability of obtaining a result of less than 5 seconds, substitute 5 for t.
=2.868*SINH(0.0342*5)
Therefore, the result is 0.4928215977. This means that for every 100 experiments, the result is obtained approximately 49 times.

2. What are the uses of SINH in Google Sheets?

SINH can be particularly useful when we have to calculate exponential growth or decay. Besides, the SINH function is helpful when performing calculations involving hyperbolic trigonometry. It is also used to study systems involving simple harmonic motion. In the field of finance, it can be used in certain financial models that require hyperbolic functions. It can be used when analyzing the oscillation of a pendulum to find the displacement, velocity, and acceleration of the system over time. It is also useful in various analyses, such as hypothesis testing or regression modeling.

3. What are the common errors when using SINH in Google Sheets?

Here are a few common errors to watch out for when working with the SINH function
• The #VALUE! error occurs when the input value is not in the correct format.
• The #NUM! error occurs when the input value is outside the range in which the hyperbolic sine can be calculated.

Download Template

This article must be helpful to understand the Sinh in Google Sheets, with its formula and examples. You can download the template here to use it instantly.

SINH-in-Google-Sheets Download

SinH in Google Sheets