What Is SIN Function in Google Sheets?
The SIN function in Google Sheets calculates the trigonometric sine of an angle that is given in radians. It’s a mathematical function used in fields like trigonometry, physics, and engineering. It can be used for modeling waveforms, angles, and periodic motion. Since the angles in real-time are often given in degrees, remember to convert them to radians using the ra using the formula angle * PI()/180.
In the following example, we must find the sine of a 30° angle. For this, we must first convert it to radians and then apply the SIN function:
=SIN(RADIANS(30)) = 0.5
Therefore, the sine of 30 degrees is 0.5, a value commonly used in trigonometry.
Key Takeaways
- The SIN function in Google Sheets calculates the trigonometric sine of an angle and requires the angle to be in radians for accurate results.
- Its syntax is =SIN(angle), where the angle represents the angle in radians. The value can be a constant, cell reference, or a formula.
- It is commonly used in mathematical, engineering, and scientific calculations, especially those involving wave patterns, rotations, or periodic data.
- To work with angles in degrees, they must be converted to radians using the RADIANS function or by multiplying the degree value by PI()/180.
Syntax
The syntax of the SIN Function in Google Sheets is a
=SIN(angle)
angle – a numeric value in radians for which we must calculate the sine.
For example, the argument can be any of the following:
- A number (e.g., SIN(1.23))
- A cell reference (e.g., SIN(A1))
- A formula that returns a number (e.g., SIN(RADIANS(60)))
Note: If your angle is in degrees, convert it using RADIANS(angle) or multiply by PI()/180.
Understanding Output Values of the SIN Function
The SIN function returns values between -1 and 1. It represents the vertical position of a point on the unit circle for a given angle in radians. These values repeat in a wave-like pattern, making the function ideal for modeling periodic behaviors like sound waves, or seasons.
- When the angle is 0 or π (180°), the sine is 0.
- At π/2 (90°), the sine reaches its maximum value of 1.
- At 3π/2 (270°), the sine reaches its minimum value of -1.
- The pattern repeats every 2π radians (360°) due to its periodic nature.
Thus, you can simulate oscillating trends or calculate components of vectors in geometry and physics.
How To Use SIN Function in Google Sheets?
The SIN function in Google Sheets can be used in two main ways:
- Manually Enter the Function
- Using the Google Sheets Menu
Manually Enter the Function
To calculate the SIN value of a particular radian value in Google Sheets, follow these steps.
Step 1: Select the cell where you want the result to appear.
Type = to start the formula, then enter the SIN function with an open parenthesis:
=SIN(
Step 3: Enter the value or cell reference that contains the angle in radians. For example:
=SIN(A1)
If the angle is in degrees, convert it like this:
=SIN(RADIANS(A1))
Step 4: Press Enter to get the result. Drag the formula down to apply it to other cells if needed.
Using the Google Sheets Menu
1: Click on the cell where you want to insert the formula.
2: Go to the menu bar and click on Insert > Function > Math > SIN.
tep 3: The formula =SIN() will appear in the selected cell. Add your angle inside the parentheses in radians and press Enter.
This method is very useful if you’re not familiar with the function name.
Examples
Example #1 – Model Seasonal Sales Fluctuations Over Months
Let’s model the seasonal fluctuation in ice cream sales over 12 months using the SIN function in Google Sheets. Let us suppose there is an ice cream business whose sales fluctuate based on the time of year. We wish to model the sales using a sinusoidal pattern, where sales peak in summer during May/June/July and dip in winter during November/December.
Step 1: We enter the months as numbers in Column A.
Step 2: In column B, calculate the monthly sales using the SIN function. Here, $1250 is the average monthly sales. The fluctuation or amplitude is calculated to be $400.
B1 =1000 + 400 * SIN(RADIANS(A1 * 30))
Press Enter.
Step 3: Click and drag the formula from B2 to B12 to find the sales for all months.
We find that the sales create a wave-like sales pattern.
You can notice that the peak sales occur around April-May. The lowest sales are during the winter months.
Step 4: To check the sinusoidal wave pattern, lets plot a graph. Go to Insert -> Chart after selecting the range A1:B12.
Step 5: Select the line chart. You can observe the sinusoidal wave pattern. You can customize the chart as needed.
This approach is simple but powerful for forecasting trends, managing inventory, and scheduling promotions based on seasonal demand.
Example #2 – Calculate Angles and Sides of Triangles
One can use the SIN function in Google Sheets to solve triangle problems. Most trigonometric formulas use the SIN function. Here, we use the Google Sheets SIN function to find the opposite side of an angle in a right triangle.
We can consider a practical scenario. A person is working on a construction project. He has to calculate the height of a triangular ramp. A piece of information that is clear is that the ramp’s angle with the ground is 45° and the hypotenuse (the ramp length) = 15 meters.
You need to find the height of the ramp (opposite side).
Step 1: Enter all the known values in a Google Sheet. In cell A1, the angle in Degrees is 45 and the hypotenuse (meters) is 15 m.
Step 2: Use SIN to calculate the opposite side. In cell B3, enter:
= B2 * SIN(RADIANS(B1))
B2 is the hypotenuse (15 m). SIN(RADIANS(B1)) calculates sin(45°).
Therefore, 15 * SIN(45°) gives 10.6 meters (height of the ramp)
Important Things to Note
- The SIN function in Google Sheets requires the angle to be in radians, not degrees, so you must convert degrees using the RADIANS function or by multiplying with PI()/180. To convert radians to degrees, you use 180/PI().
- If you enter a non-numeric value as the argument, the SIN function will return a #VALUE! error.
- The output of the SIN function will always be between -1 and 1, as it represents the sine of an angle on the unit circle.
Frequently Asked Questions (FAQs)
The #VALUE error occurs if the argument passed to the SIN function is not numeric. We should always make sure that we reference a cell that contains a number or input a valid numeric value We must also verify that your angle is properly converted to radians if it was originally in degrees.
The SIN function in Google Sheets needs an input in radians. If the supplied input is in degrees, we must convert it to RADIANS() using the following formula: =SIN(RADIANS(45)). You can also manually convert by multiplying the angle by PI()/180.
The SIN function returns the trigonometric sine of an angle. It is mainly used for circular or periodic functions. The SINH function in Google Sheets returns the hyperbolic sine, used in exponential growth modeling and hyperbolic geometry. Both of these functions are different mathematical formulas and give different outputs.
Yes, the SIN function is ideal for modeling periodic or wave-like trends, such as seasonal sales or temperature variations. For this, we must apply the SIN function to a sequence of values to generate data points that follow a smooth, cyclical pattern, which can then be plotted on a graph.
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This article must help understand SIN Function in Google Sheets with its formulas and examples. You can download the template here to use it instantly.
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