What is ACOS function in Google Sheets?
The ACOS function in Google Sheets returns the arccosine of a value in radians. Here, arccosine is the inverse of the cosine function. For the uninitiated, the cosine of an angle is defined as the sine of the complementary angle. Hence, we can say that for any angle θ, cos θ = sin (90° – θ). Mathematically, arccosine can be written as cos-1.
When we use this function in Google Sheets, the angle returned by ACOS is in radians. The range of values is from 0 to Pi. Radians are used in mathematics to measure angles. Thus, the ACOS formula returns the inverse cosine of a value in Google Sheets. As an example, let us look at the following spreadsheet where we use the ACOS Function to calculate the arccosine of different values.
- =ACOS(0)
- =ACOS(1)
- =ACOS(-1)
Here, the function takes only one argument.
Table of contents
Key Takeaways
- The ACOS function in Google Sheets calculates a given number’s arccosine (inverse cosine).
- Its syntax is as follows: =ACOS(number). Here, number: The value whose arccosine you must calculate. It must be between -1 and 1, inclusive.
- The function returns the value in radians, and it will be between 0 and π (pi) radians.
- To convert the result to degrees from radians, you can use the DEGREES function.
- The ACOS function is commonly used in geometry, trigonometrical calculations, and in the fields of physics and engineering.
- If the input number is not within the range of -1 to 1, the function will return an #NUM! error.
ACOS () Syntax
The syntax of the ACOS function in Google Sheets is straightforward. The function only takes one parameter, which is a number ranging from -1 to 1.
=ACOS(value)
Here,
value: It is the cosine value for which you calculate the arccosine.
How to use ACOS function in Google Sheets?
There are two ways to enter the ACOS function in Google Sheets: manually and through the Google Menu bar.
Entering the ACOS Function manually
We are finding the arccosine of a value using the ACOS function. The value is inserted in Google sheets, as shown below.
Here, we use the ACOS formula Google Sheets for finding the inverse cosine of the supplied values. Here’s how you do it:
Step 1: First, click on the cell, where you want the result to appear. Let us click on cell B2. Now, type =ACOS( in the formula bar.
Step 2: Now, enter the cosine value of the angle you want to find. In this case, we have entered it in cell A2. Remember, this value must be between -1 and 1.
=ACOS(A2)
Step 3: Press Enter, and we will have Google Sheets calculate the arccosine value.
Step 4: To apply the formula to the other value as well, drag the autofill handle to cell B2. You get the result as shown below.
Now, converting the radians to degrees is as simple as it gets! Multiply the result by 180/PI() or use the DEGREES function. For instance, =ACOS(0.5)*180/PI(). This formula converts the radians to degrees, making the output more relatable for those accustomed to measuring angles in degrees.
Using the Google Menu bar
- Choose the cell where you want to enter the ACOS formula.
- Go to the menu bar and click on “Insert” – “Function” – “Math” – “ACOS.”
- Enter the required argument. Close the bracket and press the “Enter” key.
Examples
Let us look at some ACOS in Google Sheets examples to find values in radians. With the examples below, we will learn how to calculate the ACOS values for different scenarios.
Example #1
In this simple example, let us try classifying angles based on their slopes as steep or gradual.
We have some given values below for which we will find the inverse cosine.
Step 1: Find the inverse cosine of these angles using the ACOS function in Google Sheets. To classify them, we use the IF function. So, the formula to be entered in cell B1 is as follows:
Step 2: Press Enter. Now, you will know details about that particular slope.
Step 3: Now, drag the fill handle all the way down to B6 to get the results of the slopes for the other values.
Example #2
The ACOS function in Google Sheets returns the arccosine of x. In the example below, we are looking to find the inverse cosine of 5 values. The result in radians is calculated, and we can try to draw a graph.
Let us look at the table below.
Step 1: Let’s enter the formula to find the inverse cosine in cell B2, as shown below.
=ACOS(A2)
Step 2: Now, press Enter. You can get the value of the inverse cosine of -1.
Drag the fill handle to get the results for the other values from A2 to A6. The inverse cosine of the supplied values is obtained in radians.
Let us plot a graph using the values in Columns A and B. For this, go to Insert – Chart – Line. In the pane that appears on the right side, you can customize the chart according to your requirements, as shown below.
Now, you can observe the shape of the graph.
Example #3
In this interesting example, let’s calculate the angle made by a ball that has been kicked and look at the steps.
The points A and B are represented by the coordinates (x1,y1) and (x2,y2). Here, the values are (2,3) and (9,12). Let us enter these values in the Google spreadsheet.
Step 1: The following formula can calculate the distance between these points.
d=√((x2 – x1)² + (y2 – y1)²).
Applying this formula in cell B5, we get,
=SQRT((B3-B1)^2 + (B4-B2)^2)
Step 2: Press Enter. You get the value of the distance between the points. Now, let us calculate the cosine of the angle as follows
Cosine = (x2-x1) / Distance.
Hence, we apply the following formula in cell B6.
=(B3-B1)/B5
Step 3: Now, you can calculate the angle of the ball kick in radians using the ACOS function. For better understanding, you can convert the result to degrees using 180/PI().
Apply the following formula to B7.
=ACOS(B6)*180/PI()
Step 4: Press Enter and get the final result in degrees.
Important Things to Note
- If you wish to convert the result of the ACOS function in Google Sheets into degrees, use the DEGREES function or multiply its output by 180/PI().
- Cosine is periodic; so the inverse has many solutions. ACOS returns the solution between 0 and Pi.
- Inverse Cosine is a trigonometric function, also called the arccosine function. Its argument x can be a real or a complex number.
- By integrating the ACOS function with other Google sheets functions, you can enhance your data analysis capabilities.
- With the ACOS function in Google Sheets, you can unlock deeper insights into your data and foster a deeper understanding of the scientific principles at play.
Frequently Asked Questions (FAQs)
If you get an error from the ACOS function in Google Sheets, the reason could be as follows.
1. The #NUM! error – This error occurs if the argument supplied is outside the range -1 to +1.
2. The #VALUE! error – It occurs if the supplied argument is non-numeric.
Besides, other common mistakes include entering an argument that is not a number, or mistyping the formula, or entering the wrong arguments.
Note: If you want to convert the result from radians to degrees, multiply it by 180/PI() or use the DEGREES function
We can use the ACOS function to calculate the angle of a triangle given the lengths of its sides.
We can also use the ACOS function to calculate the distance between two points on the Earth’s surface, given their latitude and longitude coordinates.
It can also be used to calculate the angle between two vectors in three-dimensional space, given their components.
If you are analyzing wave patterns or the construction of a skyscraper, you can use the ACOS function to measure the angles at which waves hit a shoreline.
Using ACOS, you can find the precise tilt of a skyscraper against the wind when constructing it, enabling you to calculate angles with precision.
The input value must be between -1 and 1. If the value is outside this range, the function will return an error.
Download Template
This article must be helpful to understand the ACOS Function in Google Sheets, with its formula and examples. You can download the template here to use it instantly.
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