If you have the value obtained from a cosine but you want to know the angle of origin, then you should apply the arccosine function. To avoid any calculation by hand, we have developed an online tool in such a way that you have to enter the value you have, which must be between -1 and 1.
Then click on the calculate button to obtain the angle and possible equivalents for that result, you can also select whether you want to see it in degrees or radians. The choice is yours.
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What is the arcocosene?
As explained above, the arccosine is the inverse of the cosine function. By applying the arccos we can get the starting angle, something that we will certainly use a lot in trigonometry problems.
The arccos formula is represented as follows:
arccos(x) = cos-1(x)
By example,if we want to calculate the arccosine of 0, then we have that:
arccos(0) = cos-1(0) = 90 degrees.
Derivative of arccosine
The arccosine derivative of a function is equal to the derivative of the function divided by the square root of one minus the square of the function itself, all with a minus sign in front.
Integral of arcocosene
To make the integral of the arccos function it is necessary to use integration by parts as follows:
To finally arrive at the following result:
Calculate arccosine in Excel
If you want, you can use Excel to calculate the arccosine of a value within the range of the function, i.e., between -1 and 1.
When using the Excel ACOS function you will automatically get the angle equivalent to that value through its arccosine. Let's see how it is used in each case to display the result in degrees or radians.
Result in radians
By default, when apply the arccosine in Excel we will get the result in radians. If this is what you are looking for, just type the following formula in a cell of your spreadsheet:
=ACOS(A1)
Result in degrees
If what you are looking for is to obtain the value of the angle in degrees, Excel also allows you to nest a second function so that when applying the arccosine, we obtain the result in degrees instead of radians. To do so, you must use this formula:
=DEGREES(ACOS(A1))
Remember that A1 corresponds to the coordinates of a cell in which the value of y is located (between -1 and 1). You can modify these coordinates to adapt them to those of your spreadsheet.
If you have any doubts, we recommend that you watch the video above these lines in which we demonstrate how to use the ACOS function in Excel for calculating the arccosine.
Arccos function table
Below we have collected some of them results of the arcocosine function applied to the most used values, that is, values for which we obtain a correspondence with angles such as 0º, 30º, 45º or 90º among others.
| y | x=Arccos(y) | |
|---|---|---|
| Grades | Radians | |
| -1 | 180° | π |
| -0.8660254 | 150° | 5π/6 |
| -0.7071068 | 135° | 3π/4 |
| -0.5 | 120° | 2π/3 |
| 0 | 90° | π/2 |
| 0.5 | 60° | π/3 |
| 0.7071068 | 45° | π/4 |
| 0.8660254 | 30° | π/6 |
| 1 | 0° | 0 |
Arcocosene in Matlab
If you have to calculating the arccosine in Matlab for a class assignment or any other task, here's how to solve the exercise.
If you want to calculate the inverse cosine and get the result in radians, this is the syntax of the matlab function:
acos(x)
If you want to get the arccos in Matlab with the result in degrees, then you should use this formula:
acosd(x)
We leave you with this link in which you can see more related information for Matlab and in which they show you with examples how to calculate acos(x) or even represent it in a graph.
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