The ACOS function is used to return the arccosine of a number.
Contents:
Syntax
= ACOS(number)number - The cosine value for which you want to calculate the arccosine
Note: the results will be returned as radians. To return a degree, use the DEGREES function like so:
= DEGREES(ACOS(number))Explanation
The ACOS function is part of the "Math and Trigonometry" group of functions within Excel.
This function calculates an arccosine which is the inverse of the cosine function, and calculates the angle in radians.
Arccosine is used to measure an unknown angel when the adjacent side and hypotenuse are known.
What is an Arccosine
To understand arccosine, consider the relationship between angles and the ratios of sides in right-angled triangles.
The cosine of an angle (a) is the ratio of the length of the hypotenuse (y) to the length of the adjacent side (x).
Conversely, arccosine (arccos or ACOS) finds the inverse angle. The inverse of cosine is useful when the cosine is known, but the angle itself is not.
For example, if the cosine of an angle is calculated as:
a = adjacent / hypotenuse = x / y = 26/ 30 ≈ 0.867, then a = arccos(0.867) ≈ 40°.
In trigonometry, every function has an inverse that works in reverse. These inverses are prefixed with 'arc', making the inverse of cos the arccos.
Examples
How to Calculate Arccosine Using the Adjacent Side and Hypotenuse of a Triangle
Let's say we have table representing triangles with two know sides, the side adjacent to the angle that we want to calculate, and the hypotenuse, and want the answer in degrees.
The formula to calculate the arccosine in degrees would be:
= DEGREES(ACOS(adjacent/hypotenuse))If we plug this formula into the table, we get the correct arccosine angles (rounded here to the nearest degree.
This table uses the ACOS function to calculate the angle from the given sides of a right-angled triangle, and converts that result into degrees.
If you don't want to use the DEGREES function, you can also multiply the result by 180/pi.