The ACOT function is used to return the arccotangent of a number.
Contents:
Syntax
= ACOT(number)number - The cotangent value for which you want to calculate the arccotangent
Note: the results will be returned as radians. To return a degree, use the DEGREES function like so:
= DEGREES(ACOT(number))Explanation
The ACOT function is part of the "Math and Trigonometry" group of functions within Excel.
This function calculates an arccotangent which is the inverse of the cotangent function, and calculates the angle in radians.
Arccotangent is used to measure an unknown angel when the adjacent and opposite sides are known.
What is Arccotangent
To understand arccotangent, consider the relationship between angles and the ratios of sides in right-angled triangles.
The cotangent of an angle (a) is the ratio of the length of the adjacent side (x) to the length of the opposite side (y).
Conversely, arccotangent (arccot or ACOT) finds the inverse angle. The inverse of cotangent is useful when the cotangent is known, but the angle itself is not.
For example, if the cotangent of an angle is calculated as:
a = adjacent / opposite = x / y = 26/ 30 ≈ 0.867, then a = arccot(0.867) ≈ 49°.
In trigonometry, every function has an inverse that works in reverse. These inverses are prefixed with 'arc', making the inverse of cot the arccot.
Examples
How to Calculate Arccotangent Using the Adjacent and Opposite Sides of a Triangle
Let's say we have table representing triangles with two know sides, the opposite and adjacent sides to the angle that we want to calculate, and want the answer in degrees.
The formula to calculate the arccotangent in degrees would be:
= DEGREES(ACOT(adjacent/opposite))If we plug this formula into the table, we get the correct arccotangent angles (rounded here to the nearest degree).
This table uses the ACOT 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.