# Power Pivot Principles: The A to Z of DAX Functions - ACOTH

*13 July 2021*

*In our long-established Power Pivot Principles articles, we are starting a new series on the A to Z of Data Analysis eXpression (DAX) functions. This week it’s all a load of hyperbolics…*

*The ACOTH function*

Welcome to the wonderful world of “Functions You May Not Use in This or Your Next Life”. Today’s presentation is on the DAX function **ACOTH**, which represents the inverse hyperbolic cotangent function. That’s probably as far as I need to go, right..?

If like me, when you were at school you had a life rather than multiple maths lessons, inverse hyperbolic cotangent functions may have passed you by. To understand let’s consider the following functions first:

and

These sorts of functions are used in differential equations and may also be used to derive trigonometric functions with complex arguments, *e.g. *

and

The hyperbolic cotangent function is defined (when **x** does not equal one [1]) as follows:

The inverse hyperbolic cotangent function, **ACOTH**, is the inverse of **coth x ***(above)*.

For a given value of a hyperbolic function, the corresponding inverse hyperbolic function provides the corresponding hyperbolic angle. The size of this hyperbolic angle is equal to the area of the corresponding hyperbolic sector of the hyperbola **xy** **= 1**, or twice the area of the corresponding sector of the unit hyperbola **x ^{2} − y^{2} = 1**, just as a circular angle is twice the area of the circular sector of the unit circle. Some call the inverse hyperbolic functions "area functions" as a consequence.

The syntax is straightforward:

**=ACOTH(number)**

There is only one argument:

**number:**the absolute value of which must be greater than one [1].

Please see my example below:

You see? Who would have thought inverse hyperbolic cotangents in Data Analysis eXpressions would be so easy!

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