Purpose
Return value
Syntax
=ACOSH(number)
- number - The number to get the inverse hyperbolic cosine of.
Using the ACOSH function
The Excel ACOSH function returns the inverse hyperbolic cosine of a number. Given the input 2.0, the function returns the value 1.316957897.
=ACOSH(2) // returns 1.316957897
Explanation
Given the x -component of a point that lies on the right branch of the unit hyperbola given by the equation x² - y² = 1, the ACOSH function returns the hyperbolic angle formed by the point.
=ACOSH(1.543080634) // returns 1
In other words, the ACOSH function returns twice the area of the sector formed between the origin, the x-axis, and the point on the hyperbola.
Notes
- The function throws a #NUM! Error when given a number less than 1.
Images courtesy of wumbo.net .
Purpose
Return value
Syntax
=ACOT(number)
- number - The value of the cotangent of an angle.
Using the ACOT function
The Excel ACOT function returns the arc cotangent of a number. Given the input 1, the function returns 0.785398163 radians as the output.
=ACOT(1) // Returns 0.785398163 radians
Explanation
The arc cotangent function is the inverse of the cotangent function, with a branch cut that maps to related angles.
=ACOT(COT(a)) // returns the angle or a branch cut angle
For example, the angle π/4 is mapped to π/4 with no branch cut.
=ACOT(COT(PI()/4)) // returns π/4
Where the angle -π/2 is mapped to positive π/2 with a branch cut.
=ACOT(COT(-PI()/2)) // returns positive π/2
In Excel, when we talk about ACOT as the inverse of COT , angles outside the range of 0 to π are mapped with a branch cut. Below is the output of the cotangent function with the branch cut highlighted.
Other implementations of the function may have different branch cuts. Below is the plot of the output of the ACOT function in Excel.
Images courtesy of wumbo.net .
