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.