Inverse cot in C#

Question

We know that the inverse of tan is Math.Atan, what about the inverse of cot? cot(x) is defined as

cot(x)=1/tan(x)

Answer 1

See Inverse Cotangent. For some values, the inverse would be atan(1/x).

Answer 2

There are two commonly used conventions for the inverse of Cotangent, since e.g. cot(1) = cot(1-pi). It is important to think through which definition one wishes to use.

1. Let arccot(x) match atan(1/x), with values between -pi/2 and pi/2. This gives a discontinuity at 0 (jumps from -pi/2 to pi/2). This is the convention used in Greg Hew's answer.

   

   public static double Acot(double x)
   {
       return (x < 0 ? -Math.PI/2 : Math.PI/2) - Math.Atan(x);
   }
   

   or

   public static double Acot(double x)
   {
       return x == 0 ? 0 : Math.Atan(1/x);
   }
   

2. Let arccot(x) be a continuous function with values between 0 and pi. This is the convention used in Daniel Martin's answer.

   

   public static double Acot(double x)
   {
       return Math.PI/2 - Math.Atan(x);
   }