Generalized inverse trigonometric functions

Assume that we have $\cos(\beta)= U$ where $U$ is an interval and $\beta$ should lie in an arbitrary range. The procedure Filtre_Arc_Cos allows to update the range for $\beta$. It returns -1 is $\beta$ and $U$ are incompatible, 0 otherwise. Its syntax is:

 
int Filtre_Arc_Cos(INTERVAL &U,INTERVAL &beta)

A similar procedure exist for the inverse sine with

The procedure Arc_Cos_Multiple allows to determine all possible ranges for $\beta$, assuming that $\beta$ is restricted to a range included in $[-2\pi,2\pi]$::

 
int Arc_Cos_Multiple(INTERVAL &U,INTERVAL &beta,INTERVAL_VECTOR &BETA)

This procedure returns the number of possible ranges for $\beta$ and their values in BETA.