I'm looking for the following notion in english if exists, called in french "la mesure principale" ( the main measure )
Let $\theta$ be an angle in standard position the main measure for $\theta$ is angle $\in (-\pi;\pi]$ but i didn't found that notion in lots of books i just found reference angle ([James_Stewart,_Lothar_Redlin,_Saleem_Watson] Precalculus ) but it's not what i'm looking for
In complex analysis, this is commonly referred to as the principal value between two nonzero complex numbers. In general, if you wrote "the principal value $\theta \in (-\pi,\pi]$ of the angle between $v$ and $w$" for $v$ and $w$ in $\mathbb R^n$ for some $n$, mathematicians would know what you mean.