# General observations on series whose terms proceed as the sines and cosines of multiples of angles - Mathematics > History and Overview

Abstract: Translated from the Latin original -Observationes generales circa series,quarum termini secundum sinus vel cosinus angulorum multiplorum progrediuntur-1777. E655 in the Enestrom index. Euler looks at the binomial expansion$1+x^n$ for $x=\cos \phi+i\sin\phi$. He does $n=$ positive and negativeintegers, and $n={1-2} -{1-2}$, and particular values of $\phi$.

Author: Leonhard Euler

Source: https://arxiv.org/