On one visual description of a historical event using a trigonometric equation and its solution

In this article, an attempt is made to analyse historical events by methods of mathematics, and by means that do not go beyond the school curriculum. The process of Dzungar invasion 1643-1745 with the help of trigonometric equation is modelled. Graphs of characteristic functions of the Dzungar state and Kazakh people are constructed. The theorem (criterion) for the solution of the set problem is formulated.
It seems that this approach will be interesting not only from the historical and mathematical points of view, but will also make it possible to interest students in the study of both history and mathematics, enrich the methodology of teaching these disciplines in secondary schools, and make it possible to substantiate the interdisciplinary connection between mathematics and history.