DOI: https://doi.org/10.36719/2663-4619/122/115-122
Aynur Aliyeva
Heydar Aliyev Military Institute
https://orcid.org/0000-0003-1173-8898
aynur.197025@gmail.com
Nazira Bayramova
Heydar Aliyev Military Institute
https://orcid.org/0009-0006-7155-3536
nazira.bayramova@gmail.com
Union and Intersection of Solutions of Trigonometric Equations
Abstract
The article investigates the union and intersection of solution sets of trigonometric equations. It analyzes cases where such equations may have multiple solution series and where these series may be subsets of one another or share common elements. The authors present methods for expressing these solutions analytically in a unified formula. The solution sets are systematized through the union of solutions and the depiction of their intersections on a single unit circle. Additionally, the concept of equivalent equations is introduced, and conditions are determined for reducing a system of equations to a general solution form. Through the analysis of examples, it is demonstrated that combining intersecting or overlapping solution series can yield simpler and more general expressions. The proposed approach aims to enhance consistency and efficiency in solving trigonometric equations.
Keywords: trigonometric equation, solution set, arithmetic progression, intersection, equivalent equation, unit circle