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Trigonometry, as part of the "Differential Equations" hierarchy in Mathematics and Science, explores the relationships between angles and the lengths of corresponding sides of triangles, offering valuable tools for solving geometric problems. By establishing connections to other branches of mathematics, it facilitates a deeper understanding of differential equations through concepts such as trigonometric identities and functions, periodic phenomena, and infinite series expansions. In this context, Trigonometry serves as an essential foundation for the analysis and solution of complex problems within the broader realms of Science and Mathematics.