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Trigonometry, as part of the hierarchy Science/Mathematics/Linear Algebra, delves into the study of relationships between angles and the lengths of the corresponding sides of triangles. It establishes functions such as sine, cosine, and tangent, which find extensive use in various mathematical models and calculations. In the context of Linear Algebra, trigonometry helps to understand and solve systems of linear equations in three dimensions, thus proving instrumental in vector analysis and transformations.