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Trigonometry is the branch of mathematics dealing with relationships between angles and the lengths of the corresponding sides of triangles. It originated as a method for computing distances and angles in astronomy, but its applications now range from physics and engineering to computer science and statistics. In the context of geometry, trigonometry provides the tools necessary to analyze polygons, circles, and other geometric figures by breaking them down into their constituent triangles. It establishes functions such as sine, cosine, and tangent that allow for the calculation of unknown angles or side lengths based on known values. Thus, trigonometry is a crucial component of geometry, enabling the precise measurement and analysis of geometric shapes and their properties.