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Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.[2] In particular, 3rd-century astronomers first noted[citation needed] that the ratio of the lengths of two sides of a right-angled triangle depends only on one acute angle of the triangle. These dependencies are now called trigonometric functions.