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Trigonometry (from Greek trigōnon, “triangle” and metron, “measure”) 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. In particular, 3rd-century astronomers first noted 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.
Trigonometry is the foundation of all applied geometry, including geodesy, surveying, celestial mechanics, solid mechanics, and navigation.
Trigonometric functions have been extended as functions of a real or complex variable, which are today pervasive in all mathematics.
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