# Trigonometry

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Trigonometry (from Greek trigōnon "triangle" + metron"measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry. |
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\History
Main article: History of trigonometry

The first trigonometric tablewas apparently compiled byHipparchus, who is now consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle measure, using a division of circles into 360 degrees.[4] They and their successors theBabylonians studied the ratios of the sides of similar triangles and discovered some properties of these ratios, but did not turn that into a systematic method for finding sides and angles of triangles. The ancient Nubians used a similar methodology.[5] The ancient Greeks transformed trigonometry into an ordered science.[6]
Classical Greek mathematicians (such as Euclid and Archimedes) studied the properties of chords and inscribed angles in circles, and proved theorems that are equivalent to modern trigonometric formulae, although they

References: 2. ^ R. Nagel (ed.), Encyclopedia of Science, 2nd Ed., The Gale Group (2002) 3 4. ^ Aaboe, Asger. Episodes from the Early History of Astronomy. New York: Springer, 2001. ISBN 0-387-95136-9 5 7. ^ Marlow Anderson, Victor J. Katz, Robin J. Wilson (2004)."Sherlock Holmes in Babylon: and other tales of mathematical history". MAA. p.36. ISBN 0-88385-546-1 8 13. ^ Kelly Dempski (2002)."Focus on Curves and Surfaces". p.29. ISBN 1-59200-007-X 14 15. ^ Sentences more appropriate for high schools are, "Some old horse came a 'hopping through our alley".Foster, Jonathan K. (2008). Memory: A Very Short Introduction. Oxford. p. 128. ISBN 0-19-280675-0. Bibliography * Boyer, Carl B. (1991). A History of Mathematics (Second Edition ed.) * Christopher M. Linton (2004). From Eudoxus to Einstein: A History of Mathematical Astronomy . Cambridge University Press. * Trigonometric Delights, by Eli Maor, Princeton University Press, 1998. Ebook version, in PDF format, full text presented. * Trigonometry by Alfred Monroe Kenyon and Louis Ingold, The Macmillan Company, 1914. In images, full text presented.

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