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Trigonometry (from Ancient Greek τρίγωνον (trígōnon) 'triangle' and μέτρον (métron) 'measure') [1] is a branch of mathematics concerned with relationships between angles and side lengths of triangles.
The term "trigonometry" was derived from Greek τρίγωνον trigōnon, "triangle" and μέτρον metron, "measure". [3]The modern words "sine" and "cosine" are derived from the Latin word sinus via mistranslation from Arabic (see Sine and cosine § Etymology).
50 – Aryabhata writes the "Aryabhata-Siddhanta", which first introduces the trigonometric functions and methods of calculating their approximate numerical values. It defines the concepts of sine and cosine , and also contains the earliest tables of sine and cosine values (in 3.75-degree intervals from 0 to 90 degrees)
He also discovered the binomial theorem for integer exponents, which "was a major factor in the development of numerical analysis based on the decimal system". 975 – Mesopotamia, al-Battani extended the Indian concepts of sine and cosine to other trigonometrical ratios, like tangent, secant and their inverse functions.
Glen Van Brummelen has published the first major history in English of the origins and early development of trigonometry, The Mathematics of the Heavens and the Earth: The Early History of Trigonometry. [4] His second book, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, concerns spherical trigonometry. [5] [6]
The state of trigonometry advanced during the Song dynasty (960–1279), when Chinese mathematicians had greater need of spherical trigonometry in calendrical science and astronomical calculations. [33] Shen Kuo used trigonometric functions to solve mathematical problems of chords and arcs. [33]
Geometry is used extensively in trigonometry. Angle – the angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane.
In Chapter XI of The Age of Reason, the American revolutionary and Enlightenment thinker Thomas Paine wrote: [1]. The scientific principles that man employs to obtain the foreknowledge of an eclipse, or of any thing else relating to the motion of the heavenly bodies, are contained chiefly in that part of science that is called trigonometry, or the properties of a triangle, which, when applied ...