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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).
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.
4th to 5th centuries: The modern fundamental trigonometric functions, sine and cosine, are described in the Siddhantas of India. [75] This formulation of trigonometry is an improvement over the earlier Greek functions, in that it lends itself more seamlessly to polar co-ordinates and the later complex interpretation of the trigonometric functions.
ca. 1000 – Law of sines is discovered by Muslim mathematicians, but it is uncertain who discovers it first between Abu-Mahmud al-Khujandi, Abu Nasr Mansur, and Abu al-Wafa. ca. 1100 – Omar Khayyám "gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections."
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.
The state of trigonometry advanced during the Song dynasty (960–1279), where Chinese mathematicians began to express greater emphasis for the 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]
It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of 7 + 1 / 2 ° = π / 24 radians). [2]
The 18th-century Swiss mathematician Leonhard Euler (1707–1783) is among the most prolific and successful mathematicians in the history of the field.His seminal work had a profound impact in numerous areas of mathematics and he is widely credited for introducing and popularizing modern notation and terminology.