和春老神棍根本不知sine, cosine来源,又来亵渎数学先贤。
While the early study of trigonometry can be traced to antiquity, the trigonometric functions as they are in use today were developed in the medieval period. The chord function was discovered by Hipparchus of Nicaea (180–125 BCE) and Ptolemy of Roman Egypt (90–165 CE).[10]
The sine and cosine functions can be traced to the jyā and koṭi-jyā functions used in Indian astronomy during the Gupta period (Aryabhatiya and Surya Siddhanta), via translation from Sanskrit to Arabic and then from Arabic to Latin.[11]
All six trigonometric functions in current use were known in Islamic mathematics by the 9th century, as was the law of sines, used in solving triangles.[12] With the exception of the sine (which was adopted from Indian mathematics), the other five modern trigonometric functions were discovered by Arabic mathematicians, including the cosine, tangent, cotangent, secant and cosecant.[12] Al-Khwārizmī (c. 780–850) produced tables of sines, cosines and tangents.[13][14] Muhammad ibn Jābir al-Harrānī al-Battānī (853–929) discovered the reciprocal functions of secant and cosecant, and produced the first table of cosecants for each degree from 1° to 90°.[14]
The first published use of the abbreviations sin, cos, and tan is by the 16th-century French mathematician Albert Girard; these were further promulgated by Euler (see below). The Opus palatinum de triangulis of Georg Joachim Rheticus, a student of Copernicus, was probably the first in Europe to define trigonometric functions directly in terms of right triangles instead of circles, with tables for all six trigonometric functions; this work was finished by Rheticus' student Valentin Otho in 1596.
In a paper published in 1682, Leibniz proved that sin x is not an algebraic function of x.[15] Roger Cotes computed the derivative of sine in his Harmonia Mensurarum (1722).[16] Leonhard Euler's Introductio in analysin infinitorum (1748) was mostly responsible for establishing the analytic treatment of trigonometric functions in Europe, also defining them as infinite series and presenting "Euler's formula", as well as the near-modern abbreviations sin., cos., tang., cot., sec., and cosec.[11]
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