sin ø) n cos n ø i sin n ø, which allows one to find the n th root of any complex number. His tables of logarithms greatly facilitated the art of numerical computationincluding the compilation of trigonometry tables and were hailed as one of the greatest contributions to science. Passage to Europe Until the 16th century it was chiefly spherical trigonometry that interested scholarsa consequence of the predominance of astronomy among the natural sciences. To compute the various parts of the triangle, one has to find the length of each chord as a function of the central angle that subtends itor, equivalently, the length of a chord as a function of the corresponding arc width.
Thus, rewriting Ptolemys formula as c /120 sin B, where B A /2, the relation expresses the half-chord as a function of the arc B that subtends itprecisely the modern sine function. Based on this rule he constructed a table of shadowsessentially a table of cotangentsfor each degree from 1. He lived in Alexandria, the intellectual centre of the Hellenistic world, but little else is known about him. Modern trigonometry From geometric to analytic trigonometry In the 16th century trigonometry began to change its character from a purely geometric discipline to an algebraic-analytic subject. Fitcations: How to Plan the Perfect Guilt-Free Getaway! Trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. In the sexagesimal system, multiplication or division by 120 (twice 60) is analogous to multiplication or division by 20 (twice 10) in the decimal system.
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Their extension to nonperiodic functions played a key role in the development of quantum mechanics in the early years of the 20th century. Viète was also the first to legitimize the use of infinite processes in mathematics. 858929 gave a rule for finding the elevation of the Sun above the horizon in terms of the length s of the shadow cast by a vertical gnomon of height. Until about the 16th century, trigonometry was chiefly concerned with computing the numerical values of the missing parts of a triangle (or any shape that can be dissected into triangles) when the values of other parts were given. For example, the sawtooth function can be written as 2(sin x sin 2 x /2 sin 3 x /3 as successive terms in the series are added, an ever-better approximation to the sawtooth function results.
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