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Eenheidsirkel Definisie

The unit circle is a circle with a radius of 1 which is centered at the origin on the x-y plane. The unit circle plays a significant role in several different areas of mathematics. In particular the functions of trigonometry are most simply defined using the unit circle. As shown in the figure below, a point p on the terminal side of an angle θ in angle standard position measured along an arc of the unit circle has as its coordinates (cos θ, sin θ) so that cos θ is the horizontal coordinate of p and sin θ is its vertical component. As a result of this definition, the trigonometric functions are periodic with period 2π.

'N Ander onmiddellike resultaat van hierdie definisie is die vermoë om die koördinate van verskillende punte wat op die eenheidsirkel lê, eksplisiet met baie min berekening te skryf. In die figuur hierbo stem punte A, B, C en D byvoorbeeld ooreen met hoeke van ^{π & FRASL; _{3 , 3 π & frasl; 4 , 7 π & frasl; 6 , en 11 π & frasl ; 6 radiale, waardeur dit volg dat a = ( 1 & frasl; 2 , 3 & frasl; < Sub> 2} ), b = ( -1} & frasl; 2 , 1 & frasl; 2 ), C = ( ^-3 & frasl; 2 , -1 & frasl; 2 ), en d = ( 3 & frasl; 2 , -1 & frasl; 2 ). Net so kan hierdie metode gebruik word om trigonometriese waardes te vind wat verband hou met heelgetal -veelvoude van π & frasl; 2 , plus 'n aantal ander hoeke verkry deur helfte -hoek , dubbelhoek , en ander meervoudige formules .

The unit circle can also be considered to be the contour in the complex plane defined by |z| = 1, where |z| denotes the complex modulus. This role of the unit circle also has a number of significant results, not the least of which occurs in applied complex analysis as the subset of the complex plane where the Z-transform reduces to the discrete Fourier transform.

Vanuit nog 'n perspektief word die eenheidsirkel beskou as die sogenaamde ideale grens van die tweedimensionele hiperboliese vlak ℍ 2 in beide die Poincaré-hiperboliese skyf en Klein-Beltrami-modelle van Hiperboliese meetkunde . In albei hierdie modelle word die hiperboliese vlak as die oop eenheidskyf beskou, waardeur die eenheidsirkel die versameling van Infinite Limit Points van rye verteenwoordig in ℍ 2 .

❮ Unie Eenheidsirkel TRIG -definisies ❯