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Vienības aplis Definīcija
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.
Vēl viens tūlītējs šīs definīcijas rezultāts ir spēja skaidri uzrakstīt vairāku punktu koordinātas, kas atrodas uz vienības loka, ar ļoti nelielu aprēķinu. Iepriekš redzamajā attēlā, piemēram, punkti a, b, c un d atbilst
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.
Raugoties no vēl viena viedokļa, vienības aplis tiek uzskatīts par tā saukto divdimensiju hiperboliskās plaknes un#8461; 2 modeļu
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“Unit Circle.” From Wolfram MathWorld, mathworld.wolfram.com/UnitCircle.html.