मुख्यपृष्ठ ❯ सर्व व्याख्या ❯ भूमिती ❯ त्रिकोणमिती ❯ युनिट सर्कल व्याख्या
युनिट सर्कल व्याख्या
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.
या परिभाषाचा आणखी एक त्वरित परिणाम म्हणजे युनिट सर्कलवर पडलेल्या अनेक बिंदूंचे निर्देशांक अगदी कमी मोजणीसह स्पष्टपणे लिहिण्याची क्षमता. वरील आकृतीमध्ये, उदाहरणार्थ, ए, बी, सी आणि डी पॉईंट्स <सुप> π & frasl;
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.
आणखी एका दृष्टीकोनातून, युनिट वर्तुळात <स्पॅन या दोन्ही-आयामी हायपरबोलिक प्लेनची तथाकथित आदर्श सीमा म्हणून पाहिले जाते ℍ > हायपरबोलिक भूमिती . या दोन्ही मॉडेल्समध्ये, हायपरबोलिक विमान ओपन युनिट डिस्क म्हणून पाहिले जाते, ज्यायोगे युनिट सर्कल अनंत
संबंधित व्याख्या
स्त्रोत
“Unit Circle.” From Wolfram MathWorld, mathworld.wolfram.com/UnitCircle.html.