I-Trigonometry: Imiqondo, Umlando, kanye Nokusetshenziswa Empilweni Yansuku Zonke
I-Pendahuluan
I-Trigonometry, igatsha elisha lezibalo, idlala indima ebalulekile emikhakheni ehlukahlukene yesayensi nobunjiniyela. Ifunda ubudlelwano phakathi kwama-engeli nobude obuseceleni konxantathu. Ingxenye ebalulekile yezibalo, i-trigonometry inezinhlobo eziningi zezicelo, kusukela kusayensi yezinkanyezi nobunjiniyela bezokwakha kuya ekuzulazuleni nasebuchwephesheni bolwazi. Lesi sihloko sichaza imiqondo eyisisekelo ye-trigonometry, intuthuko yayo yomlando, kanye nezicelo zayo empilweni yansuku zonke.
Imiqondo Eyisisekelo Ye-Trigonometry
Ngokwemvelaphi, i-trigonometry ivela emagameni amabili esiGreki: "trigonon," okusho ama-engeli amathathu, kanye ne-"metron," okusho isilinganiso. Ngakho-ke, i-trigonometry ngokwezwi nezwi isho 'ukulinganiswa kwama-engeli amathathu.'
Imisebenzi ye-Trigonometric
Enhliziyweni ye-trigonometry kukhona imisebenzi eyisisekelo ye-trigonometric: i-sine (sin), i-cosine (cos), kanye ne-tangent (tan). Le misebenzi ichazwa ngokomongo wonxantathu ongakwesokudla, lapho:
– I-sine (isono) ye-angle θ iyisilinganiso esiphakathi kobude bohlangothi oluphambene lwe-angle nobude be-hypotenuse.
– I-cosine (cos) ye-angle θ iyisilinganiso esiphakathi kobude bohlangothi oluseduze lwe-angle (eduze) nobude be-hypotenuse.
– I-tangent (tan) ye-engeli θ yisilinganiso esiphakathi kobude bohlangothi oluphambene lwe-engeli nobude bohlangothi oluseduze lwe-engeli.
Kuma-engeli angaphezu kwama-degrees angu-90 noma ngaphansi kwama-degrees angu-0, amanani e-sin, cos, kanye ne-tan angabalwa kusetshenziswa umqondo wesiyingi seyunithi lapho kusetshenziswa khona indilinga ene-unit radius ukuchaza imisebenzi ye-trigonometric.
Ubunikazi be-Trigonometric
Ubunikazi be-trigonometric buyi-equation ehilela imisebenzi ye-trigonometric eyiqiniso kuwo wonke ama-engeli. Ubunikazi obuyisisekelo obaziwa kakhulu ubunikazi be-Pythagorean:
\[ \sin^2\theta + \cos^2\theta = 1 \]
Okunye ubunikazi kufaka phakathi ubunikazi be-engeli eyengeziwe kanye nokuguqulwa okuphindwe kabili:
\[ \isono(\alpha \pm \beta) = \sin\alpha \cos\beta \pm \cos\alpha \sin\beta \]
\[ \cos(\alpha \pm \beta) = \cos\alpha \cos\beta \mp \sin\alpha \sin\beta \]
Umlando Wokuthuthukiswa Kwe-Trigonometry
Ukuthuthukiswa kwe-trigonometry kwaqala ngemiphakathi yasendulo, ikakhulukazi amasiko aseGibhithe, aseBhabhiloni, kanye namaGreki.
IBhabhiloni neGibhithe
AbaseBhabhiloni lasendulo kanye nabaseGibhithe basungula izindlela eziyisisekelo zokulinganisa nokubala ezibhekwa njengezandulela ze-trigonometry. Basebenzisa amathebula e-chord ukubala ubude bezinhlangothi zonxantathu.
Izikhathi Zasendulo ZaseGrisi
Umnikelo omkhulu uvela kusosayensi wezibalo ongumGreki uHipparchus (cishe ngo-190-120 BC), owaziwa ngokuthi “uYise weTrigonometry.” UHipparchus wahlanganisa amathebula okuqala e-trigonometric, evumela ukubalwa okunembile kwama-engeli nobude bezinhlangothi.
Iminyaka ephakathi
Ngesikhathi samaSulumane, ososayensi abanjengo-Al-Battani no-Al-Khwarizmi bandisa ucwaningo lwe-trigonometry ngokungeza imisebenzi emisha ye-trigonometric nokubala amathebula e-trigonometric anembe kakhudlwana. Phakathi nalesi sikhathi, imisebenzi ye-trigonometric i-sine ne-cosine yaqashelwa kahle.
Isikhathi Sanamuhla
Intuthuko ebalulekile ku-trigonometry yesimanje yafezwa ososayensi bezibalo abanjengoLeonhard Euler nabanye. U-Euler, isibonelo, wethule umsebenzi we-exponential futhi wasungula ukuxhumana okujulile phakathi kwe-trigonometry nokuhlaziywa okuyinkimbinkimbi.
Ukusetshenziswa kwe-Trigonometry Empilweni Yansuku Zonke
I-Trigonometry ayilona nje ithuluzi lemfundiso yezibalo kodwa futhi inezindlela ezahlukahlukene zokusebenza ezingokoqobo emikhakheni eyahlukene.
astronomy
I-Trigonometry iyithuluzi elibalulekile kwezesayensi yezinkanyezi, esiza izazi zezinkanyezi ukukala amabanga phakathi kwezinkanyezi, amaplanethi, nezinye izidalwa zasezulwini. Isibonelo, inqubo yezinkanyezi ye-parallax isebenzisa i-trigonometry eyisisekelo ukubala ibanga lenkanyezi eseduze kakhulu noMhlaba.
Ubunjiniyela Bokwakha Nokwakha
Kubunjiniyela bezakhiwo kanye nokwakhiwa kwezakhiwo, i-trigonometry isetshenziswa ukubala imithambeka, amandla esakhiwo, kanye nomklamo wesakhiwo. Isibonelo, isetshenziselwa ukunquma ubude bezinhlangothi nama-engeli amabhuloho noma izakhiwo ezinde.
Ukuzulazula
Amatilosi nabashayeli bezindiza basebenzisa i-trigonometry ukuthola indawo yabo olwandle noma emoyeni. Besebenzisa amathuluzi anjenge-sextants nama-compass, bangakwazi ukubala ama-geographic coordinates ngokusekelwe ekhoneni eliphakathi komkhathizwe kanye nezidalwa ezithile zasezulwini.
Ubuchwepheshe Bolwazi kanye Nokuxhumana
Ezweni lobuchwepheshe bolwazi kanye nokuxhumana, izimpawu zedijithali zivame ukucutshungulwa kusetshenziswa imiqondo ye-trigonometric. Ukuhlaziywa kwe-Fourier, indlela yokulinganisa imisebenzi nezimpawu zesikhathi, kuncike kakhulu emisebenzini ye-sine kanye ne-cosine.
Izilinganiso
Ama-scan afana ne-CT scans kanye ne-MRIs adinga i-trigonometry ukuze athwebule izithombe ezinobukhulu obuthathu. Lokhu kuvumela odokotela ukuthola imephu ecacile nenembile yengxenye yomzimba ehlolwayo.
I-Geodesy kanye ne-Cartography
I-Trigonometry nayo iyasiza ekuhloleni umhlaba kanye nokumapha. I-Geodesy isebenzisa umqondo we-triangulation, lapho izindawo namabanga ebusweni boMhlaba kubalwa ngokusekelwe ekulinganisweni kwe-angular kusuka endaweni eqondile.
I-Penutup
I-Trigonometry ingenye yamagatsha abaluleke kakhulu ezibalo, enokutholakala okunamandla empilweni yansuku zonke kanye nobuchwepheshe besimanje. Nakuba imvelaphi yayo isekulinganisweni okulula kwama-engeli nobude obuseceleni konxantathu, ukusetshenziswa kwayo kudlule imingcele engokoqobo ukuze kube ukwesekwa okubalulekile emikhakheni eyahlukene yesayensi. Kusukela ekuthuthukisweni kwengqalasizinda kuya ekuhloleni isikhala, i-trigonometry isalokhu iyisisekelo esibalulekile kuzo zonke izici. Ngokuqonda imiqondo yayo eyisisekelo kanye nokusetshenziswa kwayo, singabona ukuthi le sayensi ibaluleke kangakanani ekucebiseni impilo yabantu.
UDavtar Pustaka
1. Boyer, Carl B. (1991). Umlando Wezibalo. Wiley.
2. Merzbach, Uta C.; Boyer, Carl B. (2011). Umlando Wezibalo.
3. Katz, Victor J. (1998). Umlando Wezibalo: Isingeniso.
Lesi isingeniso eside impela. Lesi sihloko sinikeza umbono ophelele we-trigonometry, kusukela eziyisisekelo kuya ekusetshenzisweni kwayo ekuphileni kwansuku zonke. Ungangeza imininingwane eyengeziwe noma izibonelo uma kudingeka.
