Umlando trigonometry: ukuvela nokuthuthukiswa

umlando Trigonometry kuhlangene ngokungenakuhlukaniswa ukufunda izinkanyezi, ngoba ukuhlangabezana nezinselele yalesi isayensi yasendulo, ososayensi baqala ukuhlola ubuhlobo lokwehlukile ezahlukene unxantathu.

Kuze kube manje, trigonometry kuyinto Micro-mathematics, ngitadisha ubuhlobo obuphakathi amagugu engele futhi ubude emaceleni onxantathu, kanye ekubhekaneni ukuhlaziywa ubunikazi algebraic of imisebenzi Trigonometric.

Igama elithi "trigonometry"

Igama elithi, okwakunginika igama kulesi sigaba wezibalo, labonakala okokuqala atholakala isihloko sencwadi kwentiwe ngu-German sezibalo Pitiskusa e 1505. Igama elithi "trigonometry" livela isiGreki lisho "ukukala unxantathu." Ukuze yini ukunemba kakhudlwana, akuyona ubukhulu ngokwezwi nezwi leli nani, kodwa mayelana ngesinqumo sawo, okungukuthi, ekutholeni amagugu izakhi zalo engaziwa usebenzisa ezaziwayo.

ulwazi olujwayelekile mayelana trigonometry

umlando Trigonometry waqala zeminyaka engaphezu kwamakhulu amabili edlule. Ekuqaleni, lapho ivela khona kwakuhambisana nezinga isidingo ukunquma engeli unxantathu futhi i-aspect ratio. Phakathi nocwaningo kwaba sobala ukuthi isibalo sezibalo yalezi ubudlelwane kudinga ukwethulwa kwemisebenzi ekhethekile Trigonometric, ebihlelwe ekuqaleni wenza njengoba itafula zezinombolo.

Ukuze wesayensi eziningi siyohlanganiswa wezibalo umfutho ekuthuthukiseni trigonometry kwaba ngokunembile umlando. Umsuka engela amayunithi (degrees) ezihlotshaniswa ososayensi ucwaningo wamandulo iBhabhiloni, kusekelwe uhlelo sexagesimal sibalo, okuyinto emenza lanamuhla idesimali, wasebenzisa wesayensi eziningi osetshenziswayo.

Kusolwa ukuthi ekuqaleni yayikhona njengengxenye trigonometry astronomy. Wabe eseqala ingasetshenziswa bokwakha. Futhi ngokuhamba kwesikhathi, kwaba khona iyasiza kwale sayensi emikhakheni ehlukahlukene umsebenzi womuntu. Lokhu, ikakhulukazi, ukufunda izinkanyezi, ulwandle kanye nomoya Ukuqondiswa kwemikhumbi, umsindo, yokukhanya, electronics, izakhiwo kanye nabanye.

Trigonometry phansi emakhulwini okuqala eminyaka

Báqondiswa idatha yesayensi ku izinsalela lokusinda, abacwaningi baphetha ngokuthi umlando ukuvela trigonometry lihlotshaniswa umsebenzi sezinkanyezi ngesiGreki Hipparchus, owaqala wacabanga yokuthola izindlela zokuxazulula onxantathu (eyindilinga). Imisebenzi yakhe basonta 2nd ekhulwini BC.

Libuye omunye impumelelo ebaluleke kakhulu ukuthi isikhathi ukucacisa ratio imilenze kanye hypotenuse ngendlela unxantathu wesokudla eyaziwa kamuva ngokuthi Pythagorean Theorem.

Umlando yentuthuko trigonometry eGrisi lasendulo lihlotshaniswa igama sezinkanyezi uPtolemy - nombhali uhlelo geocentric zomhlaba ezazikhona ngaphambi uCopernicus.

izazi zezinkanyezi ngesiGreki ayaziwa sine, cosine futhi tangent. Babesebenzisa amatafula ukuthola ukubaluleka kuzithinta kwendilinga usebenzisa arc contractible. Amayunithi nesilinganiso babe degrees kuzithinta, imizuzu namasekhondi. Omunye degree zazilingana sixtieth ingxenye engaba.

Futhi, izifundo ngokunqoba kwamaGreki asendulo ukunyusele ukuthuthukiswa trigonometry eyindilinga. Ikakhulukazi, Euclid e "Imisuka" ifayela echaza ifomu yakhe eholela regularities okungu ivolumu amabhola of diameters ezahlukene. Imisebenzi yakhe kulo mkhakha babé uhlobo ngiyibona ekuthuthukiseni izindawo kakhudlwana futhi eduze yolwazi. Lokhu, ikakhulukazi, ubuchwepheshe zomculo yezinkanyezi, imfundiso yokuziphendukela ibalazwe projection, yasezulwini Ukudidiyela uhlelo, nokunye. D.

Ephakathi: ekutadisheni ososayensi Indian

Inqubekela phambili izuzwe medieval izazi zezinkanyezi Indian. Kokufa isayensi yasendulo ekhulwini IV kwaholela shift ekuthuthukiseni wezibalo e-India.

Umlando ukuvela trigonometry njengenkampani yeSigaba ahlukene ukuzilolonga zezibalo waqala Ephakathi. Kulapho ososayensi esikhundleni sinuses kuzithinta. Ukutholakala kwaleli qiniso bavunyelwa ukuba bangene eZweni imisebenzi ephathelene izifundo izinhlangothi nama-engeli unxantathu kwesokudla. Okungukuthi, kwaba khona-ke ekuqaleni ahlukanise trigonometry bokufundwa, abe legatsha wezibalo.

Ithebula lokuqala Sines abekade iWindows, bavalelwa ^{3 4 5.} Kamuva, kwakunezinguqulo eningiliziwe amatafula: ngokukhethekile, Bhaskara yayidlula sine ithebula 1 ^ku.

I indatshana lokuqala ezikhethekile ku trigonometry uvele ekhulwini X-XI. Umbhali wayo kwaba Central isazi Asian al-Biruni. Umlobi medieval ngaphezulu luyajula e umsebenzi wakhe oyinhloko "Canon Mas'ud" (Book III), e trigonometry itafula Sines (e ziyakhula 15 ') kanye ithebula tangents (e ziyakhula 1 °).

Umlando yentuthuko trigonometry eYurophu

Emva ukudluliselwa azibhala Arab olimini lwesiLatini (XII-XIII c) iningi imibono yososayensi Indian kanye Persian abangu waboleka isayensi European. Lapho kukhulunywa ngaye okokuqala trigonometry basonta ngekhulu XII eYurophu.

Ngokwabacwaningi, umlando trigonometry eYurophu ezihambisana negama eyiNgisi Richard ka Wallingford, owayeneminyaka nombhali imisebenzi "Abane indatshana phezu ukulele eqondile nabokhulumile." Lokho incwadi yakhe yabangela inguquko umsebenzi wokuqala ukuthi ngokuphelele enikelwe trigonometry. Ngekhulu xv, abalobi abaningi emibhalweni yawo ngibalule imisebenzi Trigonometric.

Umlando trigonometry: isikhathi okusha

Ezikhathini zanamuhla, ososayensi abaningi baba ukubaluleka abagxeka trigonometry hhayi kuphela kwezokuhlolwa kwezinkanyezi nesayensi ukubhula ngezinkanyezi, kodwa nakwezinye izici zokuphila. Kuyinto ngokuyinhloko, wezikhali, yokukhanya namandla navigation ku eside uhambo lomkhumbi olwandle. Ngakho-ke, engxenyeni kwekhulu XVI yesibili, ngale ndaba kuye abanesifiso nabantu abavelele abaningi ngaleso sikhathi, kuhlanganise Nikolaya Kopernika, Ioganna Keplera, Fransua Vieta. UCopernicus wathatha trigonometry ezahlukweni eziningana indatshana yakhe "On the Revolutions the Sphere waseZulwini" (1543). Kamuva, e-60s kwekhulu XVI, Retik - umfundi uCopernicus - okuholela "Ingxenye Optical Yezinkanyezi" yakhe pyatnadtsatiznachnye amatafula Trigonometric.

Fransua Viet e "Mathematical njengeziyingxenye yohlu lwezincwadi zeBhayibheli" (1579) kunikeza Nokho unproven enemininingwane futhi ehlelekile, isici trigonometry flat futhi eyindilinga. Futhi Albrecht Dürer kwaba sinusoid iyilowo wazalwa.

I kokufaneleka Leonarda Eylera

Ukunika trigonometry okuqukethwe yesimanje kanye hlobo lwekhadi kwaba Leonarda Eylera. indatshana yakhe "Isingeniso imitsetfo yekuhlatiya okungenamkhawulo" (1748) iqukethe definition ukuthini igama elithi "Trigonometric Imisebenzi", okulingana lwanamuhla. Ngakho, usosayensi wakwazi ukucacisa ephambene imisebenzi. Kodwa akugcini lapho.

Definition of imisebenzi Trigonometric emgqeni yangempela lwenziwe Sibonga kungenzeka ukuba ucwaninge Euler hhayi kuphela engeli kuvunyelwe negative, kodwa engele Bole 360 °. Kwakuwusuku okokuqala esezibonakalisile emibhalweni yakhe ukuthi cosine futhi tangent engela kwesokudla ophambene. Ukunwetshwa sonke cosine futhi sine wayebuye inani le nososayensi. Imfundiso jikelele uchungechunge Trigonometric kanye ekutadisheni Kuhlanganiswe uchungechunge etholwe akuzona izinto kophenyo Euler. Nokho, abasebenza ikhambi izinkinga ezihlobene, wenza bathole okuningi kulo mkhakha. Kwakuthinta ngokusebenzisa umsebenzi wakhe waqhubeka umlando trigonometry. Kafushane emibhalweni yakhe ayesebenzelana ngayo imibuzo trigonometry eyindilinga.

izicelo trigonometry

Trigonometry akuyona ahlobene emikhakheni yesayensi isicelo, ekuphileni kwangempela kwansuku it is kuyaqabukela esetshenziswa imisebenzi. Nokho, leli qiniso akusho inciphe ukubaluleka kwayo. Kubalulekile kakhulu, isibonelo, inqubo triangulation evumela zenza izazi zezinkanyezi zikwazi ukulinganisa kahle impela ibanga izinkanyezi kuthambekela futhi ukuqapha navigation satellite izinhlelo.

Futhi, trigonometry isetshenziswa Ukuqondiswa kwemikhumbi, umculo theory, umsindo, yokukhanya, ukuhlaziywa kwezimakethe zezimali, electronics, okungenzeka theory, izibalo, isayensi yezinto eziphilayo, imithi (isibonelo, sokuqonda ultrasound ultrasound futhi computed tomography), pharmaceutics, i-chemistry, inombolo theory, seismology, i-meteorology , Oceanography, ekudwetshweni kwamabalazwe, ezindaweni eziningi physics, nesimo sendawo futhi geodesy, ubungcweti, amafonethiki, ezomnotho, unjiniyela wama-electronic, isiqoqi sama-softwe, eseyi, crystallography, nokunye. d. umlando trigonometry futhi indima yalo kuleli cwaningo enii natural sciences kanye zezibalo kufundvwe kuze kube yilolu suku. Mhlawumbe esikhathini esizayo, izicelo zayo ziyoba nkulu nakakhulu.

Umsuka nemiqondo eyisisekelo

Umlando ukuvela kanye nokuthuthukiswa trigonometry has eminyakeni engaphezu kwekhulu. Ukwethulwa imiqondo yisisekelo lesi sigaba wezibalo, futhi wayengekho ngaleso sikhathi.

Ngakho, umqondo wegama elithi "isono" linomlando omude kakhulu. Ukukhuluma izingxenye ezahlukene ubuhlobo onxantathu nemibuthano zitholakala ngisho imisebenzi yesayensi, yangekhulu BC III ekhulwini. Imisebenzi enjalo izazi ezinkulu yasendulo Euclid, Archimedes, Apollonius of ePherge, isinazo esifundweni sokuqala kulezi ubudlelwane. Ukutholakala kwezinto ezintsha safuna izinguquko ezithile terminological. Ngakho, Indian usosayensi iWindows linikeza igama kuzithinta ka "Jiva", okusho ukuthi "bowstring". Lapho kufundwa imibhalo Arab zezibalo elihunyushwe olimini lwesiLatini, igama elithi eduze indawo ngenani sine (m. E. "Bend").

Igama elithi "cosine" yavela ngemva kwesikhathi eside kakhulu. Leli gama lihlanganisa inkulumo segama ibinzana Latin "sine ezengeziwe".

Izehlo tangents elihlobene ne kulungiswa inkinga yokunquma obuphelele kwethunzi. Igama elithi "tangent" olwaqala ngo sezibalo Arab X leminyaka Abu al-Amahle, ingxenye amatafula kuqala ukunquma tangent futhi cotangent. Kodwa ososayensi AseYurophu asizange owazi ngalezi impumelelo. sezibalo German nesezinkanyezi Regimontan rediscovers lezi imiqondo 1467 Ubufakazi tangent theorem - credit wakhe. A elihunyushwe ethemini ngokuthi "ethinta inhliziyo".