Lokho tangent kulo mbuthano? Properties of tangent kulo mbuthano. Tangent zivamile tindilinga letimbili

Secants, tangents - konke lokhu kaningi kwakuzwakala izifundo geometry. Kodwa udaba esikoleni ngemuva, kudlule ngonyaka, futhi konke lokhu ulwazi ukhohlwe. Yini okufanele mina khumbula?

Ingqikithi

Igama elithi "tangent kulo mbuthano" uphawu, mhlawumbe, konke. Kodwa-ke, akunakwenzeka ukuba yonke ngeke Ngokushesha yibe sewakha definition. Phakathi naleso sikhathi ngokuthi umugqa tangent ungephansi kwemandla indiza efanayo emjikelezweni okuyinto ephambana ke iphoyinti eyodwa kuphela. inqwaba yabo kungenzeka akhona, kodwa konke ezifanayo kodwa ngesikhathi esifanayo, okuzoxoxwa ngezansi. Njengoba ungase ukuqagela, iphuzu contact okukhulunywe endaweni lapho kumbuthano futhi emgqeni aphambana. Esimweni ngasinye, kuba omunye, uma kukhona ngaphezulu, kuyobe sekuba i-yokusetshenziswa.

Umlando ukutholakala kanye cwaningo

Umqondo tangent uvele ezikhathini zasendulo. Ukusungulwa kwalezi imigqa kulo mbuthano lokuqala, bese-ke ellipses, parabolas futhi hyperbolas nombusi nekhampasi labetibambile namanje kusaqalwa ukuthuthukiswa geometry. Yiqiniso, akuwona wonke umlando uye walondoloza igama owathola, kodwa kuyacaca ukuthi ngisho ngaleso sikhathi abantu babaziwa kahle izakhiwo tangent kulo mbuthano.

Ezikhathini zanamuhla, isithakazelo lesi simanga kwagqashuka futhi - waqala esiyindilinga entsha ezifundwa umqondo ngokuhlanganyela kuvulwa Curves entsha. Ngakho, uGalileo owethulwa nomqondo cycloid futhi Fermat futhi Descartes wakha tangent kuso. Ngokuqondene imibuthano, kubonakala, ingabe kuyinkazimulo ukuba izimfihlo asendulo amshiya kule ndawo.

izakhiwo

Ububanzi badonsekela iphuzu empambana kuyoba perpendicular umugqa. lokhu main, kodwa hhayi isakhiwo kuphela okungukuthi tangent kulo mbuthano. Esinye isici esibaluleke kakade kuhlanganisa ngqo ezimbili. Ngakho, nge iphuzu elilodwa, okuyinto amanga ngaphandle mbuthano, kungenzeka ukudweba tangents ezimbili, futhi ubude babo bayalingana. Kunenye theorem ngale ndaba, kodwa kuyaqabukela labetibambile kohlaka indinganiso Yiqiniso esikoleni, kodwa kakhulu ewusizo ukuxazulula izinkinga ezithile. Lenza kanje. Kusuka kwelinye iphuzu engaphandle embuthanweni, ukudweba tangent futhi secant kuso. izingxenye Kwakheka AB, AC futhi AD. A - empambana imigqa, B iphuzu tangency, C no-D - ukuwela. Kulokhu, ezothando elandelayo isebenza: ubude tangent kulo mbuthano, yisikwele, lilingana umkhiqizo zingxenye AC futhi AD.

Kulokhu osekushiwo, kukhona eliphezulu ezibalulekile. Ukuze iphuzu umbuthano ngamunye, ungakwazi ukwakha tangent, kodwa munye kuphela. Ubufakazi lokhu ulula: ngemcondvo phansi ke perpendicular kusukela engaba, siyathola ukuthi bakha unxantathu ngeke kube khona. Futhi lokhu kusho ukuthi i-tangent - kuphela.

isakhiwo

Phakathi kwezinye imisebenzi geometry kuyisigaba esibalulekile, njengoba umthetho, ungalilahli isithandwa abafundi nabafundi. Ukuxazulula imisebenzi yalo mkhakha badinga kuphela ikhampasi nombusi wezwe. Kuyinto umsebenzi wokwakha. Kube beqhubeka bakhela a tangent.

Ngakho, inikezwe kumbuthano futhi iphuzu amanga ngaphandle kwemingcele yayo. Futhi udinga ukuba baphumelele kulolu hambo kubo tangent. Wenzenjani ukukwenza? Okokuqala, udinga ukuchitha isikhathi phakathi maphakathi umbuthano O futhi iphuzu setha. Khona-ke, ngosizo nekhampasi kumele bahlukanise ke ngesigamu. Ukuze wenze lokhu, kufanele usethe engaba - ezingaphezu kwesigamu kancane ibanga phakathi maphakathi kumbuthano futhi iphuzu yasekuqaleni. Khona-ke udinga ukwakha lwesikhathi ezimbili intersecting. Irediyasi at the ushintsho akufanele kube ikhampasi, maphakathi ohlangothini umbuthano ngamunye kuyoba iphuzu yokuqala, futhi O, ngokulandelana. Izindawo lwesikhathi ezimpambanweni kudingeka ukuba uxhume ukuthi Imi kwesigaba ngesigamu. Buza nganoma engaba ikhampasi ilingane ibanga. Ngaphezu kwalokho, nge maphakathi empambana ukwakha kweminye imibuthano. Kuzobakhuthaza esekelwe kokubili iphuzu yokuqala, futhi O. Kulokhu, kuzoba zemigwaqo emibili nale nkinga kumbuthano. Lokho bayoba amaphuzu yokuxhumana iphuzu ekuqaleni elicacisiwe.

ezithakazelisayo

It yakha tangent kulo mbuthano okwaholela ekuzalweni calculus umehluko. Umsebenzi wokuqala ngale ndaba inyatheliswa sezibalo esidumile German Leibniz. It kuhlinzekelwe amathuba okuthola i-maxima, minima futhi tangents, kungakhathaliseki ukuthi izinto eziningi wamaqhuzu engenangqondo. Awu, manje-ke isetshenziselwa ezinye izibalo eziningi.

Ngaphezu kwalokho, i-tangent kulo mbuthano elihlobene ne-Jomethri tangent umqondo. Kuyinto kulokhu, futhi iza igama layo. Lihunyushwe kwelesiHeberu elithi tangens Latin - "tangent". Ngakho, lo mqondo akuyona nje geometry futhi calculus umehluko, kodwa trigonometry.

tindilinga letimbili

Ngaso sonke isikhathi i-tangent zatragivet sibalo eyodwa kuphela. Uma angachitha imigqa enkulu eziningi kumbuthano owodwa, ke kungani kungenjalo okuphambene nalokho? Kungenzeka. Yilokho nje inkinga kulokhu nzima kakhulu, ngoba tangent kuya tindilinga letimbili abakwazi idlule noma yikuphi, futhi isikhundla isihlobo zonke lezi zibalo Ingadla ezahlukene.

Izinhlobo nezinhlobonhlobo

Lapho kuziwa emibuthanweni ezimbili futhi imigqa eyodwa noma ngaphezulu, khona-ke ngisho noma wazi ukuthi kumayelana, akuyona ngokushesha ecacile kanjani zonke lezi izingcezu ahlelwe maqondana nomunye. Kulesi sisekelo, kukhona izinhlobonhlobo eziningana. Ngakho, indingilizi angase abe iphuzu elilodwa noma amabili ezivamile, noma ayikho nhlobo. Esimweni sokuqala, bayoba idlulela, kanti eyesibili - icindezelwa. Futhi nazi izinhlobo ezimbili. Uma kumbuthano owodwa, njengoba abangu linamathele yesibili, touch libizwa yangaphakathi uma kungekhona - ke ngaphandle. Qonda Isimo eyisihlobo izingcezu kungenziwa kuphela esekelwe hhayi umdwebo, kodwa kokuba ulwazi mayelana isamba radii yabo kanye nebanga phakathi izikhungo zabo. Uma lezi zimiso ababili bayalingana, ke emibuthanweni icindezelwa. Uma kuqala ngaphezulu - aphambana ngenye indlela - Awunawo amaphuzu ezivamile.

Kunjalo-ke nangobufakazi imigca lecondzile. Uma unanoma yimiphi imibuthano ezimbili abangenalo amaphuzu ezivamile kungaba
ukwakha tangents ezine. Ababili babo ngeke kuyendlulela phakathi izibalo, bebizwa yangaphakathi. Umbhangqwana yezinye - zangaphandle.

Uma sikhuluma imibuthano, okuyinto unayo eyodwa iphuzu esivumelana ngakho, inkinga lula kakhulu. Iqiniso liwukuthi noma yimuphi ilungiselelo mutual, kulesi simo tangent bazokwazi eyodwa kuphela. Futhi siyodlula iphuzu ukunquma. Ngakho ukuthi isakhiwo ngeke okungadala ubunzima.

Uma izibalo ezimbili amaphuzu yemigwaqo, ke lingakhiwa umugqa tangent kulo mbuthano njengoba omunye, kanti owesibili, kodwa ngaphandle kuphela. Isixazululo sale nkinga, ncamashí nalokho ngakho ngokuhamba kwesikhathi.

Ukuhlangabezana izinselele

Bobabili tangent zangaphakathi nezangaphandle wemibuthano ezimbili isakhiwo akuzona ngakho elula, nakuba, futhi lokhu inkinga isixazululekile. Iqiniso lokuthi iphethini asizayo isetshenziselwa le, ngakho sesizicabangile out indlela enjalo wedwa Akuve kuyinkinga. Ngakho, inikezwe imibuthano ezimbili radii ezahlukene futhi kugxile O1 kanye O2. Kubo, isidingo sokuthi kwakhiwe amabili namabhuzu tangents.

Okokuqala, mayelana nendawo umbuthano emikhulu yokwakha esekelayo. Ngesikhathi esifanayo kwi ikhampasi kumele imiswe umehluko phakathi radii izibalo ezimbili zokuqala. Kusukela maphakathi ezincane umbuthano tangent kuya asizayo nalolwakheke kahle. Ngemva kwalokho of O1 kanye O2 aphethwe perependikulyary lezi ngqo ezimpambanweni zomgwaqo izibalo zokuqala. Njengoba ulandela kusukela izakhiwo eziyisisekelo tangent, amaphuzu adingekayo totimbili imibuthano. Inkinga isixazululekile, okungenani ngokwengxenye yayo yokuqala.

Ukuze ukwakha tangents yangaphakathi kufanele ukuxazulula cishe nenkinga efanayo. Nalapha, sidinga i-sibalo elisizayo, kodwa ngalesi sikhathi engaba salo ilingana nenani lezinombolo of the original. Ukuze wakhe ukwakha tangent kusukela maphakathi omunye mibuthano. Inkambo okwengeziwe ngesinqumo kungaqondakala esibonelweni odlule.

Tangent kulo mbuthano, noma ngisho ezimbili noma ngaphezulu - akuyona umsebenzi onzima kangaka. Yiqiniso, zezibalo Sekuyisikhathi eside saphela ukuxazulula izinkinga ezifanayo ngesandla futhi ziyakwethemba ukubala izinhlelo ekhethekile. Kodwa ungacabangi ukuthi manje akusho ukuthi bakwazi ukukwenza wena ngokwakho, ngoba okwesikhathi ekwakhiweni efanele msebenzi kwikhompyutha ukwenza okuningi kanye nokuzwisisa. Ngeshwa, kwesatshwa ukuthi emva ushintsho sokugcina ifomu yokuhlola zezinkinga ukulawula ulwazi ku ukwakhiwa kuzokwenza abafundi kakhudlwana futhi nobunzima xaxa.

Njengoba okuthola tangents ezivamile emibuthanweni ngaphezulu, akusiyo njalo kungenzeka, ngisho noma amanga indiza efanayo. Kodwa kwezinye izimo kungenzeka ukuthola umugqa ezinjalo.

izibonelo Life

Tangent zivamile tindilinga letimbili ngokuvamile atholakala umkhuba, nakuba akucaci ngaso sonke isikhathi. Zokuthutha, izinhlelo Modular, ukudluliswa amabhande izipilingi, ukungezwani wentambo endaweni umshini wokuthunga, kodwa ngisho nje uchungechunge ibhayisikili - zonke izibonelo zokuphila. Ngakho ungacabangi ukuthi izinkinga yejeyomethri ukuhlala kuphela ngemcondvo: e yobunjiniyela, ukwakhiwa kanye nezinye izindawo eziningi zisebenza esisebenzayo.