Kwezinye ye-cosine ezakhayo? Kwezinye ye sine futhi cosine ezakhayo?

Imibuzo zingaveli ekutadisheni imisebenzi Trigonometric zahlukahlukene. Ezinye zazo - ukuthi amakota zomphakathi cosine emihle nemibi, kwezinye amakota sine emihle nemibi. Konke Kulula uma wazi kanjani ukubala ukubaluleka misebenzi ezisemagumbini ezahlukene futhi ujwayelene isimiso sokwakha imisebenzi eshadini.

Iyini i-cosine

Uma sicabangela unxantathu wesokudla-angled, sinalo aspect ratio ezilandelayo esichaza ke: cosine ye-engeli a is isilinganiso umlenze eseduze hypotenuse BC AB (Figure 1.): Cos a = BC / AB.

Ngosizo unxantathu esifanayo, ungathola sine ye-engeli, tangent futhi cotangent. Sinusitis iyona ratio umlenze obuhlukile ekhoneni zezikhulumi kuya hypotenuse AB. I-tangent ye-engeli, uma i-engela oyifunayo sine ehlukaniswa cosine ye-engeli efanayo; esikhundleni Formula elihambisana ekutholeni cosine futhi sine, sithola ukuthi TG a = AC / BC. Cotangent iyona ephambene umsebenzi tangent, kuyoba njalo: ctg a = BC / AC.

Lokho, kwatholakala ukuthi ihlale ifana ngendlela efanele unxantathu aspect ratio for nezindinganiso ezifanayo ye-engeli. Kunengqondo ukuphetha ngokuthi kwaba sobala kusukela lezi zimiso, kodwa kungani inamba embi?

Ukuze wenze lokhu, cabangela unxantathu endaweni Ukudidiyela uhlelo Cartesian, lapho kukhona kokubili amagugu emihle nemibi.

Kusobala cishe ikota yebahlali, lapho ezinye

Uyini izixhumanisi Cartesian? Uma sikhuluma isikhala mgudumbili, sinalo imigqa emibili iqondiswe aphambana ngesikhathi O iphuzu - iyona x-axis (Ox) kanye y-eksisi (Oy). Kusukela O iphuzu bebheke umugqa oqondile ezibekwe izinombolo omuhle, kodwa kolunye uhlangothi - ezingezinhle. Kule, ekugcineni, lithembela ngqo, kunoma iyiphi amakota cosine uhilela izenzo, futhi lapho, ngokufanele, akukho.

kwikota yokuqala

Uma beka unxantathu wesokudla-angled kwikota yokuqala ⁽⁰ kuya ^90), lapho x-axis futhi y kukhona kweqanda (kumasegmenti AO futhi BO ezisebusweni izimbazo lapho amanani uphawu "+"), khona-ke leso sono, ukuthi i-cosine okufanayo kuyodingeka kweqanda, futhi babelwa value nge "plus." Kodwa kwenzekani uma uhambisa unxantathu engxenyeni yesibili (asuka ^ku-90 kuya ^ku-180)?

ikota yesibili

Siyabona ukuthi umlenze y-eksisi JSC wathola value ezimbi. I-cosine ye-engeli manje has a isilinganiso ohlangothini lokususa nalo, futhi ngokunjalo ukubaluleka kwalo kokugcina iba engakhi. It kuvela ukuthi nendlela ozibonakalisa ngayo ingxenye yesine ka-cosine uhilela izenzo incike indawo calantsatfu Cartesian Ukudidiyela uhlelo. Futhi kulokhu, cosine ye-engeli uthola value ezimbi. Kodwa akukho okushintshile lo itheku, njengoba ukunquma uphawu ilungelo isiqondiso OB, eye wahlala kuleli cala nge uphawu. Kufinyeta ngowokuqala ngothini ezimbili.

Ukuze uthole kulokho amakota cosine zomphakathi emihle nemibi (kanye itheku nezinye imisebenzi Trigonometric), kumele sibheke yini isibonakaliso eyabelwe omunye umlenze. Ukuze cosine ye-engeli esibucayi umlenze AB, ngoba sine - RH.

Kwikota yokuqala kuze kube manje nguye kuphela ukuze uphendule lo mbuzo: "Ngo-kuziphi sine futhi cosine omuhle ngesikhathi esifanayo?". Bheka, ngeke namanje olufana uphawu imisebenzi emibili.

Esikhathini yesibili ikota umlenze JSC waqala zinenani ongathandeki, futhi ngaleyo ndlela cosine baba ezimbi. Wenani omuhle itheku agcinwe.

ngekota yesithathu

Manje bobabili umlenze AB futhi OB waphenduka ezimbi. Khumbula ubudlelwane ngoba sine futhi cosine:

Cos a = AB / AB;

Ona = vơ / AB.

AB njalo has uphawu omuhle kule Ukudidiyela uhlelo, njengoba ezazini yimiphi ezimbili eksisi amaqembu athile. Kodwa imilenze abe negative, ngakho umphumela kokubili imisebenzi, omubi kakhulu, ngoba uma enze ukubuyabuyelela noma ophikweni izinombolo, kuhlanganise yedwa eyodwa ine uphawu "lokususa", umphumela beyoba ujwayelene nalesi.

Umphumela kulesigaba:

1) lapho ikota cosine omuhle? Emfanekisweni wokuqala ezintathu.

2) Ngo-okuyinto ikota sine omuhle? Eyokuqala nesesibili ezintathu.

Ngekwata yesine (kusuka ^mayelana 270 kuya ^cishe ku-360)

Lapha umlenze ululama JSC uphawu "plus", futhi ngaleyo ndlela cosine kakhulu.

Ngoba uma sine namanje "omubi" ngoba umlenze RH wahlala ngezansi yokuqalisa O.

okutholakele

Ukuze siqonde ukuthi amakota-cosine omuhle, negative, njll, kudingeka sikhumbule la isilinganiso ukubala cosine: eseduze ekhoneni umlenze yahlukaniswa hypotenuse. Abanye othisha ukunikela ngakho khumbula: kuya (osinus) = (a) ekhoneni. Uma ukukhumbula "ukukopela" ezokwenza ukwazi ngokuzenzakalelayo ukuthi sine - iyona ratio umlenze okuphambene kuya engela kuya hypotenuse.

Khumbula, kunoma iyiphi amakota cosine omphakathi emihle nemibi kunzima ngempela. Trigonometry isebenta eziningi, futhi konke value abo. Noma kunjalo, ngenxa yalokho, ngoba kweqanda we-sine - 1, 2 nane (kusukela ⁰ kuya ^ku-180); ngoba i-cosine 1, 4 nane (0 kuya ^{mayelana 90} futhi kusukela ^cishe 270 kuya ^cishe ku-360). Esikhathini amakota esele okuvela kuyo le imisebenzi kuchazwa nge lokususa.

Mhlawumbe othile kuyoba lula ukukhumbula lapho uphawu umsebenzi image.

Ukuze itheku kuyabonakala ukuthi kusukela zero kuya ku-180 ^phezu yokhalo ingaphezu isono (x) Inani umugqa, kusho umsebenzi omuhle. Ukuze cosine kanye: endaweni cosine ikota omuhle (isithombe 7), futhi lapho bubonakala ukuhamba omubi imigqa nangaphezulu ahlangene cos (x). Ngenxa yalokho, singakhumbula izindlela ezimbili ukucacisa uphawu imisebenzi sine, cosine:

1. umbuthano wenze sengathi uxoxa engaba lingana kuze fike (nakuba, eqinisweni, kungakhathaliseki ukuthi engaba kumbuthano, kodwa izincwadi ngokuvamile iholela nje isibonelo esinjalo; lokhu kusiza bezibona, kodwa ngesikhathi esifanayo, ngaphandle uma akunandaba, izingane angangenwa udidekile).

2. isithombe, kuye ngokuthi umsebenzi (s) kusuka ingxabano x njengoba isibalo zokugcina.

Nge indlela yokuqala kungaqondakala kulokubi ngemvume engaphansi, siye wachaza ngokuningiliziwe ngalokhu okungenhla. Umfanekiso 7, ezakhiwe ngokuvumelana nalezi idatha kanye ngangokunokwenzeka ihumusha umsebenzi okuholela futhi znakoprinadlezhnost yayo.