Indlela yokufumana i-cosine ye-angle xa i-sine yaziwa?

Indlela yokufumana i-cosine ye-angle xa i-sine yaziwa?

  • Iifomula zeTrigonometry sisihloko esithi abafundi abakwibanga le-10 nele-11. Ukufumana i-cosine ye-angle, ukwazi i-sine, kuya kufuneka usebenzise ifomula esisiseko.

    Okokuqala, sisebenzisa i-Pythagorean theorem

    Ngoku sithatha indawo efunyenweyo idatha

  • Phakathi kwe-sine ne-cosine kwinqanaba elifanayo unokufumana ulwalamano oluvumela ukuba ufumane i-cosine, ukwazi i-sine. Yiyo ndlela obu buhlobo bubukeka ngayo:

    Kuvela ukuba ufumane i-cosine kule meko, simane nje sifanele siphume ingcambu kwigama (i-1-sin kwisikwere sekona ethile).

  • Liliphi igama lefomu engingayikhumbuliyo:

    cos ^ 2 + isono ^ 2 = 1

    cos = sqrt (1-sin ^ 2).

  • Kwiimeko ezinje, kufuneka uhlale ukhumbule Ubununu obunqununu be-trigonometric

    i-cosine square alpha + yesine square alpha = 1

    cos ^ 2Alpha + isono ^ 2Alpha = 1

    kwaye apha uvela apha siyazibona

    cos ^ 2Alpha = 1-sin ^ 2Alpha

    co-alpha = sqrt (1-sin ^ 2-alpha)

  • Impendulo yam iyafana neempendulo kumbuzo ofanayo (jonga apha).

    Ukususela kubunikazi obuninzi be-trigonometric:

    Bhengeza i-cosine kwisikwere se-angle:

    Ngoko i-cosine ye-angle ilingana nenye ingcambu yesikwere sale nkulumo, okanye kuye, kuphela ngophawu-.


    Uphawu phambi kwempande luxhomekeke kumdaomiselwe ukuchaneka kwimeko yengxaki.

    Ukuba kunikwe xabiso elihle, i-angle i-1-th okanye kwikota ye-2-th. Kwikota yokuqala (0lt; alt; 90) ixabiso le-cosine liya kuba lihle. Lapha sikhetha uphawu olubanzi. Kwikota yesibini (90lt; alt; 180) ixabiso le-cosine liya kuba libi. Emva koko ingcambu khetha i-minus sign.

    ukuba ixabiso lexabiso elibi, i-angle i-3 kunye nekota ye-4. Kwiindawo ze-3 (180lt; alt; 270), i-angle cosine iya kuba ngaphantsi kwezinga.

    Kwiikota ze-4 (270lt; alt; 360), i-cosine yekona iya kuba mkhulu kune-zero.


    U mzekelo

    Umzekelo 1. Fumana i-cosine ye-angle xa i-sina = -0,6. 180lt; alt; 270 (degrees)

    Isisombululo. Sifumana umahluko we-1 kunye nesikwere senani lexabiso, i.e. isikwere (-0,6).

    -0,6 square ufana nale: (-0,6) * (- 0,6) = 0,36. Yibanike ngokungafaniyo:

    1-0,36 = 0,64

    Ndinikwe isikwere sexabiso le-cosine. Ukufumana ixabiso le-cosine ngokwayo, sikhupha ingcambu ye-0,64 kwaye siyithathe kunye + nomqondiso okanye kunye - kunye nomqondiso. Sifumana i-0,8 okanye -0,8.

    Ekubeni, ngokucinga, i-angle ikwikota ye-3, ixabiso le-cosine elifunyenweyo liya kuba ngaphantsi kwe-zero. Ngoko khetha -0,8.

    Impendulo: cos cos = = 0,8.

    Cinga ngomzekelo kwimeko apho i-angle ikwikota ze-4:

    Umzekelo 2. Fumana i-cosine ye-angle xa i-sina = -0,6. 270lt; alt; 360 (degrees)

    Isisombululo siyafana (bona umzekelo we-1).

    Ngaphambi kokukhetha impendulo, siyaqiqa ngale ndlela:

    Ekubeni ngeemeko i-angle ikwikota ye-4, inani le-cosine liza kuba likhulu kune-zero. Ngoko khetha i-0,8.

    Impendulo: cos cos = = 0,8.

  • Kwi-trigonometry, omnye wabo ulingana nobudlelwane balobu budlelwane, oko kukuthi, kuyimfuneko ukuguqula ibhodi ukuba ihlaselwe phantsi xa i-sine ye-angle ejikelezayo ingezansi kwaye ubuyele kwindawo yayo yangaphambili ukwenzela ukuba ufumane i-cosine ye-angle inclination!

  • Yonke into ilula kakhulu kwaye izibalo ezisisiseko zisekelwe kwisilinganiselo esisodwa esaziwayo, apho isibalo sendawo yezikwere kunye nesono segosa elifanayo kubangele inani elilodwa.

    Ingongoma ephambili engenza ubunzima bubekwe uphawu oluhle okanye olubi phambi kwengcambu.

  • Ukususela kwizifundo esikolweni malunga neklasi le-10-11, ndiyakhumbula indlela yobume obuninzi be-trigonometric, esiyifunde ngentliziyo:

    Sifumana umsebenzi oyifunayo:

    Ngendlela elula ungayifumana i-cosine, ukuba uyazi i-sine. Futhi uyisebenzise xa usombulula iingxaki.

  • Fumana i-cosine ye-angle ukusuka kweli binzana:

    cos ^ 2Alpha + isono ^ 2Alpha = 1

    Oko kukuthi, ukuze ufumane i-cosine, kufuneka ushiye i-cosine kwicala lasekhohlo. Eli binzana liya kuphuma-cos = sqrt (1-isono ^ 2), i-cosine ifunyenwe.

  • Ukubala i-cosine ye-engile, ukwazi ukuba i-sine yayo ilula kakhulu. Ukwenza oku, kufuneka wazi iziseko zeziseko ze-trigonometry - isamba sezikwere ze-sine ne-cosine zilingana nomnye. Ukwazi le ndlela, kulula ukubala i-cosine ye-angle. Ubunikazi be-trigonometric buboniswa ngokubonakalayo kwiifomula ezilandelayo, apho i-cosine ibalwa khona.

    Ungalibali ukuba xa ufumana i-cosine, kufuneka ususe isikwere sayo kwaye ubale ingcambu yayo. Oko kukuthi, iimpawu ezifanayo emva kokuba idijithali zilingana nokufaka ingcambu yesikwere ekubaleni.

  • Sicinga ukuba ubunikazi bokuqala be-trigonometric bukhunjulwa ngumntu wonke.

    Ukuba umntu ulibele, ndiye ndikukhumbuza:

    Inani leziikwere zesine kunye ne-cosine yezinye (enye) i-alfa ilingana kunye (1).

    I-formula yayikhunjulwa, kwaye ke konke kulula.

    Kwinqanaba elincinane le-equation sishiya i-cosine ye-angle engxenyeni, kwaye kwicala lasekunene (apho umntu sele esele khona) siphosa isikwere sine-angle. Kuvela oku kulandelayo:

    Asiyidingi isikwele se-cosine, kodwa i-cosine, ngoko sitshintsha i-equation ngasentla kwaye siyafumana:

    I-cosine ye-angle ilingana neengcambu zecala yeyunithi icima isikwere sine (cos = sqrt (1-sin ^ 2)).

Ukulayisha ...

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