Le livela i sine ye-engile lilingana i cosine ye kwinkalo enye

Dana umsebenzi kwitrigonometri elula y = Isono (x), nto differentiable kwinqanaba ngalinye yonke ithambeka. Kumelwe ukuba lo yemvelaphi i sine ye nayiphi na impikiswano ilingana i cosine ye kwinkalo enye, oko kukuthi, '= eKosi (x).

Ubungqina ngokusekelwe kwinkcazo umsebenzi esukela

We uchaze x (aliqonde) kwezinye ebumelwaneni encinane ingongoma ethile x Δh _0. Siya kubonisa ixabiso umsebenzi ngayo, kwaye kwindawo x ukufumana isongezo sika umsebenzi elinikiweyo. Ukuba Δh - ingxabano incremented, ingxoxo entsha - le x ₀ + Δx = x, ixabiso kwalo msebenzi ukuba ixabiso Kwempikiswano (x) ulingana Isono (x ₀ + Δx), ixabiso umsebenzi kwindawo ethile (x ₀₎ nalo eyaziwa .

Ngoku sinento Δu = Isono (x ₀ + Δh) -Sin (x ₀₎ - wafumana umsebenzi okukodwa.

Ngokutsho formula sum sine ye engile ezimbini ukungalingani siza ukuguqula umahluko Δu.

Δu = Isono (x ₀₎ · eKosi (Δh) + eKosi (x ₀₎ · Sin (Δx) thabatha Isono (x ₀₎ = (COS (Δx) -1 ) · Sin ( x ₀₎ + eKosi (x ₀₎ · Sin (Δh).

ngokoMthetho lobeko eyenziwa amaqela kuqala wesithathu Isono (x _0), kokurholwa common factor - sine - kwizibiyeli. Samkela yebinzana umahluko eKosi (Δh) -1. Osele ukutshintsha umqondiso phambi ipharenthesis kunye kwizibiyeli. Ukwazi oko i-eKosi 1 (Δh), senza utshintsho afumane ibinzana lula Δu, nto leyo ke lahlulwe yi Δh.
Δu / Δh uya kuba ifomu: eKosi (x ₀₎ · Sin (Δh) / Δh 2 · Sin ² (0.5 x Δh) · Sin (x ₀₎ / Δh. Olu lulwahlulo isongezo sika umsebenzi nokuvunyelwa ukuba isongezo sika ingxabano.

Kuhleli ukufumana isiphelo ngokulinganayo ezifunyenwe kuthi ngexesha lim Δh, kwase kiswano.

Yinto eyaziwayo ukuba mda Isono (Δh) / Δx ulingana no-1, phantsi imeko. Namazwi 2 · Sin ² (0.5 x Δh) / Δh kweziphumo sum utshintshwano ethile nemveliso equlathe njengoko ezininzi yokuqala mda ephawulekayo: elingezantsi iqhezu kunye znemenatel salhule ngo-2, isikweri sine endaweni imveliso. Nantsi indlela yokwenjenjalo:
(Isono (0,5 · Δx) / (0,5 · Δx)) · Sin (Δx / 2).
Umda le binzana xa Δh welusa zero, iya kulingana nenani zero (0 phindo luka-1). Kubonakala ukuba isiphelo umlinganiselo Δy / Δh yi eKosi (x ₀₎ · 1-0, oku eKos (x _0), ibinzana elithi yayo ozimeleyo Δh elusa 0. I sigqibo: ukuba yemvelaphi i sine ye nayiphi engile ulingana no'x ' cosine ye x, angabhalwa ngolu hlobo: y '= eKosi (x).

Ifomula engumphumela kuluhlu etafileni yezabelo ezaziwayo, apho yonke imisebenzi nezakhiwo

Ekucombululeni iingxaki, apho adibana khona yemvelaphi i sine, unako ukusebenzisa imithetho-hlukeneyo kunye neefomula ukulungele-ezenziwe kwetafile. Umzekelo: ufumane yemvelaphi umsebenzi y kwecacileyo = 3 · Sin (x) -15. Sisebenzisa imithetho Ukuveliswa nokususwa factor aphantsi ngamanani ukuba umqondiso yemvelaphi kwaye abale inani esukela rhoqo (leyo zero). Faka ixabiso itafile sine ye yemvelaphi angela x eKos ngokulinganayo (x). Yamkela impendulo: y '= 3 · eKos (x) kodwa kuyoze. Eli livela, yena, naye sabaqalayo umsebenzi y = H · eKos (x).

Le livela sine ophindwe nawuphi ingxabano

Xa ekubaleni ibinzana (Isono ² (x)) 'kufuneka sikhumbule umsebenzi inzima kangakanani ngokwahlukeneyo. Ngoko ke, ² = Isono (x) - ngumsebenzi igunya sine ophindwe kabini. impikiswano layo nalo umsebenzi netrigonometri, ingxabano ezintsonkothileyo. Isiphumo kulo mzekelo ilingana nemveliso lingabali lokuqala isikweri yemvelaphi entsonkothileyo Kwempikiswano, kwaye yesibini - le yemvelaphi i sine. Nazi umgaqo umehluko a umsebenzi umsebenzi: (u (v (x))) 'into (u (v (x)))' · (v (x)) '. Ukubonakaliswa v (x) - ingxoxo esimbaxa (function lwangaphakathi). Ukuba umsebenzi enikwe "y lilingana ebaxiweyo kabini x", ngoko ke yemvelaphi lo msebenzi edityanisiweyo yi y '= 2 · Sin (x) · eKos (x). Imveliso ye lingabali yokuqala kabini - ithe eyaziwa function bomtya, kunye eKosi (x) - sinus livela impikiswano ezimbaxa kwisuntswana umsebenzi equation. Isiphumo zokugqibela guqukani ngokusebenzisa indlela ye ebaxiweyo i netrigonometri-angle kabini. A: Le ithe yi Isono (2 · x). Le fomyula Kulula khumbula, isoloko isetyenziswa itafile.