Umthetho weeCosines: Ukusetyenziswa, imizekelo kunye nokuzivocavoca

Umthetho we-Cosines, owaziwa ngokuba ngumthetho we-cosines, sisixhobo esisisiseko semathematika kwi-trigonometry ekuvumela ukuba uqikelele ubude becala elinye likanxantathu ongasekunene usebenzisa amaxabiso amanye amacala amabini kunye ne-engile phakathi. bona. Lo mthetho usetyenziswa ngokubanzi kumasebe ahlukeneyo obunjineli kunye ne-physics, ukubonelela ngesisombululo esichanekileyo nesisebenzayo sokusombulula iingxaki zejometri ezinzima. Kweli nqaku, siza kuphonononga isicelo ngokweenkcukacha, imizekelo kunye nokuzilolonga iinkcazo ezisebenzayo zoMthetho weCosines, ukunika abafundi ukuqonda okuqinileyo kwesi sixhobo semathematika kunye nokusebenziseka kwayo kwiimeko ezahlukeneyo zobugcisa.

1. Isingeniso kuMthetho weCosines: Ukusetyenziswa kwiingxaki zejometri

Umthetho weCosines sisixhobo esisisiseko kwijometri ukusombulula iingxaki ezinxulumene nonxantathu. Lo mthetho uthi isikwere secala elinye likanxantathu silingana nenani lezikwere zamanye amacala amabini thabatha kabini imveliso kanxantathu. los dos lados ngecosine ye-engile ejongene nelaa cala. Ngokuqonda nokusebenzisa lo mthetho ngokuchanekileyo, sinokucombulula iintlobo ngeentlobo zeengxaki zejometri.

Ukusebenzisa uMthetho weCosine kwiingxaki zejometri, inyathelo lokuqala kukuchonga unxantathu ekuthethwa ngawo kwaye uleyibhelishe amacala kunye nee-engile. Okulandelayo, kufuneka sigqibe ukuba loluphi ulwazi esilunikwayo kwaye loluphi ulwazi esicelwa ukuba silufumane. Ukusuka apho, sinokusebenzisa ifomula yoMthetho weCosine ukusombulula ingxaki. Kubalulekile ukukhumbula ukuguqula ii-engile kwiiradians ukuba kukho imfuneko phambi kokuba usebenzise ifomula.

Ingcebiso eluncedo xa usebenzisa uMthetho weCosine kukusombulula into engaziwayo okanye icala esifuna ukulifumana kwifomula phambi kokufaka amaxabiso endaweni. Oku kuya kwenza kube lula ukusombulula i-equation kwaye ugweme iimpazamo kwizibalo. Kusenokuba luncedo ukusebenzisa imisebenzi yetrigonometric kunye neepropathi zikanxantathu (ezifana nenani leengile zangaphakathi) ukwenza lula ingxaki kwaye ufumane ubudlelwane phakathi kwamacala kunye neengile. Ukusebenzisa izixhobo zokubala zetrigonometric kungaluncedo kakhulu ekuqinisekiseni iziphumo ezifunyenweyo.

2. Ingcaciso yeMathematika yoMthetho weCosines kunye nefomula yawo

Umthetho weCosines sisixhobo esiluncedo semathematika sokusombulula oonxantathu abangengabo abasekunene. Lo mthetho useka ubudlelwane phakathi kobude bamacala kanxantathu kunye nee-engile ezijongene nazo. Ifomula yoMthetho weCosines ingasetyenziselwa ukufumana zombini ubude bamacala kanxantathu kunye neengile ezihambelanayo.

Ifomula yoMthetho weCosines iboniswe ngolu hlobo lulandelayo:
c^2 = a^2 + b^2 – 2ab * cos(C)

Apho "a" kunye "b" bubude bamacala amabini aziwayo, "C" yi-engile ejongene necala elingaziwayo "c" kunye no "cos" libhekiselele kumsebenzi we-cosine. Le fomula ikuvumela ukuba ufumane amaxabiso emacaleni kunye nee-engile zikanxantathu xa ubude bamacala amabini kunye ne-angle echaseneyo ziyaziwa.

Ukusebenzisa uMthetho weCosines, la manyathelo alandelayo kufuneka alandelwe:
1. Chonga ixabiso lamacala aziwayo kunye ne-engile ejongene necala elingaziwayo.
2. Faka endaweni amaxabiso kuMthetho weCosines formula.
3. Sombulula i-equation ukufumana ixabiso lecala elingaziwayo okanye i-engile ehambelanayo.
4. Phinda inkqubo ukuba kuyimfuneko kwamanye amacala okanye ii-angles.

Kubalulekile ukuqaphela ukuba ii-engile kufuneka zilinganiswe kwiiradians ukusebenzisa i-Law of Cosines formula, ngoko unokufuna ukuziguqula ukuba zibonakaliswe ngeedigri. Ukongezelela, xa usebenzisa ifomula, kufuneka ubeke ingqalelo kwiimpawu ezintle kunye nezibi kwi-equation yokugqibela ukuqinisekisa ukuba ufumana ixabiso elichanekileyo. Ukusebenzisa uMthetho weCosine kunokuba luncedo olukhulu ekusombululeni iingxaki ezibandakanya oonxantathu abangekho ekunene kunye nokumisela iimpawu zabo.

3. Ukusetyenziswa koMthetho weCosines kwiscalene kunye nonxantathu obtuse

Umthetho weCosines yithiyori ebalulekileyo esetyenziswa kwijometri ukusombulula iingxaki kwi-scalene kunye ne-obtuse triangles. Lo mthetho useka ubudlelwane phakathi kwamacala kunye nee-angles zonxantathu, okusivumela ukuba sinqume amaxabiso angaziwayo. Ngezantsi ngamanyathelo ayimfuneko ukuze usebenzise ngokufanelekileyo uMthetho weCosines kulolu hlobo loonxantathu.

Inyathelo 1: Chonga isikali okanye unxantathu obtuse. Qinisekisa ukuba unxantathu akalingani kwaye akakho ekunene, njengoko kukho iifomyula ezithile zaloo meko.

Inyathelo lesi-2: Yazi amaxabiso akhoyo. Ukusebenzisa uMthetho weCosines, kuyimfuneko ukwazi ubuncinane ezintathu kwizinto ezintandathu zonxantathu: amacala kunye neengile ezichasene naloo macala.

4. Imizekelo yeengxaki ezisonjululwe kusetyenziswa uMthetho weCosines

5. Ukubalwa kwamacala angaziwayo kunye nee-engile kunye noMthetho weCosines

Umthetho we-cosines sisixhobo esisisiseko ekubaleni amacala angaziwayo kunye nee-angles kunxantathu. Lo mthetho useka ubudlelwane phakathi kwamacala kanxantathu kunye nee-engile ezichasene nabo. Ukusebenzisa umthetho we-cosines, kuyimfuneko ukuba ube nolwazi malunga ubuncinane nezinto ezintathu zonxantathu: macala amabini kunye ne-angle phakathi kwabo.

Isinyathelo sokuqala ekusebenziseni umthetho we-cosines kukuchonga izinto ezaziwayo nezingaziwayo kunxantathu. Emva koko, ifomula efanelekileyo iya kusetyenziswa ukufumana ixabiso lecala elingaziwayo okanye i-angle. Ifomula ngokubanzi yomthetho we-cosines yile:

c^2 = a^2 + b^2 – 2ab * cos(C)

Apho u-"c" licala elingaziwayo, "a" kunye no "b" ngamagama aziwayo kwaye "C" yi-engile echaseneyo "c". Ukusebenzisa le fomyula, kuyimfuneko ukusombulula ixabiso lecala elingaziwayo okanye i-angle kwaye wenze izibalo eziyimfuneko. Kuyacetyiswa ukuba usebenzise ikhalityhuleyitha yenzululwazi ukuze ufumane iziphumo ezichanekileyo.

6. Iimeko ezikhethekileyo zoMthetho weCosines: unxantathu ochanekileyo kunye ne-isosceles

6. Iimeko ezikhethekileyo zoMthetho weCosines: unxantathu ochanekileyo kunye ne-isosceles

Umthetho weCosines, onxibelelanisa amacala kanxantathu kwii-engile ezichaseneyo, sisixhobo esinamandla ekusombululeni iingxaki zejometri. Nangona kunjalo, kukho iimeko ezikhethekileyo apho lo mthetho unokwenziwa lula kwaye izibalo zenziwe lula. Kweli nqaku, siza kugxininisa kwiimeko ezimbini: unxantathu ochanekileyo kunye nonxantathu we-isosceles.

Triángulo rectángulo

Unxantathu wasekunene ngulowo uneengile enye yangaphakathi Iidigri ezingama-90. Kule meko, uMthetho weCosine uyancitshiswa kwifomula eyaziwayo yePythagoras. Ukufumana umlinganiselo welinye lamacala, kufuneka sisebenzise ifomula:

a² = b² + c²

Apho "a" yihypotenuse (elona cala lide likanxantathu) kunye no "b" kunye no "c" yimilenze (amanye amacala amabini). Le fomula iluncedo kakhulu kwiingxaki ezibandakanya ubude bamacala kanxantathu ochanekileyo, njengoko ilula kakhulu izibalo eziyimfuneko.

Triángulo isósceles

Unxantathu we-isosceles ngunxantathu onamacala amabini anobude obufanayo. Kule meko, uMthetho weCosine wenziwa lula ngakumbi. Ukuba siyabazi ubude bamacala amabini alinganayo (a) kunye ne-engile eyenziwe ngawo (θ), sinokufumana ubude becala eliseleyo (b) sisebenzisa le fomula ilandelayo:

b = 2a * cos(θ / 2)

Le fomyula iluncedo xa sifuna ukumisela ubude belinye lamacala kunxantathu we-isosceles ngaphandle kokusebenzisa ifomula ngokubanzi yoMthetho weCosines. Ikuvumela ukuba wenze izibalo lula kwaye ufumane iziphumo ezichanekileyo ngokufanelekileyo.

7. Isisombululo soqheliselo olusebenzayo usebenzisa uMthetho weCosines

Ukusombulula imithambo kusetyenziswa uMthetho weCosines, kubalulekile ukulandela la manyathelo alandelayo:

1. Hlalutya ingxaki: Funda isiteyitimenti somsebenzi ngononophelo ukuze uqonde ukuba yintoni na ebuzwayo kwaye ucace malunga nedatha enikiweyo.
2. Chonga izakhi: Chonga amacala kunye neeengile zikanxantathu ekuthethwa ngawo uze uwabele ngoonobumba abahambelanayo okanye iisimboli.
3. Sebenzisa ifomyula: UMthetho weCosines umisela ukuba isikwere secala elinye likanxantathu silingana nenani lezikwere zamanye amacala amabini, thabatha imveliso ephindwe kabini yobukhulu bamacala akhankanyiweyo aphindaphindwe yi-cosine ye-engile echaseneyo. . Ukusebenzisa le fomyula, sinokucombulula umthambo ngenyathelo.

Kubalulekile ukukhumbula ukuguqula nayiphi na i-engile ebonakaliswe ngokwezidanga ukuya kwiiradians phambi kokuba wenze izibalo. Iikhaltyhuleyitha zobuNzululwazi okanye izixhobo ze-intanethi nazo zingasetyenziselwa ukuququzelela izibalo eziyimfuneko zetrigonometric.

Umzekelo unikiwe apha ngezantsi ukubonisa inkqubo:

1. Masithi sinonxantathu u-ABC, apho icala u-a lilinganisa iiyunithi ezi-8, icala b lilinganisa iiyunithi ezili-10, kunye ne-engile C kwicala elichaseneyo no-c lilinganisa ama-45°.
2. Sichonga izinto: a = 8, b = 10, kunye ne-angle C = 45 °.
3. Sisebenzisa ifomula: c² = a² + b² – 2ab * cos(C)
4. Sifaka endaweni yamaxabiso aziwayo: c² = 8² + 10² – 2(8)(10) * cos(45°)
5. Sibala i-cos (45 °) = √2 / 2 ≈ 0.707
6. Siqhubeka nefomula: c² ≈ 64 + 100 - 2(8) (10) * 0.707
7. Senza imisebenzi: c² ≈ 64 + 100 - 113 ≈ 51
8. Okokugqibela, simisela ixabiso lika c ngokuthatha ingcambu ye amacala omabini: c ≈ √51 ≈ 7.14 iiyunithi

Ngokulandela la manyathelo kunye nokugcina indlela engqongqo, kunokwenzeka ukusombulula ngempumelelo uqheliselo olusebenzayo usebenzisa uMthetho weCosines.

8. Ukusetyenziswa koMthetho weCosine kuhambo lwaselwandle kunye nenzululwazi ngeenkwenkwezi

Umthetho weCosines sisixhobo esisisiseko esisetyenziswa kuhambo lwaselwandle kunye ne-astronomy ukubala imigama kunye nee-engile koonxantathu abangengawo ekunene.

Kuhambo lwaselwandle, uMthetho weCosines uyasetyenziswa ukumisela umgama kunye nesalathiso phakathi kwamanqaku amabini kwimephu yolwandle. Ukwazi ii-angles kunye nobude bamacala onxantathu owenziwe ngamanqaku okuqala kunye nokugqiba kuvumela oomatiloshe ukuba bacwangcise iindlela ezifanelekileyo kwaye baphephe imiqobo. Ukusebenzisa lo mthetho, kuyimfuneko ukuba ube nolwazi oluchanekileyo malunga nokulungelelaniswa kwendawo yamanqaku kwaye usebenzise iifomyula ezithile ezibandakanya ukusetyenziswa kwe-cosine.

Kwi-astronomy, uMthetho weCosines usetyenziselwa ukubala umgama phakathi kwezinto ezimbini zasesibhakabhakeni, ezinjengeeplanethi okanye iinkwenkwezi. Ukwazi le migama kubalulekile ukumisela indawo yakho kwaye uqikelele intshukumo yakho. Izazi ngeenkwenkwezi zisebenzisa iifomula ezisekelwe kuMthetho weCosines ukubala la maxabiso, ukudibanisa imilinganiselo yee-engile kunye nemigama efunyenwe ngeeteleskopu ezinamandla. Ukufumana iziphumo ezichanekileyo, kubalulekile ukusebenzisa idatha ethembekileyo kwaye usebenzise izibalo ngokuchanekileyo nangendlela.

Isishwankathelo, uMthetho weCosines sisixhobo esixabisekileyo kuhambo lwaselwandle kunye ne-astronomy yokubala imigama kunye nee-engile koonxantathu abangekho ekunene. Ukusetyenziswa kwayo kufuna ulwazi lweefomula ezithile kunye nokusetyenziswa kwedatha echanekileyo. Bobabini oomatiloshe kunye nezazi ngeenkwenkwezi zisebenzisa lo mthetho ukwenza izibalo ezisisiseko kumacandelo abo kwaye bafumane iziphumo ezithembekileyo.

9. Ukusetyenziswa koMthetho weCosine ukumisela imigama kunye nobude

Umthetho weCosines yindlela eluncedo kakhulu yokumisela imigama kunye nokuphakama kwiingxaki zejometri. Lo mthetho usetyenziswa xa ubude bamacala amabini kunye ne-engile phakathi kwawo baziwa, okanye xa kusaziwa ubude bamacala amathathu obunxantathu. Ngezantsi inkcazo yesinyathelo ngesinyathelo sendlela yokusebenzisa lo mthetho ukusombulula ingxaki.

1. Okokuqala, chonga idatha enikezelwe kuwe kunye nedatha eceliwe. Qinisekisa ukuba ubhala yonke into kwiyunithi efanayo yomlinganiselo. Ukuba iiengile zizidanga, ziguqulele kwiiradians.

2. Sebenzisa uMthetho weCosine ukufumana inani elingaziwayo. Ifomula ngokubanzi yoMthetho weCosines yile: c² = a² + b² – 2ab*cos(C). Apho 'c' bubude obungaziwa, 'a' kunye 'b' bubude obaziwayo, kwaye 'C' yi-engile phakathi kwamacala aziwayo. Ukuba uyawazi amacala amathathu kanxantathu, ungasebenzisa ifomula ukufumana i-engile engaziwayo: icos(C) = (a² + b² – c²) / (2ab).

10. Ukusetyenziswa koMthetho weCosine kwiingxaki zangempela zobomi bemihla ngemihla

Kweli candelo, siza kukubonisa ezinye. Umthetho weCosines sisixhobo semathematika esivumela ukuba sibale ubude becala elinye likanxantathu xa siwazi amanye macala amabini kunye ne-engile ejongene nela cala.

1. Umsebenzi 1: Masithi sifuna ukumisela umgama phakathi kwamanqaku amabini emephini. Kuba sinofikelelo kuphela kwimephu enemacala amabini, asinako ukulinganisa umgama kumgca othe ngqo. Endaweni yoko, kufuneka sisebenzise uMthetho weCosines. Ukusombulula le ngxaki, kufuneka kuqala sichonge amacala amabini awaziwayo kunye ne-engile echasene necala elingaziwayo. Emva koko, sisebenzisa uMthetho weCosines formula ukufumana ubude becala elingaziwayo.

2. Umsebenzi wesi-2: Yiba nomfanekiso wakho usenza irempu yokufikelela kwiqonga eliphakamileyo. Uyabazi ubude bethambeka kunye nobude ekufuneka inyukele kubo, kodwa kufuneka umisele i-engile irempu ekufuneka ibe yiyo ukwenza uthambeka olufanelekileyo. Ukusombulula le ngxaki, sinokusebenzisa uMthetho weCosines. Ukwazi ubude bethambeka kunye nokuphakama, sinokufumana i-engile echasene nerempu usebenzisa i-Law of Cosines formula. Oku kuya kusivumela ukuba sakhe irempu enethambeka elichanekileyo.

3. Umsebenzi 3: Kuhambo lokuhamba ngenqanawa, ufuna ukubala umgama phakathi kwamanqaku amabini elwandle. Unokufikelela kwi-GPS ekunika i-latitude kunye ne-longitude yazo zombini amanqaku. Nangona kunjalo, amanqaku awabekwanga kumgca othe ngqo kwaye awukwazi ukulinganisa umgama ngokuthe ngqo kwimephu. Ukusombulula le ngxaki, ungasebenzisa uMthetho weCosines. Ukusebenzisa uMthetho weCosine ifomula, unokubala umgama phakathi kwamanqaku amabini usebenzisa i-latitude kunye ne-longitude.

Ukusetyenziswa koMthetho weCosine kwiingxaki zokwenyani zobomi bemihla ngemihla kusinika isixhobo esinamandla semathematika ukusombulula iimeko ezisebenzayo. Ngokulandela olu qheliselo kunye nendlela echaziweyo, uya kuba nakho ukubala ubude bamacala angaziwayo, ukugqiba ii-engile kwaye uqikelele imigama kwiimeko ezahlukeneyo. Phonononga le mithambo kwaye ufumane izakhono ezintsha kwijometri nakwitrigonometry!

11. Umngeni weengxaki eziphambili ezifuna ukusetyenziswa koMthetho weCosines

Ukusombulula iingxaki eziphambili ezifuna ukusetyenziswa koMthetho weCosines, kubalulekile ukulandela uluhlu lwamanyathelo ukufumana isisombululo esichanekileyo. Nali inyathelo ngenyathelo isikhokelo sokukunceda ukoyisa lo mngeni:

Inyathelo lesi-1: Yiqonde nzulu ingxaki. Funda ingxelo ngononophelo kwaye uqiniseke ukuba uyayiqonda into ebuzwa kuwe kwaye loluphi ulwazi olunikwayo. Chonga ukuba yeyiphi i-engile kunye namacala owaziyo kwaye kufuneka uwafumane.

Inyathelo lesi-2: Sebenzisa uMthetho weCosines. Lo mthetho uthi isikwere secala elinye likanxantathu silingana nenani lezikwere zamanye amacala amabini thabatha kabini imveliso yaloo macala ngokuphinda-phinda i-cosine ye-engile echaseneyo. Sebenzisa le fomula ukuseka i-equation onokuthi uyisombulule ukufumana ixabiso elingaziwayo.

Inyathelo lesi-3: Sombulula inxaki usebenzisa iikhonsepthi zeeengile kunye netrigonometry. Kusenokuba yimfuneko ukusebenzisa iinkcukacha zetrigonometric okanye usebenzise imisebenzi eguqukileyo yetrigonometric ukufumana ixabiso leengile engaziwayo okanye icala. Ukuba kuyimfuneko, sebenzisa ikhalityhuleyitha yenzululwazi ukwenza izibalo.

12. Izinto eziluncedo kunye nezithintelo zokusebenzisa uMthetho weCosine kwizibalo zetrigonometric

13. Ubudlelwane phakathi koMthetho weCosines kunye nezinye iifomyula zejometri yetrigonometric

1. Umthetho weCosine: Umthetho weCosines yifomula esisiseko kwijometri yetrigonometric esivumela ukuba sibale icala okanye i-engile yawo nawuphi na unxantathu. Lo mthetho uthi isikwere selinye icala likanxantathu silingana nenani lezikwere zamanye amacala amabini, thabatha kabini imveliso yala macala umphinda-phinde i-cosine ye-engile echaseneyo necala elithethiweyo.
2. Ubudlelwane kunye neTheorem yePythagorean: Umthetho we-Cosines yi-generalization ye-Pythagorean Theorem, ekubeni xa unxantathu unoxande kwaye enye yee-engile zayo zangaphakathi ilinganisa i-90 degrees, i-cosine yaloo angle iya kulingana no-zero kunye nefomula yoMthetho we-Cosines iyancitshiswa ibe yifomula. yeTheorem yePythagorean.
3. Ejemplos de aplicación: Umthetho weCosines uluncedo kakhulu kwiimeko apho uwazi amaxabiso amacala amabini kanxantathu kunye ne-engile phakathi kwawo, okanye xa uwazi amaxabiso amacala amathathu kwaye ufuna ukubala enye yee-engile. Umzekelo, ukuba sinonxantathu onamacala obude obu-5, 7 kunye neeyunithi ze-9, sinokusebenzisa uMthetho we-Cosines ukubala i-angle echasene nobude besi-7. Ukwenza oku, sisebenzisa ifomyula yoMthetho weCosines. , endaweni yamaxabiso aziwayo kunye nokusombulula i-equation enesiphumo.

14. Izigqibo ngokubaluleka kunye nokuba luncedo koMthetho weCosines kwiinkalo ezahlukeneyo zokufunda nokusebenza.

Isishwankathelo, uMthetho weCosines sisixhobo esisisiseko kwiinkalo ezahlukeneyo zokufunda kunye nokuziqhelanisa, njengetrigonometry, ifiziksi, ubunjineli kunye nokuzoba. Lo mthetho usivumela ukuba sicombulule iingxaki ezibandakanya oonxantathu abangengabo abasekunene, usinika indlela echanekileyo yokubala macala okanye ii-engile ezingaziwayo. Ifomula yayo jikelele, c^2 = a^2 + b^2 – 2ab * cos(C), isinika isiseko esiluqilima sokujongana neemeko ezahlukeneyo zemathematika kunye nejometri.

Ukusebenziseka koMthetho weCosines kukukwazi ukusombulula oonxantathu ngokusekelwe kulwazi olungaphelelanga, oluluncedo ngakumbi kwiimeko apho kungekho macala onke okanye ama-engile awaziwayo. Ngaphezu koko, ngokubonga kulo mthetho, sinokumisela ubukho bonxantathu kunye nokuma kwayo, nakwiimeko apho iTheorem yePythagorean ingenakusetyenziswa. Ke ngoko, isicelo sayo sinabela kwiingxaki zokuhamba, i-geolocation, uyilo lwesakhiwo, ukubala amandla kunye nezinye iindawo ezininzi.

Ukuqukumbela, uMthetho weCosines utyhilwe njengesixhobo esixabisekileyo nesiguquguqukayo kwiinkalo ezahlukeneyo zokufunda nokuziqhelanisa. Ifomula yayo ivumela ukuba sisombulule oonxantathu abangengawo ngokuchanekileyo nangokuchanekileyo, kusinika ukuqonda okunzulu kobudlelwane phakathi kwamacala kunye nee-angles. Ukusetyenziswa koMthetho weCosines kusinceda senze izibalo ezichanekileyo kwaye sihlalutye kwiindawo ezahlukeneyo njengokwakha iimephu, ukugqiba imigama kunye nee-engile kwi-astronomy, kunye nokusombulula iingxaki zejometri kubunjineli. Kubalulekile ukuwenza kakuhle lo mthetho ukuze sikwazi ukujongana ngempumelelo neemeko ezahlukeneyo zemathematika nezejiyometri kumsebenzi wethu wokufunda nowokwenza.

Ukuqukumbela, uMthetho weCosines sisixhobo esisisiseko semathematika kwintsimi ye-trigonometric evumela ukuba oonxantathu abangekho ekunene basonjululwe ngokuchanekileyo nangempumelelo. Ukusetyenziswa kwayo kubalulekile kwiinkalo ezahlukeneyo, ezifana nobunjineli, i-physics kunye nokuhamba.

Ukusebenzisa uMthetho weCosine formula, kunokwenzeka ukubala ubude becala elingaziwayo likanxantathu, kunye nokumisela ii-angles zayo zangaphakathi. Oku kufezekiswa ngokusebenzisa imilinganiselo yamacala aziwayo kunye nee-angles, okwenza kube lula ukuxazulula iingxaki ezinzima kwijometri yendiza.

Ngoluhlu lwemizekelo kunye nokuzivocavoca okusebenzayo, siye sabonisa indlela yokusebenzisa uMthetho weCosines ukusombulula iingxaki zokwenyani. Ukusuka ekumiseleni umgama phakathi kwamanqaku amabini kwinqwelomoya ukuya ekubaleni umkhondo yento Ekuhambeni, esi sixhobo semathematika sinamandla sinika izisombululo ezichanekileyo nezithembekileyo.

Ukuqonda uMthetho weCosines kubalulekile kuye nawuphi na umfundi okanye ingcali efuna ukungena kwihlabathi elinomdla letrigonometry. Ngokufunda le fomyula, ufumana amandla okusombulula iingxaki zejiyometri ezintsonkothileyo, wandise iiprojekthi zobunjineli, kwaye wenze izibalo ezichanekileyo kwiinkalo ezahlukeneyo.

Ngamafutshane, uMthetho weCosines umele intsika esisiseko kwi-trigonometry kwaye unika iingcali ithuba lokusombulula iingxaki zejometri ngendlela engqongqo. Ukusetyenziswa kwayo kunye nokuziqhelanisa rhoqo komeleza izakhono zemathematika kwaye kunika umbono onzulu wehlabathi elisingqongileyo. Ngaphandle kwamathandabuzo, lo mthetho sisixhobo esinamandla sokuqhubela phambili kwenzululwazi nobuchwepheshe kuluntu lwethu lwangoku.