Umthetho wesine usetshenziswa uma sinikezwa noma a) ama-engeli amabili nohlangothi olulodwa, noma b) izinhlangothi ezimbili kanye ne-engeli engafakiwe. Umthetho we-cosine usetshenziswa uma sinikezwa a) izinhlangothi ezintathu noma b) izinhlangothi ezimbili kanye ne-engeli efakiwe.
Ngokufanayo, Uwusebenzisa kanjani umthetho wama-cosine ukuxazulula i-SSS?
Uyini umehluko phakathi komthetho we-sine kanye nomthetho we-cosine? Umthetho wesines usebenzisa izinhlangothi ezimbili kuphela kanye ama-engeli aphambene nawo kuyilapho umthetho we-cosines usebenzisa zonke izinhlangothi ezintathu kanye nohlangothi olulodwa kuphela olubhekene ne-engeli. Umthetho wama-sines usebenzisa isilinganiso se-sine kuyilapho umthetho wama-cosine usebenzisa isilinganiso se-cosine.
Ungakwazi yini ukusebenzisa umthetho wama-sines futhi ungalokothi uzihluphe ngomthetho wama-cosine? Cha, futhi awukwazi ukuxazulula unxantathu usebenzisa kuphela imithetho ye-sines nemithetho yama-cosine.
Okwesibili Ingabe umthetho we-sine ungasetshenziswa kunxantathu ongakwesokudla? ISine Umthetho ungasetshenziswa kunoma yimuphi unxantathu (hhayi nje onxantathu abama-engeli angakwesokudla) lapho kwaziwa khona uhlangothi ne-engeli yalo ephambene. Uzodinga kuphela izingxenye ezimbili zefomula yeSine Rule, hhayi zonke ezintathu. Uzodinga ukwazi okungenani ipheya eyodwa yohlangothi olune-engeli ephambene ukuze usebenzise iSine Rule.
Ingabe uMthetho wamaCosine ungasetshenziswa ukuxazulula noma yimuphi unxantathu owaziwa ngawo ama-engeli amabili nohlangothi?
Okungukuthi, uma kunikezwe ulwazi oluthile mayelana nonxantathu singathola okwengeziwe. Kulokhu ithuluzi liwusizo uma wazi izinhlangothi ezimbili kanye ne-angle yazo efakiwe. Kusukela lapho, ungasebenzisa uMthetho we-Cosines ukuthola i- uhlangothi lwesithathu. Isebenza kunoma yimuphi unxantathu, hhayi nje onxantathu abalungile.
Khona-ke Ungakwazi yini ukucaphuna ukuphila kwangempela kokusebenza komthetho we-cosines? Umthetho we-cosines usetshenziswa emhlabeni wangempela ngabahloli bomhlaba ukuze bathole uhlangothi lukanxantathu olungekho, lapho ezinye izinhlangothi ezimbili zaziwa khona futhi i-engeli ebhekene nohlangothi olungaziwa yaziwa. Umthetho wama-cosines nawo usetshenziswa noma nini lapho kubandakanyeka unxantathu.
Iliphi icala elingeke lixazululwe kusetshenziswa imithetho yeSines? Uma sinikezwa izinhlangothi ezimbili kanye ne-engeli ehlanganisiwe kanxantathu noma uma sinikezwa izinhlangothi ezi-3 zikanxantathu, asikwazi ukusebenzisa i-Law of Sines ngoba asikwazi ukumisa noma yiziphi izilinganiso lapho ulwazi olwanele lwaziwa khona. Kulezi zimo ezimbili kufanele sisebenzise uMthetho kaCosines.
Ingabe i-Law of Sines ingasetshenziswa ukuxazulula unxantathu olungile?
Ngakho-ke, umthetho we-sines usebenza konxantathu abangakwesokudla ivumelekile. Yebo, imithetho iyasebenza nakonxantathu abama-engeli kwesokudla.
Ungayisebenzisa kanjani i-sine nama-cosine ukuxazulula onxantathu oblique? Njengomthetho wama-cosines, ungasebenzisa umthetho wama-cosine ku izindlela ezimbili. Okokuqala, uma wazi ama-engeli amabili kanye nohlangothi olubhekene nelinye lawo, khona-ke ungakwazi ukunquma uhlangothi oluphambene nolunye lwazo. Isibonelo, uma i-engeli A = 30°, i-engeli B = 45°, kanye nohlangothi a = 16, khona-ke umthetho we-sines uthi (isono 30°)/16 = (isono 45°)/b.
Ingabe umthetho wama-cosine ungasetshenziswa konxantathu abangakwesokudla nakonxantathu abangebona abalungile?
Yebo, imithetho iyasebenza nakonxantathu abama-engeli kwesokudla. Kodwa, awathakazelisi kakhulu lapho: Ku-△ABC eno-θ=∠ABC i-engeli elungile, singazama ukusebenzisa umthetho we-cosine mayelana ne-engeli elungile, futhi sithole AC2=AB2+BC2−AB⋅BC⋅cosθ=AB2 +BC2, njengoba i-cos90∘ = 0. Kodwa lokhu akuyona into engaphezu kwethiyori kaPythagoras!
Ungakwazi yini ukusebenzisa umthetho we-cosine konxantathu abama-engeli angakwesokudla? Yebo, Imithetho ye-sine ne-cosine ingasetshenziswa kubo bonke onxantathu kungakhathaliseki ukuthi i-engeli yesokudla noma i-scalene. a/isono A = b/isono B = c/sin C, ayihlukanisi phakathi kwezinhlobo ezahlukene zonxantathu. c^2 = a^2 + b^2 + 2ab cos C, ayihlukanisi phakathi kwezinhlobo ezihlukahlukene zonxantathu.
Ingabe uMthetho wamaCosine ungasetshenziswa konxantathu abangakwesokudla nakonxantathu abangebona abalungile?
Yebo, imithetho iyasebenza nakonxantathu abama-engeli kwesokudla. Kodwa, awathakazelisi kakhulu lapho: Ku-△ABC eno-θ=∠ABC i-engeli elungile, singazama ukusebenzisa umthetho we-cosine mayelana ne-engeli elungile, futhi sithole AC2=AB2+BC2−AB⋅BC⋅cosθ=AB2 +BC2, njengoba i-cos90∘ = 0. Kodwa lokhu akuyona into engaphezu kwethiyori kaPythagoras!
Uwusebenzisa kanjani uMthetho wamaCosine ngohlangothi olulodwa kuphela?
“Isikwele sohlangothi olulodwa lukanxantathu silingana nesamba sezikwele zezinye izinhlangothi ezimbili kukhishwe kabili umkhiqizo wezinye izinhlangothi ezimbili kanye ne-cosine ye-engeli ephakathi kwazo.” Qaphela ukuthi uMthetho we-Cosines usebenza nge-engeli EYODWA kuphela nezinhlangothi ezintathu kufomula ngayinye.
Ucabanga ukuthi kungani uMthetho wamaCosine uwusizo ekuxazululeni izinkinga ngonxantathu oblique? Onxantathu abanjalo babizwa ngonxantathu oblique. Umthetho wamaCosine usetshenziswa kabanzi kakhulu kunoMthetho wamaSines. Ngokuqondile, lapho sazi izinhlangothi ezimbili zikanxantathu kanye ne-engeli yazo ehlanganisiwe, khona-ke uMthetho we I-Cosines isenza sikwazi ukuthola uhlangothi lwesithathu.
Iwusizo kangakanani imithetho ye-sine ne-cosine ekuphileni kwethu kwansuku zonke? Izinhlelo zokusebenza eziningi zomhlaba wangempela zifaka onxantathu abatshekile, lapho Imithetho ye-Sine ne-Cosine ingasetshenziswa ukuthola izilinganiso ezithile. Kubalulekile ukukhomba ukuthi yiliphi ithuluzi elifanele. Itiye I-Cosine Law isetshenziselwa ukuthola uhlangothi, unikezwe i-engeli phakathi kwezinye izinhlangothi ezimbili, noma ukuthola i-engeli enikezwe zontathu izinhlangothi.
Ungayisebenzisa kanjani imiqondo yemithetho ye-Sines nama-cosine ezinhlelweni zempilo yangempela?
Empilweni yangempela, imisebenzi ye-sine ne-cosine ingasetshenziswa endizeni yasemkhathini nasekuxhumaneni kwe-polar, umculo, ama-ballistic trajectories, kanye ne-GPS nomakhalekhukhwini.
Kungani umthetho wama-cosine ubalulekile? Umthetho we-cosines luwusizo ekubaleni ohlangothini lwesithathu lukanxantathu lapho izinhlangothi ezimbili kanye ne-engeli yazo evalekile zaziwa, kanye nasekubaleni ama-engeli kanxantathu uma zonke izinhlangothi zontathu zaziwa.
Ingabe umthetho wama-cosine ungasetshenziswa ukuxazulula noma yimuphi unxantathu owaziwa ngawo ama-engeli amabili nohlangothi?
Okungukuthi, uma kunikezwe ulwazi oluthile mayelana nonxantathu singathola okwengeziwe. Kulokhu ithuluzi liwusizo uma wazi izinhlangothi ezimbili kanye ne-angle yazo efakiwe. Kusukela lapho, ungasebenzisa uMthetho we-Cosines ukuthola i- uhlangothi lwesithathu. Isebenza kunoma yimuphi unxantathu, hhayi nje onxantathu abalungile.
Ingabe uMthetho Wezinyosi ungasetshenziswa konxantathu abalungile nabangalungile? I-Law of Sines ithi kunoma yimuphi unxantathu onikeziwe, isilinganiso sanoma iluphi uhlangothi ubude kuya ku-sine we-engeli ephikisanayo siyefana kuzo zontathu izinhlangothi zikanxantathu. Lokhu kuyiqiniso kunoma yimuphi unxantathu, hhayi nje onxantathu abalungile.
Yiziphi izindlela ezingenzeka zomthetho wama-cosine?
(1) uma isixazululo “singesona Sangempela”, unxantathu akekho (asikho isixazululo). (2) uma ikhambi “lingamavelu amabili Angempela aqondile”, kukhona onxantathu abangaba khona ababili (izixazululo ezi-2). (3) uma ikhambi “liyi-positive eyodwa nenye enegethivu amanani angempela”, kunonxantathu owodwa (1 isixazululo).
Ungakwazi yini ukusebenzisa i-Law of Sines kanye nama-cosine kanxantathu ongakwesokudla? Umthetho Umthetho. I-Trigonometry iqala ngezilinganiso ezilungile zonxantathu, futhi ekugcineni ithola amagugu, uMthetho wamaCosine kanye noMthetho wamaSines. Le mithetho iqale ezilinganisweni zikanxantathu olungile ngakho izosebenzela onxantathu abalungile. Leyo yincazelo ye-sine, ephambene ne-hypotenuse.
Ingabe umthetho wama-cosine ungasetshenziswa kunoma yimuphi unxantathu?
Yebo, Umthetho wamaCosine usebenza kubo bonke onxantathu. Nokho, ubufakazi buncike ekubunjweni kukanxantathu, ngokunembile, ukuthi i-altitude evela kwelinye i-vertex iwela kanjani ngakolunye uhlangothi.