Umthetho wesine usetyenziswa xa sinikwa nokuba a) ii-engile ezimbini kunye necala elinye, okanye b) amacala amabini kunye ne-engile engabandakanywanga. Umgaqo we-cosine usetyenziswa xa sinikwa nokuba a) amacala amathathu okanye b) amacala amabini kunye ne-engile efakiweyo.
Ngokufanayo, Uwusebenzisa njani umthetho we-cosines ukusombulula i-SSS?
Yintoni umahluko phakathi komthetho wesine kunye nomthetho we-cosine? Umthetho wezono usebenzisa kuphela amacala amabini kunye iiengile zijongene nazo ngelixa umthetho we-cosines usebenzisa amacala amathathu kunye nelinye icala elijongene ne-engile. Umthetho wesines usebenzisa i-sine ratio ngelixa umthetho we-cosines usebenzisa i-cosine ratio.
Ngaba ungasoloko usebenzisa umthetho wesines kwaye ungaze uzikhathaze ngomthetho we-cosines? Hayi, kwaye awukwazi ukusombulula unxantathu usebenzisa kuphela imithetho ye-sines kunye nemithetho ye-cosines.
Okwesibini Ingaba umthetho wesine ungasetyenziswa kunxantathu wasekunene? USine Umgaqo ungasetyenziswa kuwo nawuphi na unxantathu (hayi nje oonxantathu aba-engile ekunene) apho icala ne-engile yalo echaseneyo zaziwa khona. Uya kufuna kuphela iinxalenye ezimbini zeSine Rule formula, hayi zontathu. Kuya kufuneka wazi iperi enye yecala elineengile echaseneyo ukuze usebenzise iSine Rule.
Ngaba uMthetho weCosines unokusetyenziselwa ukusombulula nawuphi na unxantathu owaziwa ngawo iiengile ezimbini kunye necala?
Oko kukuthi, sinikwe ulwazi malunga nonxantathu sinokufumana ngakumbi. Kule meko isixhobo siluncedo xa usazi amacala amabini kunye ne-angle yawo efakiweyo. Ukusuka apho, ungasebenzisa uMthetho weCosine ukufumana i icala lesithathu. Isebenza nakuwuphi na unxantathu, hayi nje oonxantathu abalungileyo.
emva koko Ngaba unokucaphula ukusetyenziswa kobomi bokwenyani komthetho we-cosines? Umthetho we-cosines usetyenziswa kwihlabathi lenene ngabahloli bomhlaba ukuze bafumane icala likanxantathu elingekhoyo, apho amanye amacala amabini aziwa khona kwaye i-engile echasene necala elingaziwayo liyaziwa. Umthetho we-cosines uyasetyenziswa nanini na xa kukho unxantathu.
Leliphi ityala elingenakusonjululwa kusetyenziswa imithetho yeSines? Ukuba sinikwe amacala amabini kunye ne-engile equkiweyo kanxantathu okanye ukuba sinikwe amacala ama-3 kanxantathu, asikwazi ukusebenzisa uMthetho weSines kuba asikwazi ukumisa nayiphi na imilinganiselo apho ulwazi olwaneleyo luyaziwa. Kule meko mibini kufuneka sisebenzise uMthetho weCosines.
Ngaba uMthetho weSines ungasetyenziselwa ukusombulula unxantathu ochanekileyo?
Ngoko ke, umthetho wesines usebenza koonxantathu abafanelekileyo iyasebenza. Ewe, imithetho isebenza koonxantathu abaneengile ekunene ngokunjalo.
Ungayisebenzisa njani i-sine kunye ne-cosines ukusombulula oonxantathu oblique? Njengomthetho we-cosines, ungasebenzisa umthetho we-cosines kwi iindlela ezimbini. Okokuqala, ukuba uyazazi ii-engile ezimbini kunye necala elijongene nelinye lazo, ngoko unokumisela icala elijongene nelinye lazo. Umzekelo, ukuba i-engile A = 30 °, i-engile B = 45 °, kunye necala a = 16, ngoko umthetho we-sines uthi (isono 30 °)/16 = (isono 45 °)/b.
Ngaba umthetho we-cosines unokusetyenziswa koonxantathu abafanelekileyo kwaye kungekhona koonxantathu abafanelekileyo?
Ewe, imithetho isebenza koonxantathu abaneengile ekunene ngokunjalo. Kodwa, azinamdla kakhulu apho: Ku-△ABC ene-θ=∠ABC i-engile echanekileyo, singazama ukusebenzisa umthetho we-cosine malunga ne-engile elungileyo, kwaye sifumane AC2=AB2+BC2−AB⋅BC⋅cosθ=AB2 +BC2, njenge cos90∘ = 0. Kodwa le asiyonto engaphezu kwethiyori kaPythagoras!
Ngaba ungasebenzisa umthetho we-cosine koonxantathu abasekunene? Ewe, sine kunye nemithetho ye-cosine ingasetyenziselwa bonke oonxantathu nokuba i-engile yasekunene okanye isikali. a/isono A = b/isono B = c/sono C, ayahluli phakathi kweentlobo ngeentlobo zoonxantathu. c^2 = a^2 + b^2 + 2ab cos C, ayahluli phakathi kweentlobo ngeentlobo zoonxantathu.
Ngaba uMthetho weCosine unokusetyenziswa koonxantathu abasekunene hayi koonxantathu abalungileyo?
Ewe, imithetho isebenza koonxantathu abaneengile ekunene ngokunjalo. Kodwa, azinamdla kakhulu apho: Ku-△ABC ene-θ=∠ABC i-engile echanekileyo, singazama ukusebenzisa umthetho we-cosine malunga ne-engile elungileyo, kwaye sifumane AC2=AB2+BC2−AB⋅BC⋅cosθ=AB2 +BC2, njenge cos90∘ = 0. Kodwa le asiyonto engaphezu kwethiyori kaPythagoras!
Uwusebenzisa njani uMthetho weCosines ngecala elinye kuphela?
"Isikwere selinye icala likanxantathu silingana nenani lezikwere zamanye amacala amabini thabatha kabini imveliso yamanye amacala amabini kunye ne-cosine ye-engile ephakathi kwawo." Qaphela ukuba uMthetho weCosines usebenza nge-engile enye kuphela kunye namacala amathathu kwifomula nganye.
Kutheni ucinga ukuba uMthetho weCosines uluncedo ekusombululeni iingxaki ngonxantathu oblique? Oonxantathu abanjalo babizwa ngokuba ngoonxantathu oblique. Umthetho weCosines usetyenziswa ngokubanzi ngakumbi kunoMthetho weSines. Ngokukodwa, xa sisazi amacala amabini kanxantathu kunye ne-angle yabo efakiwe, ngoko ke uMthetho we I-Cosines isenza sikwazi ukufumana icala lesithathu.
Iluncedo kangakanani imithetho ye-sine kunye ne-cosine kubomi bethu bemihla ngemihla? Izicelo ezininzi zehlabathi lokwenene zibandakanya oonxantathu oblique, apho iSine kunye neCosine Laws ingasetyenziselwa ukufumana imilinganiselo ethile. Kubalulekile ukuchonga ukuba sesiphi isixhobo esifanelekileyo. Iti Umthetho weCosine usetyenziselwa ukufumana icala, kunikwe i-engile phakathi kwamanye amacala amabini, okanye ukufumana i-engile enikwe onke macala.
Ungazisebenzisa njani iikhonsepthi zemithetho yeSines kunye ne-cosines kwizicelo zobomi bokwenyani?
Kubomi bokwenyani, imisebenzi ye-sine kunye ne-cosine ingasetyenziswa kwinqwelomoya yasemkhathini kunye nolungelelwaniso lwepolar, umculo, iitrajethi zebhola, kunye neGPS kunye neeselfowuni.
Kutheni le nto umthetho we-cosines ubalulekile? Umthetho we-cosines ngu luncedo ekubaleni icala lesithathu likanxantathu xa amacala amabini kunye ne-engile yawo evaliweyo esaziwa, nasekubaleni iiengile zikanxantathu ukuba amacala omathathu ayaziwa.
Ngaba umthetho wee-cosines unokusetyenziselwa ukusombulula nawuphi na unxantathu owaziwa ngawo iiengile ezimbini necala?
Oko kukuthi, sinikwe ulwazi malunga nonxantathu sinokufumana ngakumbi. Kule meko isixhobo siluncedo xa usazi amacala amabini kunye ne-angle yawo efakiweyo. Ukusuka apho, ungasebenzisa uMthetho weCosine ukufumana i icala lesithathu. Isebenza nakuwuphi na unxantathu, hayi nje oonxantathu abalungileyo.
Ngaba uMthetho weSines ungasetyenziswa koonxantathu abalungileyo kwaye hayi abalungileyo? Umthetho weSines uthi kuwo nawuphi na unxantathu onikiweyo, umlinganiselo walo naliphi na icala ubude ukuya kwisine ye-engile echaseneyo uyafana kuwo onke amacala amathathu kanxantathu. Oku kuyinyaniso kuwo nawuphi na unxantathu, hayi nje oonxantathu abalungileyo.
Zeziphi iindlela ezinokubakho kumthetho we-cosines?
(1) ukuba isisombululo "asiyinyani", unxantathu akakho (akukho sisombululo). (2) ukuba isisombululo "zimbini zokwenyani ezichanekileyo", kukho oonxantathu abanokubakho (2 izisombululo). (3) ukuba isisombululo "sinye esilungileyo kunye nesinye esingalunganga Amaxabiso angempela", kukho unxantathu omnye (1 isisombululo).
Ngaba unokusebenzisa uMthetho weSine kunye neecosine zikanxantathu wasekunene? Umthetho ngumthetho. I-Trigonometry iqala ngokulinganisa unxantathu ochanekileyo, kwaye ekugqibeleni ifumana amatye anqabileyo, uMthetho weCosines kunye noMthetho weSines. Le mithetho iqale kumlinganiselo kanxantathu ochanekileyo ukuze isebenze koonxantathu abalungileyo. Leyo yinkcazelo kasine, ngokuchaseneyo ne-hypotenuse.
Ngaba umthetho we-cosines unokusetyenziswa nakuwuphi na unxantathu?
Ewe, Umthetho weCosine usebenza kubo bonke oonxantathu. Nangona kunjalo, ubungqina buxhomekeke kwimilo kanxantathu, ngokuchanekileyo ngakumbi, ukuba umphakamo ovela kwelinye i-vertex uwela njani kwelinye icala.