Txoj cai sine yog siv thaum peb muab ib qho a) ob lub kaum sab xis thiab ib sab, los yog b) ob sab thiab lub kaum sab xis tsis suav nrog. Txoj cai cosine yog siv thaum peb muab ob qho a) peb sab lossis b) ob sab thiab lub kaum sab xis.
Ib yam li ntawd, koj siv txoj cai lij choj ntawm cosines los daws SSS li cas?
Qhov txawv ntawm txoj cai ntawm sine thiab txoj cai ntawm cosine yog dab tsi? Txoj cai ntawm sines tsuas siv ob sab thiab cov ces kaum yog opposite lawv thaum txoj cai ntawm cosines siv tag nrho peb sab thiab tsuas yog ib sab ntawm lub kaum sab xis. Txoj cai ntawm sine siv qhov sib piv sine thaum txoj cai ntawm cosine siv cov cosine piv.
Koj puas tuaj yeem siv txoj cai ntawm kev txhaum thiab tsis txhob cuam tshuam nrog txoj cai ntawm cosines? Tsis yog, thiab koj tsis tuaj yeem daws ib daim duab peb sab siv tsuas yog cov cai ntawm sines thiab cov cai ntawm cosines.
Thib ob Puas siv txoj cai sine ntawm daim duab peb sab? Lub Sine Txoj cai siv tau rau hauv txhua daim duab peb sab (tsis yog lub kaum sab xis xwb) qhov twg ib sab thiab nws lub kaum sab xis yog paub. Koj tsuas yog xav tau ob feem ntawm Sine Rule formula, tsis yog tag nrho peb. Koj yuav tsum paub tsawg kawg yog ib khub ntawm ib sab nrog nws lub kaum sab xis los siv Sine Rule.
Txoj cai lij choj ntawm Cosines puas tuaj yeem siv los daws cov duab peb sab uas ob lub kaum sab xis thiab ib sab paub?
Qhov ntawd yog, muab qee cov ntaub ntawv hais txog daim duab peb sab peb tuaj yeem nrhiav tau ntxiv. Hauv qhov no, cov cuab yeej siv tau zoo thaum koj paub ob sab thiab lawv lub kaum sab xis. Los ntawm qhov ntawd, koj tuaj yeem siv Txoj Cai ntawm Cosines los nrhiav qhov peb sab. Nws ua haujlwm ntawm txhua daim duab peb sab, tsis yog daim duab peb sab txoj cai xwb.
Tom qab ntawd koj puas tuaj yeem hais lub neej tiag tiag ntawm kev cai lij choj ntawm cosines? Txoj cai ntawm cosine yog siv nyob rau hauv lub ntiaj teb tiag los ntawm cov neeg tshawb nrhiav kom pom qhov ploj ntawm ib daim duab peb sab, qhov twg lwm ob sab paub thiab lub kaum sab xis ntawm sab tsis paub yog paub. Txoj cai ntawm cosines kuj tseem siv thaum twg ib daim duab peb sab koom nrog.
Cov ntaub ntawv twg Tsis tuaj yeem daws tau siv cov cai ntawm Sines? Yog tias peb muab ob sab thiab ib lub kaum sab xis ntawm daim duab peb sab lossis yog tias peb muab 3 sab ntawm daim duab peb sab, peb tsis tuaj yeem siv Txoj Cai ntawm Sines vim tias peb tsis tuaj yeem teeb tsa ib qho kev faib ua feem uas paub txog cov ntaub ntawv txaus. Hauv ob qhov xwm txheej no peb yuav tsum siv Txoj Cai ntawm Cosines.
Txoj Cai ntawm Sines puas tuaj yeem siv los daws cov duab peb sab?
Yog li ntawd, txoj cai ntawm sines siv rau txoj cai triangles yog siv tau. Yog lawm, cov kev cai lij choj siv rau txoj cai-angled daim duab peb sab thiab.
Koj tuaj yeem siv sine thiab cosines los daws oblique daim duab peb sab? Zoo li txoj cai ntawm cosines, koj tuaj yeem siv txoj cai ntawm cosines hauv ob txoj kev. Ua ntej, yog tias koj paub ob lub kaum sab xis thiab sab nraud ntawm ib qho ntawm lawv, koj tuaj yeem txiav txim siab sab nraud ntawm lwm tus ntawm lawv. Piv txwv li, yog lub kaum sab xis A = 30 °, lub kaum sab xis B = 45 °, thiab sab a = 16, ces txoj cai ntawm kev txhaum hais tias (kev txhaum 30 °) / 16 = (kev txhaum 45 °) / b.
Txoj cai lij choj ntawm cosines puas tuaj yeem siv rau txoj cai peb tog thiab tsis yog daim duab peb sab?
Yog lawm, cov kev cai lij choj siv rau txoj cai-angled daim duab peb sab thiab. Tab sis, lawv tsis nthuav tshwj xeeb rau qhov ntawd: Rau △ABC nrog θ = ∠ABC lub kaum sab xis, peb tuaj yeem sim siv txoj cai cosine txog lub kaum sab xis, thiab tau AC2 = AB2 + BC2 AB⋅BC⋅cosθ = AB2 +BC2, as cos90∘ = 0. Tab sis qhov no tsis muaj dab tsi ntau tshaj li Pythagoras' theorem!
Koj puas tuaj yeem siv txoj cai cosine ntawm cov duab peb sab txoj cai? Yog lawm, sine thiab cosine txoj cai siv tau rau txhua daim duab peb sab txawm yog txoj cai kaum los yog scalene. a/sin A = b/sin B = c/sin C, tsis txawv ntawm ntau hom duab peb sab. c^2 = a^2 + b^2 + 2ab cos C, tsis txawv ntawm ntau hom duab peb sab.
Txoj cai lij choj ntawm Cosines puas tuaj yeem siv rau txoj cai peb tog thiab tsis yog daim duab peb sab?
Yog lawm, cov kev cai lij choj siv rau txoj cai-angled daim duab peb sab thiab. Tab sis, lawv tsis nthuav tshwj xeeb rau qhov ntawd: Rau △ABC nrog θ = ∠ABC lub kaum sab xis, peb tuaj yeem sim siv txoj cai cosine txog lub kaum sab xis, thiab tau AC2 = AB2 + BC2 AB⋅BC⋅cosθ = AB2 +BC2, as cos90∘ = 0. Tab sis qhov no tsis muaj dab tsi ntau tshaj li Pythagoras' theorem!
Koj siv txoj cai lij choj ntawm Cosines li cas nrog ib sab?
"Lub xwmfab ntawm ib sab ntawm daim duab peb sab yog sib npaug rau cov lej ntawm cov squares ntawm ob sab rho tawm ob zaug ntawm cov khoom ntawm ob sab thiab cov cosine ntawm lub kaum sab xis ntawm lawv." Daim ntawv ceeb toom tias Txoj Cai ntawm Cosines ua haujlwm nrog tsuas yog ib lub kaum sab xis thiab peb sab hauv txhua tus qauv.
Vim li cas koj xav tias Txoj Cai ntawm Cosines muaj txiaj ntsig hauv kev daws teeb meem nrog oblique daim duab peb sab? Cov duab peb sab no hu ua oblique triangles. Txoj Cai ntawm Cosines tau siv ntau dua li Txoj Cai ntawm Sines. Tshwj xeeb, thaum peb paub ob sab ntawm daim duab peb sab thiab lawv lub kaum sab xis, ces Txoj Cai ntawm Cosines pab kom peb nrhiav tau sab thib peb.
Cov kev cai ntawm sine thiab cosine muaj txiaj ntsig zoo li cas hauv peb lub neej niaj hnub? Ntau daim ntawv thov hauv ntiaj teb no suav nrog oblique daim duab peb sab, qhov twg Sine thiab Cosine Laws tuaj yeem siv los nrhiav qee qhov kev ntsuas. Nws yog ib qho tseem ceeb kom paub tias lub cuab yeej twg tsim nyog. Tshuaj yej Cosine Law yog siv los nrhiav ib sab, muab lub kaum sab xis ntawm ob sab, lossis nrhiav lub kaum sab xis muab tag nrho peb sab.
Koj tuaj yeem siv cov ntsiab lus ntawm cov cai ntawm Sines thiab cosines hauv kev siv lub neej tiag tiag?
Hauv lub neej tiag tiag, sine thiab cosine tuaj yeem siv tau nyob rau hauv qhov chaw ya davhlau thiab polar coordinates, suab paj nruag, ballistic trajectories, thiab GPS thiab xov tooj ntawm tes.
Vim li cas txoj cai ntawm cosines tseem ceeb? Txoj cai ntawm cosines yog pab tau rau kev xam qhov thib peb ntawm daim duab peb sab thaum ob sab thiab lawv lub kaum sab xis paub, thiab hauv kev suav cov kaum ntawm daim duab peb sab yog tias tag nrho peb sab paub.
Txoj cai ntawm cosines puas tuaj yeem siv los daws cov duab peb sab uas ob lub kaum sab xis thiab ib sab paub?
Qhov ntawd yog, muab qee cov ntaub ntawv hais txog daim duab peb sab peb tuaj yeem nrhiav tau ntxiv. Hauv qhov no, cov cuab yeej siv tau zoo thaum koj paub ob sab thiab lawv lub kaum sab xis. Los ntawm qhov ntawd, koj tuaj yeem siv Txoj Cai ntawm Cosines los nrhiav qhov peb sab. Nws ua haujlwm ntawm txhua daim duab peb sab, tsis yog daim duab peb sab txoj cai xwb.
Txoj Cai ntawm Sines puas tuaj yeem siv rau txoj cai thiab tsis yog daim duab peb sab? Txoj Cai ntawm Sines hais tias nyob rau hauv ib daim duab peb sab, qhov piv ntawm ib sab ntev rau lub sine ntawm nws lub kaum sab xis yog tib yam rau tag nrho peb sab ntawm daim duab peb sab. Qhov no muaj tseeb rau txhua daim duab peb sab, tsis yog txoj cai triangles xwb.
Dab tsi yog cov txheej txheem ua tau rau txoj cai ntawm cosines?
(1) Yog tias qhov kev daws teeb meem yog "tsis muaj tiag", daim duab peb sab tsis muaj (tsis muaj kev daws teeb meem). (2) yog tias qhov kev daws teeb meem yog "ob qhov txiaj ntsig zoo", muaj ob txoj kev ua tau zoo (2 qhov kev daws teeb meem). (3) yog tias kev daws yog "ib qho zoo thiab qhov tsis zoo tiag tiag", muaj ib daim duab peb sab (1 daws).
Koj puas tuaj yeem siv Txoj Cai ntawm Sines thiab cosines ntawm daim duab peb sab? Txoj Cai yog Txoj Cai. Trigonometry pib nrog txoj cai daim duab peb sab sib piv, thiab nws thiaj li muab tau cov jewels, Txoj Cai ntawm Cosines thiab Txoj Cai ntawm Sines. Cov kev cai lij choj no pib los ntawm qhov sib piv ntawm txoj cai daim duab peb sab kom lawv mus ua haujlwm rau txoj cai daim duab peb sab. Qhov ntawd yog lub ntsiab lus ntawm sine, opposite dua hypotenuse.
Kev cai lij choj ntawm cosines puas siv tau rau ntawm ib daim duab peb sab?
Yog, Txoj Cai ntawm Cosines ua haujlwm rau txhua daim duab peb sab. Txawm li cas los xij, cov pov thawj nyob ntawm daim duab peb sab, ntau qhov tseeb, qhov siab ntawm qee qhov vertex poob mus rau sab nraud.