高中数学必修五第一章解三角形知识点总结及练习题

1CabcCRC2sinsinsinabcRC22sinaR2sinbR2sincRCsin2aRsin2bRsin2cCR::sin:sin:sinabcCsinsinsinsinsinsinabcabcCC12ABCabAABaCADBBBCD=bsinA,aabsinABbsinAab,Ba=bsinAabBA3111sinsinsin222CSbcabCac4C2222cosabcbc2222cosbacac2222coscababC5222cos2bcabc222cos2acbac222cos2abcCab(12)DbsinAAbaC6abcCC222abc90Co222abc90Co222abc90Co7AB,3CDACB=75O,BCD=45O,ADC=30O,ADB=45O(ABCD)AB....1ABCa10B=60,C=45,cBA310B1310C13D31025325760xxA52B213C16D43ABC)())((cbbcacaACA090B060C0120D01504ABCDAb=10A=45B=70Ba=60c=48B=100Ca=7b=5A=80Da=14b=16A=455ABCabc132ABC(A)A12B23C132D3126ABC20310A60BCCA5B6C7D85,25CABD7ABC4:5:6sin:sin:sinCBAcosA___________8ABCA=60b=1,3sinsinsinabcABC=9ABCAB=4AC=7BC27ADBC=10ABCABCabc72c60CABC332ab________________24013ABCsin()1CA,sinB=13.IsinA(II)AC=6ABC.1ABC0030,6,90BaCbcA1B1C32D322AABCAAsinBAcosCAtanDAtan13ABC,AB,sincosBAABCABCD43060A2B23C3D325ABCBabsin2AA006030B006045C0060120D001503065,7,8A090B0120C0135D01501RtABC090CBAsinsin_______________2ABCAcbcba,222_________3ABCaCBb,135,30,200_________4ABCsinAsinBsinC7813C_____________1ABC,coscoscosCcBbAaABC2ABC)coscos(aAbBcabba3ABCCBACBAcoscoscossinsinsin1ABC::1:2:3ABC::abcA1:2:3B3:2:1C1:3:2D2:3:12ABCBsinsinBAABCD3ABCBA2aAAbsin2BAbcos2CBbsin2DBbcos24ABC2lgsinlgcoslgsinlgCBAABCABCD5ABC,3))((bcacbcbaA()A090B060C0135D01506ABC1413cos,8,7CbaA51B61C71D811ABC060,1,3,ABCAbSCBAcbasinsinsin=_______2,ABBAtantan_____13ABCCBCBAtantan,coscos2sin_________4ABC,12,10,9cbaABC_________5ABCAcba,226,2,3_________1ABC0120,,21,3ABCAcbaSVcb,2ABC1tantantanCBA3ABC2cos2cos2cos4sinsinsinCBACBA4ABC0120BA1cabcba5ABC223coscos222CAbac2acb1AABCAAcossinA)2,2(B)2,2(C]2,1(D]2,2[2ABC,900CcbaA2cos2BAB2cos2BAC2sin2BAD2sin2BA3ABC8,3,7cbaA12B221C28D364ABC090C00450AAsincosAABsincosBACsincosABDsincosBB5ABC)())((cbbcacaAA090B060C0120D01506ABC22tantanbaBAABCABCD1ABC,sinsinBAAB_________2ABC,1coscoscos222CBAABC______________3ABCC,coscos,sinsin,sinBAzBAyCxzyx,,___________________________4ABCbca2CACACAsinsin31coscoscoscos______5ABC,tanlgtanlgtanlg2CABB_______________6ABCacb2BBCA2coscos)cos(_________1ABC)sin()()sin()(2222BAbaBAba2ABCR,sin)2()sin(sin222BbaCARABC3ABCcba2,2CAbca::abc4ABC()()3abcabcactantan33ACAB43,,ABC,,abc1.C00tan30,tan3023,244,23bbacbcba2.A0,sin0AA3.Ccossin()sin,,22AABAB,,222ABABC4.D5.D012sin,sin2sinsin,sin,302baBBABAA01506.B22200005871cos,60,1806012025821.1211sinsinsincossin222ABAAA2.012022201cos,12022bcaAAbc3.2600sin6215,,4sin4sin154sinsinsin4abbAAaAABB4.0120abcsinAsinBsinC78137,8,13akbkck22201cos,12022abcCCab1.coscoscos,sincossincossincosaAbBcCAABBCCsin2sin2sin2,2sin()cos()2sincosABCABABCCcos()cos(),2coscos0ABABABcos0Acos0B2A2BABC2.acbcaB2cos222bcacbA2cos2222222222222()222acbbcaabcabcabcab22abababba)coscos(aAbBcabba3ABC,2AB022ABsinsin()2ABsincosABsincosBCsincosCACBACBAcoscoscossinsinsin1.C132,,,::sin:sin:sin::1:3:2632222ABCabcABC2.A,ABAB,ABsinsin()sinABB3.Dsinsin22sincos,2cosABBBabB4.Dsinsinlglg2,2,sin2cossincossincossinAAABCBCBCsin()2cossin,sincoscossin0,BCBCBCBCsin()0,BCBC5.B22()()3,()3,abcbcabcbcabc222222013,cos,6022bcabcabcAAbc6.C2222cos9,3cababCcB1cos7B1.33922113sin3,4,13,13222ABCSbcAccaa13239sinsinsinsin332abcaABCA2.,22ABABsin()2tantan()2cos()2BABBcos1sintanBBB1tan,tantan1tanAABB3.2sinsintantancoscosBCBCBCsincoscossinsin()2sin1coscossinsin2BCBCBCABCAA4.Ccos0,CC5.060222843233114cos226222(31)222bcaAbc1.1sin3,4,2ABCSbcAbc2222cos,5abcbcAbccb4,1cb2.ABC,2AB022ABsinsin()2ABsincosABsincosBCsincosCAsinsinsinsinsinsincoscoscos,1coscoscosABCABCABCABC1tantantanCBA3.sinsinsin2sincossin()22ABABABCAB2sincos2sincos2222ABABABAB2sin(coscos)222ABABAB2cos2coscos222CAB4coscoscos222ABC2cos2cos2cos4sinsinsinCBACBA41cabcba2221aacbbcabbcacc222abcab0120,AB060C2222220cos,2cos602abcCabcababab5223coscos222CAbac1cos1cos3sinsinsin222CABACsinsincossinsincos3sinAACCCABsinsinsin()3sinACACBsinsin2sinACB2acb1.Csincos2sin(),4AAA520,sin()144424AAA2.BsinsinsinsinsinabABABcC2sincos2cos222ABABAB3.D011cos,60,sin6322ABCAASbcAV4.D090ABsincos,sincosABBA00045,AsincosAA004590,sincosBBB5.C22222201,,cos,1202acbbcbcabcAA6.B22sincossincossin,,sincossincoscossinsincossinABABAAABBABBABsin2sin2,2222ABABAB1.,sinsinBA22ababABRR2.21(1cos21cos2)cos()1,2ABAB21(cos2cos2)cos()0,2ABAB2cos()cos()cos()0ABABABcoscoscos0ABC3.zyx,,sincos,sincos,22ABABABBAyz,sinsinsin,,cabCABxyxyz41sinsin2sin,2sincos4sincos2222ACACACACACBcos2cos,coscos3sinsin222222ACACACAC221sinsin4sinsin322ACAC1coscoscoscossinsin3ACACAC22(1cos)(1cos)14sinsin22ACAC22222sin2sin4sinsin112222ACAC5.)2,3[2tantantantantan,tantan()tantan1ACBACBACAC2tantantantan()tan1ACBACB3tantantantan2tantan2tanBBACACB3tan3tan,tan0tan33BBBBB6122,sinsinsin,bacBACBBCA2coscos)cos(2coscossinsincos12sinACACBBcoscossinsincos12sinsinACACBACcoscossinsincos1ACACBcos()cos11ACB1.22222222sin()sincossin,sin()cossinsinabABaABAabABbABBcossin,sin2sin2,222cossinBAABABABAB22.2sinsin2sinsin(2)sin,RAARCCabB222sinsin(2)sin,2,aAcCabBacabb222222022,cos,4522abcabcabCCab2222,2sin2,22,sincRcRCRabRabC22222222,22RRabababab21222sin,24422RSabCab2max212RS122sin2sin2sin244SabCabRARB222sin2sin2sinsin4RARBRAB212[cos()cos()]2RABAB22122[cos()]2222(1)22RABR2max212SR