三角函数、导数、微分、积分

三角公式汇总任意角的三角函数在角的终边上任取．．一点),(yxP，记：22yxr，正弦：rysin余弦：rxcos正切：xytan余切：yxcot正割：xrsec余割：yrcsc诱导公式tgA=tanA=aacossinaasin)sin(sin(2-a)=cosasin(2+a)=cosasin(π-a)=sinasin(π+a)=-sinacos(-a)=cosacos(2-a)=sinacos(2+a)=-sinacos(π-a)=-cosacos(π+a)=-cosa两角和差公式sin(A+B)=sinAcosB+cosAsinBcos(A+B)=cosAcosB-sinAsinBsin(A-B)=sinAcosB-cosAsinBcos(A-B)=cosAcosB+sinAsinBtan(A+B)=tanAtanB-1tanBtanAcot(A+B)=cotAcotB1-cotAcotBtan(A-B)=tanAtanB1tanBtanAcot(A-B)=cotAcotB1cotAcotB倍角公式三倍角公式半角公式tan2A=Atan12tanA2sin3A=3sinA-4(sinA)3sin(2A)=2cos1ASin2A=2SinA•CosAcos3A=4(cosA)3-3cosAcos(2A)=2cos1ACos2A=Cos2A-Sin2A=2Cos2A-1=1-2sin2Atan3a=tana·tan(3+a)·tan(3-a)tan(2A)=AAcos1cos1cot(2A)=AAcos1cos1tan(2A)=AAsincos1=AAcos1sin和差化积积化和差sina+sinb=2sin2bacos2basinasinb=-21[cos(a+b)-cos(a-b)]sina-sinb=2cos2basin2bacosacosb=21[cos(a+b)+cos(a-b)]cosa+cosb=2cos2bacos2basinacosb=21[sin(a+b)+sin(a-b)]cosa-cosb=-2sin2basin2bacosasinb=21[sin(a+b)-sin(a-b)]tana+tanb=babacoscos)sin(万能公式sina=2)2(tan12tan2aacosa=22)2(tan1)2(tan1aatana=2)2(tan12tan2aa其他非重点三角函数csc(a)=asin1aa22csc1cotsec(a)=acos1aaa222cos1sec1tan双曲函数sinh(a)=2e-e-aacosh(a)=2ee-aatgh(a)=)cosh()sinh(aa辅助角公式)sin(cossin22xbaxbxa（）其中：角的终边所在的象限与点),(ba所在的象限相同，22sinbab，22cosbaa，abtan。正弦定理RCcBbAa2sinsinsin（R为ABC外接圆半径）余弦定理Abccbacos2222Baccabcos2222Cabbaccos2222三角形的面积公式高底21ABCSBcaAbcCabSABCsin21sin21sin21（两边一夹角）RabcSABC4（R为ABC外接圆半径）rcbaSABC2（r为ABC内切圆半径）))()((cpbpappSABC…海仑公式（其中2cbap）等价无穷小xx~sinxxxarctan~~arcsinxx~)1ln(xex~1xx~tan2~cos12xxuxxu~1)1(nxxn~11axaxln~1两个重要的极限1sinlim0xxxexxx)11(lim导数、微分、积分函数的和差积商求导法则函数的和差积商微分法则函数的和差积商求导法则'''vuvudvduvud)()1(11ucuxdxxuu''CuCuCduCud)(dxxfkdxxkf'''uvvuuvudvvduuvd)(dxxgdxxfdxxgxf2'''vuvvuvu2)(vudvvduvudxuduufdxxxf'xy)2,2(Ao0yxcossincossincossinxy)2,2(Ao0yx0cossin0cossin0cossin高阶导数函数)(xfy的导数)(''xfy称为一阶导数，记作'y或dxdy；把)(''xfy的导数称为二阶导数，记作''yy或22dxyd＝dxdydxd；类似的，二阶导数的导数称为三阶导数；三阶导数的导数称为四阶导数；（n－1）导数的导数叫做n阶导数记作nndxyd导数公式微分公式积分公式0'Cdxxfdy)('Ckxkdx1')(uuuxxdxuxxduu1)(Cuxdxxuu112'1)1(xxdxd()Cxdxxln1xxcos)(sin'xdxxdcos)(sinCxxdxsincosxxsin)(cos'xdxxdsin)(cosCxxdxcossinxx2'sec)(tanxdxxd2sec)(tanCxxdxdxxtanseccos122Cxxdxcoslntanxx2'csc)(cotxdxxd2csc)(cotCxxdxdxxcotcscsin122Cxxdxsinlncotxxxtansec)(sec'xdxxxdtansec)(secCxxxdxtanseclnsecCxxdxxsectansecxxxcotcsc)(csc'xdxxxdcotcsc)(cscCxxxdxcotcsclncscCxxdxxcsccotcscaaaxxln)('adxaadxxln)(Caadxaxxlnxxee')(dxeedxx)(Cedxexxaxxaln1)(log'dxaxxdaln1)(logCdxxx1)(ln'dxxxd1)(lnCxdxxln12'11)(arcsinxxdxxxd211)(arcsinCxdxxarcsin1122'11)(arccosxxdxxxd211)(arccosCdx2'11)(arctanxxdxxxd211)(arctanCxdxxarctan1122'11)cot(xxarcdxxarcd211cot)(Cdxchxshx')(Cchxshxdxshxchx')(Cshxchxdxxchthx2'1)(Caxadxxaarctan11222'11)(xarshxCaxaxadxaxln2112211)(2'xarchxCaxdxxaarcsin1222'11)(xarthxCaxxdxax)ln(12222Caxxdxax2222ln1