高考文科三角函數(shù)知識(shí)點(diǎn)總結(jié)高中數(shù)學(xué)三角函數(shù)知識(shí)點(diǎn)總結(jié)一(知識(shí)點(diǎn)00360,2,,180,,,1(角度制與弧度制的互化:180,rad,??57.30?=57?18ˊ(1?,?0.01745(rad)1,000369182736,0,,,,,3,5,3,22,643234622.特殊角的三角函數(shù)值:12300000=sin30sin=0=1sin900sin=sin6=45022212300000=cos60cos=1cos9=000cos3=cos=0452223000003tan=0tan3=tan=1tan6=tan9無(wú)意義00450033.弧長(zhǎng)及扇形面積公式1弧長(zhǎng)公式:扇形面積公式:S=l,,.rl.r2----是圓心角且為弧度制。r-----是扇形半徑,4.任意角的三角函數(shù)22x，y設(shè)是一個(gè)任意角，它的終邊上一點(diǎn)p(x,y),r=,yxy(1)正弦sin=余弦cos=正切tan=,,,rrx(2)各象限的符號(hào):(一全二正弦，三切四余弦)yyy+—++—++Oxx,,,cossin,,,,,,2,,OO-+———++—sin,cos,tan,5、三角函數(shù)線yT正弦線:MP;余弦線:OM;正切線:AT.PAxOM16.幾個(gè)重要結(jié)論:yy(2)(1)|sinx|>|cosx|sinx>cosx|cosx|>|sinx||cosx|>|sinx|OOxxcosx>sinx|sinx|>|cosx|,(3)若o<x<,則sinx<x<tanx26(同角三角函數(shù)的基本關(guān)系:22(1)平方關(guān)系:sin+cos=1。,,,,sin(2)商數(shù)關(guān)系:=tan(),,,，k,,k,zcos,222,(3)(其中輔助角與點(diǎn)(a,b)在同一asin,，bcos,,a，bsin(,，,)b象限，且)tg,,a7.誘導(dǎo)公式:函數(shù)名不變，符號(hào)看象限，，(1sin2sink,,,，,cos2cosk,,,，,tan2tankk,,,，,,,，，，，，，，，，，，，(2sinsin,,,，,,coscos,,,，,,tantan,,,，,，，，，，，，，，，(3sinsin,,,,,coscos,,,,tantan,,,,,，，，，，，，，，，(4sinsin,,,,,coscos,,,,,,tantan,,,,,,，，，，，，，，函數(shù)名改變，符號(hào)看象限,,,,,,5sincoscossin,,,,，(,,,,，，,,,,22,,,,,,,,,,6sincoscossin，,，,,，(,,,,，，,,,,22,,,,8(正弦函數(shù)、余弦函數(shù)和正切函數(shù)的圖象與性質(zhì)9(函數(shù)y=Asin(,,x，,)，k的圖象及性質(zhì):(),,0,A,0,21,振幅A，周期T=,頻率f=,相位，初相,,x，,,T,,3，，10(五點(diǎn)作圖法:令依次為求出x與y，依點(diǎn)作圖x,y0,,,,2,,x，,2211(三角函數(shù)的伸縮變化先平移后伸縮向左(>0),,或向右(0),,,,,,,,,的圖象yx,sin平移個(gè)單位長(zhǎng)度,橫坐標(biāo)伸長(zhǎng)(0<<1),,或縮短(>1),,,,,,,,,,的圖象得yx,，sin(),1到原來(lái)的縱坐標(biāo)不變(),AA,縱坐標(biāo)伸長(zhǎng)(1)或縮短(0<<1),,,,,,,,,,得的圖象yx,，sin(),,A()為原來(lái)的倍橫坐標(biāo)不變向上或向下(0)(0)kk,,,,,,,,,,得的圖象yAx,，sin(),,平移個(gè)單位長(zhǎng)度k得的圖象(yAxk,，，sin(),先伸縮后平移縱坐標(biāo)伸長(zhǎng)或縮短(1)(01)AA,,,,,,,,,,,,,的圖象yx,sin為原來(lái)的倍A(橫坐標(biāo)不變)橫坐標(biāo)伸長(zhǎng)或縮短(01)(1),,,,,,,,,,,,,,,得的圖象yAx,sin1到原來(lái)的縱坐標(biāo)不變(),向左或向右(0)(0),,,,,,,,,,,,,得的圖象yAx,sin(),平移個(gè)單位,向上或向下(0)(0)kk,,,,,,,,,,得的圖象得的圖象(yAxx,，sin(),,yAxk,，，sin(),,平移個(gè)單位長(zhǎng)度k12(三角函數(shù)和差角公式,兩角和與差的三角函數(shù)關(guān)系倍角公式,,sin(,)=sin?cos,cos?sin,,,,sin2=2sin?cos,,,,,cos(,)=cos?cos,sin?sin,,,,22cos2=cos,sin,,,,,tan,tan2,,tan(,),，=2cos,1,1,tan,,tan,2=1,2sin，,tg,,tg,,tg(,,,)(1,tg,,tg,),2tan,tan2,21,tan,降冪公式:升冪公式:1cos2,，,221+cos=cos,,2cos,221cos2,,,221-cos=sin,,2sin,22,,,,21sin(cossin)cossin,,,,,,2222abc正弦定理.,,,2R13(sinsinsinABC14.余弦定理:222;abcbcA,，,2cos222;bcacaB,