高中數(shù)學(xué)反三角函數(shù)的公式小結(jié)-文庫吧
2024-10-13 10:01 本頁面
【正文】 os179。a3cosa=4cosa(cos178。a3/4)=4cosa[cos178。a(√3/2)178。]=4cosa(cos178。acos178。30176。)=4cosa(cosa+cos30176。)(cosacos30176。)=4cosa*2cos[(a+30176。)/2]cos[(a30176。)/2]*{2sin[(a+30176。)/2]sin[(a30176。)/2]}=4cosasin(a+30176。)sin(a30176。)=4cosasin[90176。(60176。a)]sin[90176。+(60176。+a)]=4cosacos(60176。a)[cos(60176。+a)]=4cosacos(60176。a)cos(60176。+a)上述兩式相比可得tan3a=tanatan(60176。a)tan(60176。+a)半角公式tan(A/2)=(1cosA)/sinA=sinA/(1+cosA)。cot(A/2)=sinA/(1cosA)=(1+cosA)/^2(a/2)=(1cos(a))/2cos^2(a/2)=(1+cos(a))/2tan(a/2)=(1cos(a))/sin(a)=sin(a)/(1+cos(a))三角和sin(α+β+γ)=sinαcosβcosγ+cosαsinβcosγ+cosαcosβsinγsinαsinβsinγcos(α+β+γ)=cosαcosβcosγcosαsinβsinγsinαcosβsinγsinαsinβcosγtan(α+β+γ)=(tanα+tanβ+tanγtanαtanβtanγ)/(1tanαtanβtanβtanγtanγtanα)兩角和差cos(α+β)=cosαcosβsinαsinβcos(αβ)=cosαcosβ+sinαsinβsin(α177。β)=sinαcosβ177。cosαsinβtan(α+β)=(tanα+tanβ)/(1tanαtanβ)tan(αβ)=(tanαtanβ)/(1+tanαtanβ)和差化積sinθ+sinφ = 2 sin[(θ+φ)/2] cos[(θφ)/2]sinθsinφ = 2 cos[(θ+φ)/2] sin[(θφ)/2]cosθ+cosφ = 2 cos[(θ+φ)/2] cos[(θφ)/2]cosθcosφ =2 sin[(θ+φ)/2] sin[(θφ)/2]tanA+tanB=sin(A+B)/cosAcosB=tan(A+B)(1tanAtanB)tanAtanB=sin(AB)/cosAcosB=tan(AB)(1+tanAtanB)積化和差sinαsinβ = [cos(αβ)cos(α+β)] /2cosαcosβ = [cos(α+β)+cos(αβ)]/2sinαcosβ = [sin(α+β)+sin(αβ)]/2cosαsinβ = [sin(α+β)sin(αβ)]/2誘導(dǎo)公式sin(α)=sinαcos(α)= cosαtan(—a)=tanαsin(π/2α)= cosαcos(π/2α)= sinαsin(π/2+α)= cosαcos(π/2+α)=sinαsin(πα)= sinαcos(πα)=cosαsin(π+α)=sinαcos(π+α)=cosαtanA= sinA/cosAtan（π/2＋α）＝－cotαtan（π/2－α）＝cotαtan（π－α）＝－tanαtan（π＋α）＝tanα誘導(dǎo)公式記背訣竅：奇變偶不變，符號看象限萬能公式sinα=2tan(α/2）/［1+tan＾(α/2)］cosα=［1tan＾(α/2)］/1
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