高考数学知识点-三角函数公式大全.docx

高考数学知识点:三角函数公式大全 sin=的对边/斜边 cos=的邻边/斜边 tan=的对边/的邻边 cot=的邻边/的对边 Sin2A=2SinA?CosA Cos2A=CosA^2-SinA^2=1-2SinA^2=2CosA^2-1 tan2A=(2tanA)/(1-tanA^2) (注:SinA^2是sinA的平方sin2(A)) sin3=4sinsin(/3+)sin(/3-) cos3=4coscos(/3+)cos(/3-) tan3a=tanatan(/3+a)tan(/3-a) sin3a =sin(2a+a) =sin2acosa+cos2asina Asin+Bcos=(A^2+B^2)^(1/2)sin(+t),其中 sint=B/(A^2+B^2)^(1/2) cost=A/(A^2+B^2)^(1/2) tant=B/A Asin+Bcos=(A^2+B^2)^(1/2)cos(-t),tant=A/B sin^2()=(1-cos(2))/2=versin(2)/2 cos^2()=(1+cos(2))/2=covers(2)/2 tan^2()=(1-cos(2))/(1+cos(2)) tan+cot=2/sin2 tan-cot=-2cot2 1+cos2=2cos^2 1-cos2=2sin^2 1+sin=(sin/2+cos/2)^2 =2sina(1-sina)+(1-2sina)sina =3sina-4sina cos3a =cos(2a+a) =cos2acosa-sin2asina =(2cosa-1)cosa-2(1-sina)cosa =4cosa-3cosa sin3a=3sina-4sina =4sina(3/4-sina) =4sina =4sina(sin60-sina) =4sina(sin60+sina)(sin60-sina) =4sina*2sincos*2sincos =4sinasin(60+a)sin(60-a) cos3a=4cosa-3cosa =4cosa(cosa-3/4) =4cosa =4cosa(cosa-cos30) =4cosa(cosa+cos30)(cosa-cos30) =4cosa*2coscos*{-2sinsin} =-4cosasin(a+30)sin(a-30) =-4cosasinsin =-4cosacos(60-a) =4cosacos(60-a)cos(60+a) 上述两式相比可得 tan3a=tanatan(60-a)tan(60+a) tan(A/2)=(1-cosA)/sinA=sinA/(1+cosA); cot(A/2)=sinA/(1-cosA)=(1+cosA)/sinA. sin^2(a/2)=(1-cos(a))/2 cos^2(a/2)=(1+cos(a))/2 tan(a/2)=(1-cos(a))/sin(a)=sin(a)/(1+cos(a)) sin(++)=sincoscos+cossincos+coscossin-sinsinsin cos(++)=coscoscos-cossinsin-sincossin-sinsincos tan(++)=(tan+tan+tan-tantantan)/(1-t