高中数学三角函数公式知识点.docx

高中数学三角函数公式知识点 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 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)) cos(+)=coscos-sinsin cos(-)=coscos+sinsin sin()=sincoscossin tan(+)=(tan+tan)/(1-tantan) tan(-)=(tan-tan)/(1+tantan) sin+sin=2sinc