三角公式大全.doc

角和与差的三角函数cos(+)=coscos-sinsin cos(-)=coscos+sinsin sin()=sincoscossin tan(+)=(tan+tan)/(1-tantan) tan(-)=(tan-tan)/(1+tantan) 和差化积公式sin+sin=2sin(+)/2cos(-)/2 sin-sin=2cos(+)/2sin(-)/2 cos+cos=2cos(+)/2cos(-)/2 cos-cos=-2sin(+)/2sin(-)/2 积化和差公式sincos=(1/2)sin(+)+sin(-) cossin=(1/2)sin(+)-sin(-) coscos=(1/2)cos(+)+cos(-) sinsin=-(1/2)cos(+)-cos(-) 倍角公式sin(2)=2sincos=2/(tan+cot) cos(2)=cos2-sin2;=2cos2;-1=1-2sin2; tan(2)=2tan/(1-tan2;) cot(2)=(cot2;-1)/(2cot) sec(2)=sec2;/(1-tan2;) csc(2)=1/2*seccsc 三倍角公式sin(3) = 3sin-4sin3; = 4sinsin(60+)sin(60-) cos(3) = 4cos3;-3cos = 4coscos(60+)cos(60-) tan(3) = (3tan-tan3;)/(1-3tan2;) = tantan(/3+)tan(/3-) cot(3)=(cot3;-3cot)/(3cot-1) n倍角公式sin(n)=ncos(n-1)sin-C(n,3)cos(n-3)sin3+C(n,5)cos(n-5)sin5- cos(n)=cosn-C(n,2)cos(n-2)sin2+C(n,4)cos(n-4)sin4- 半角公式sin(/2)=(1-cos)/2) cos(/2)=(1+cos)/2) tan(/2)=(1-cos)/(1+cos)=sin/(1+cos)=(1-cos)/sin cot(/2)=(1+cos)/(1-cos)=(1+cos)/sin=sin/(1-cos) sec(/2)=(2sec/(sec+1) csc(/2)=(2sec/(sec-1) 辅助角公式Asin+Bcos=(A2;+B2;)sin(+arctan(B/A) Asin+Bcos=(A2;+B2;)cos(-arctan(A/B) 万能公式sin(a)= (2tan(a/2)/(1+tan2;(a/2) cos(a)= (1-tan2;(a/2)/(1+tan2;(a/2) tan(a)= (2tan(a/2)/(1-tan2;(a/2) 降幂公式sin2;=(1-cos(2)/2=versin(2)/2 cos2;=(1+cos(2)/2=covers(2)/2 tan2;=(1-cos(2)/(1+cos(2) 三角和的三角函数sin(+)=sincoscos+cossincos+coscossin-sinsinsin cos(+)=coscoscos-cossinsin-sinc