三角函数公式大全.docx

三角函数公式 付远祥信计一班两角和与差的三角函数cos(+)=coscos-sinsincos(-)=coscos+sinsinsin()=sincoscossintan(+)=(tan+tan)/(1-tantan)tan(-)=(tan-tan)/(1+tantan)和差化积公式：sin+sin=2sin(+)/2cos(-)/2sin-sin=2cos(+)/2sin(-)/2cos+cos=2cos(+)/2cos(-)/2cos-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)=(cos)2-(sin)2 =2(cos)2-1 = 1-2(sin)2tan(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)/(3cot2-1)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+co s) =(1-cos)/sincot(/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(+）（tan=B/A）Asin+Bcos=(A2+B2)cos(-）（tan=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)/2cos2=(1+cos(2)/2=covers(2)/2tan2=(1-cos(2)/(1+cos(2)三角和的三角函数：sin(+)=sincoscos+cossincos+coscossin-sinsinsincos(+)=coscoscos-cossinsin-sincossin-sinsincostan(+)=(tan+tan+tan-tantantan)/(1-tantan-tantan-tantan) 其它公式两角和与差的三角函数cos(+)=coscos-sinsincos(-)=coscos+sinsinsin()=sincoscossintan(+)=(tan+tan)/(1-tantan)tan(-)=(tan-tan)/(1+tantan)和差化积公式：sin+sin=2sin(+)/2cos(-)/2sin-sin=2cos(+)/2sin(-)/2cos+cos=2cos(+)/2cos(-)/2cos-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)=(cos)2-(sin)2 =2(cos)2-1=1-2(sin)2tan(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)/(3cot2-1)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)/sincot(/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(+）（tan=B/A）Asin+Bcos=(A2+B2)cos(-）（tan=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)/2cos2=(1+cos(2)/2=covers(2)/2tan2=(1-cos(2)/(1+cos(2)三角和的三角函数：sin(+)=sincoscos+cossincos+coscossin-sinsinsincos(+)=coscoscos-cossinsin-sincossin-sinsincostan(+)=(tan+tan+tan-tantantan)/(1-tantan-tantan-tantan)其它公式1+sin(a)=(sin(a/2)+cos(a/2)2 1-sin(a)=(sin(a/2)-cos(a/2)2csc(a)=1/sin(a) sec(a)=1/cos(a)cos30=sin60sin30=cos60推导公式tan+cot=2/sin2tan-cot=-2cot21+cos2=2cos21-cos2=2sin21+sin=sin(/2)+cos(/2)21+sin(a)=(sin(a/2)+cos(a/2)2 1-s