1、三角函数公式两角和公式sin(A+B) = sinAcosB+cosAsinB sin(A-B) = sinAcosB-cosAsinB cos(A+B) = cosAcosB-sinAsinB cos(A-B) = cosAcosB+sinAsinBtan(A+B) = tanAB-1tan(A-B) = cot(A+B) = cot-cot(A-B) = AB1t倍角公式tan2A = tan12Sin2A=2SinACosACos2A = Cos2A-Sin2A=2Cos2A-1=1-2sin2A三倍角公式sin3A = 3sinA-4(sinA)3cos3A = 4(cosA)3-3c
2、osAtan3a = tanatan( +a)tan( -a)半角公式sin( )=2Acos1cos( )= tan( )=2Acos1cot( )= tan( )= =2Asinco1Asi和差化积 sina+sinb=2sin cos2basina-sinb=2cos sincosa+cosb = 2cos coscosa-cosb = -2sin sin2batana+tanb= cos)in(积化和差 sinasinb = - cos(a+b)-cos(a-b)21cosacosb = cos(a+b)+cos(a-b)sinacosb = sin(a+b)+sin(a-b)cosa
3、sinb = sin(a+b)-sin(a-b)21万能公式sina= 2)(tan1cosa= 2)(tatana= 2)(tan1其它公式asina+bcosa= sin(a+c) 其中tanc= )b(2abasin(a)-bcos(a) = cos(a-c) 其中tan(c)= a1+sin(a) =(sin +cos )21-sin(a) = (sin -cos )2其他非重点三角函数csc(a) = asin1sec(a) = co双曲函数sh(a)= 2e-ach(a)=-ath(a)= )(achsch2A-sh2A=1sh2A=2shAchAch2A=ch2A+sh2A设为任意角, +的三角函数值与的三角函数 值之间的关系:假设 为锐角时2n,先计算 +的值,再确定符号,如果n为偶数,则三角函数不变,否则转换函数,同时去掉 ,例如 sin( ) cos( )22tan( ) cot ( )nn