1、一三角函數公式1.誘導公式sin(-a) = - sin(a) cos(-a) = cos(a)sin(/2（90度） - a) = cos(a)cos(/2（90度） - a) = sin(a)sin(/2 （90度）+ a) = cos(a)cos(/2 （90度）+ a) = - sin(a)sin(（180度）- a) = sin(a)cos(（180度） - a) = - cos(a)sin(（180度）+ a) = - sin(a)cos(（180度）+ a) = - cos(a)2.兩角和與差的三角函數sin(a + b) = sin(a)cos(b) + cos()sin(b)

2、cos(a + b) = cos(a)cos(b) - sin(a)sin(b)sin(a - b) = sin(a)cos(b) - cos(a)sin(b)cos(a - b) = cos(a)cos(b) + sin(a)sin(b)tan(a + b) = tan(a) + tan(b) / 1 - tan(a)tan(b)tan(a - b) = tan(a) - tan(b) / 1 + tan(a)tan(b) 3.和差化積公式 sin(a) + sin(b) = 2sin(a + b)/2cos(a - b)/2sin(a) sin(b) = 2cos(a + b)/2sin(

3、a - b)/2 cos(a) + cos(b) = 2cos(a + b)/2cos(a - b)/2 cos(a) - cos(b) = - 2sin(a + b)/2sin(a - b)/2 4.積化和差公式 sin(a)sin(b) = - 1/2cos(a + b) - cos(a - b) cos(a)cos(b) = 1/2cos(a + b) + cos(a -b) sin(a)cos(b) = 1/2sin(a + b) + sin(a - b)5.二倍角公式 sin(2a) = 2sin(a)cos(b) cos(2a) = cos2(a) - sin2(a) = 2cos

4、2(a) -1=1 - 2sin2(a)6.半角公式 sin2(a/2) = 1 - cos(a) / 2cos2(a/2) = 1 + cos(a) / 2tan(a/2) = 1 - cos(a) /sin(a) = sina / 1 + cos(a)7.萬能公式 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)二反三角函數公式反三角函數其他公式：cos(arcsinx)=(1-x2)arcsin(-x)=-arcsinxarccos(-x)=

5、-arccosxarctan(-x)=-arctanxarccot(-x)=-arccotxarcsinx+arccosx=/2=arctanx+arccotxsin(arcsinx)=cos(arccosx)=tan(arctanx)=cot(arccotx)=xarcsin x = x + x3/(2*3) + (1*3)x5/(2*4*5) + 1*3*5(x7)/(2*4*6*7）+(2k+1)!*x(2k-1)/(2k!*(2k+1)+（|x|<1) !！表示雙階乘arccos x = -(x + x3/(2*3) + (1*3)x5/(2*4*5) + 1*3*5(x7)/(2*4*6*7）（|x|<1)arctan x = x - x3/3 + x5/5 -舉例當 x-/2，/2 有arcsin(sinx)=xx0， arccos(cosx)=xx（-/2，/2）， arctan(tanx)=xx（0，）， arccot(cotx)=xx>0，arctanx=/2-arctan1/x，arccotx類似若 (arctanx+arctany）（-/2，/2），則 arctanx+arctany=arctan(x+y)