定義:sin正弦值; cos餘弦值 ; tan正切值
公式:
1、基本性質:
tanx=sinx/cosx
sinx^x+cos^x=1
2、奇偶性:
sin(-x)=-sinx
cos(-x)=cosx
tan(-x)=-tanx
3、兩角和差公式:
sin(x+-y)=sinxcosy+-cosxsiny
cos(x+-y)=cosxcosy-+sinxsiny
tan(x+-y)=(tanx+-tany)/(1-+tanxtany)
4、二倍角公式:
sin2x=2sinxcosx
cos2x=cos^x-sin^x=2cos^x-1=1-2sin^x
tan2x=2tanx/(1-tan^x)
5、半角公式:
sin^x/2=(1-cosx)/2
cos^x/2=(1+cosx)/2
tan^x/2=sinx/(1+cosx)=(1-cosx)/sinx
1-cosx=2sin^x/2
1+cosx=2sin^x/2
6、萬能公式:
sinx=(2tanx/2)/(1+tan^x/2)
cosx=(1-tan^x/2)/(1+tan^x/2)
tanx=(2tanx/2)/(1-tan^x/2)
7、三倍角公式:
sin3x=3sinx-4sin^3 x (sinx的三次方)
cos3x=4cos^3 x-3cosx
8、積化和差公式:
sinxcosy=1/2[sin(x+y)+sin(x-y)]
cosxsiny=1/2[sin(x+y)-sin(x-y)]
cosxcosy=1/2[cos(x+y)+cos(x-y)]
sinxsiny-1/2[cos(x+y)-cos(x-y)]
9、和差化積公式:
sinx+siny=2sin(x+y)/2cos(x-y)/2
sinx-siny=2cos(x+y)/2sin(x-y)/2
cosx+cosy=2cos(x+y)/2cos/(x-y)2
cosx-cosy=-2sin(x+y)/2*sin(x-y)/2
定義:sin正弦值; cos餘弦值 ; tan正切值
公式:
1、基本性質:
tanx=sinx/cosx
sinx^x+cos^x=1
2、奇偶性:
sin(-x)=-sinx
cos(-x)=cosx
tan(-x)=-tanx
3、兩角和差公式:
sin(x+-y)=sinxcosy+-cosxsiny
cos(x+-y)=cosxcosy-+sinxsiny
tan(x+-y)=(tanx+-tany)/(1-+tanxtany)
4、二倍角公式:
sin2x=2sinxcosx
cos2x=cos^x-sin^x=2cos^x-1=1-2sin^x
tan2x=2tanx/(1-tan^x)
5、半角公式:
sin^x/2=(1-cosx)/2
cos^x/2=(1+cosx)/2
tan^x/2=sinx/(1+cosx)=(1-cosx)/sinx
1-cosx=2sin^x/2
1+cosx=2sin^x/2
6、萬能公式:
sinx=(2tanx/2)/(1+tan^x/2)
cosx=(1-tan^x/2)/(1+tan^x/2)
tanx=(2tanx/2)/(1-tan^x/2)
7、三倍角公式:
sin3x=3sinx-4sin^3 x (sinx的三次方)
cos3x=4cos^3 x-3cosx
8、積化和差公式:
sinxcosy=1/2[sin(x+y)+sin(x-y)]
cosxsiny=1/2[sin(x+y)-sin(x-y)]
cosxcosy=1/2[cos(x+y)+cos(x-y)]
sinxsiny-1/2[cos(x+y)-cos(x-y)]
9、和差化積公式:
sinx+siny=2sin(x+y)/2cos(x-y)/2
sinx-siny=2cos(x+y)/2sin(x-y)/2
cosx+cosy=2cos(x+y)/2cos/(x-y)2
cosx-cosy=-2sin(x+y)/2*sin(x-y)/2