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  • 1 # 髒話比謊話乾淨558

    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

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