三角函数诱导公式,要全部!

2个回答

  • 1.诱导公式

    sin(-a)=-sin(a)

    cos(-a)=cos(a)

    sin(π2-a)=cos(a)

    cos(π2-a)=sin(a)

    sin(π2+a)=cos(a)

    cos(π2+a)=-sin(a)

    sin(π-a)=sin(a)

    cos(π-a)=-cos(a)

    sin(π+a)=-sin(a)

    cos(π+a)=-cos(a)

    2.两角和与差的三角函数

    sin(a+b)=sin(a)cos(b)+cos(α)sin(b)

    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.和差化积公式

    sin(a)+sin(b)=2sin(a+b2)cos(a-b2)

    sin(a)−sin(b)=2cos(a+b2)sin(a-b2)

    cos(a)+cos(b)=2cos(a+b2)cos(a-b2)

    cos(a)-cos(b)=-2sin(a+b2)sin(a-b2)

    4.积化和差公式 (上面公式反过来就得到了)

    sin(a)sin(b)=-12⋅[cos(a+b)-cos(a-b)]

    cos(a)cos(b)=12⋅[cos(a+b)+cos(a-b)]

    sin(a)cos(b)=12⋅[sin(a+b)+sin(a-b)]

    5.二倍角公式

    sin(2a)=2sin(a)cos(b)

    cos(2a)=cos2(a)-sin2(a)=2cos2(a)-1=1-2sin2(a)

    6.半角公式

    sin2(a2)=1-cos(a)2

    cos2(a2)=1+cos(a)2

    tan(a2)=1-cos(a)sin(a)=sina1+cos(a)

    7.万能公式

    sin(a)=2tan(a2)1+tan2(a2)

    cos(a)=1-tan2(a2)1+tan2(a2)

    tan(a)=2tan(a2)1-tan2(a2)

    8.其它公式(推导出来的 )

    a⋅sin(a)+b⋅cos(a)=a2+b2sin(a+c) 其中 tan(c)=ba

    a⋅sin(a)+b⋅cos(a)=a2+b2cos(a-c) 其中 tan(c)=ab

    1+sin(a)=(sin(a2)+cos(a2))2

    1-sin(a)=(sin(a2)-cos(a2))2