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  • 1 # 無為輕狂

    條件如果是x--pi/2時,cosx為無窮小量,

    sinx則是x---0時的無窮小量,無窮大量與無窮小量都是在一定條件下才成立。

    三角函式公式

    兩角和公式

    sin(A+B) = sinAcosB+cosAsinB

    sin(A-B) = sinAcosB-cosAsinB

    cos(A+B) = cosAcosB-sinAsinB

    cos(A-B) = cosAcosB+sinAsinB

    tan(A+B) = (tanA+tanB)/(1-tanAtanB)

    tan(A-B) = (tanA-tanB)/(1+tanAtanB)

    cot(A+B) = (cotAcotB-1)/(cotB+cotA

    cot(A-B) = (cotAcotB+1)/(cotB-cotA)

    倍角公式

    tan2A = 2tanA/(1-tan^2 A)

    Sin2A=2SinA•CosA

    Cos2A = Cos^2 A--Sin^2 A

    =2Cos^2 A—1

    =1—2sin^2 A

    三倍角公式

    sin3A = 3sinA-4(sinA)^3;

    cos3A = 4(cosA)^3 -3cosA

    tan3a = tan a • tan(π/3+a)• tan(π/3-a)

    半形公式

    sin(A/2) = √{(1--cosA)/2}

    cos(A/2) = √{(1+cosA)/2}

    tan(A/2) = √{(1--cosA)/(1+cosA)}

    cot(A/2) = √{(1+cosA)/(1-cosA)}

    tan(A/2) = (1--cosA)/sinA=sinA/(1+cosA)

    和差化積

    sin(a)+sin(b) = 2sin[(a+b)/2]cos[(a-b)/2]

    sin(a)-sin(b) = 2cos[(a+b)/2]sin[(a-b)/2]

    cos(a)+cos(b) = 2cos[(a+b)/2]cos[(a-b)/2]

    cos(a)-cos(b) = -2sin[(a+b)/2]sin[(a-b)/2]

    tanA+tanB=sin(A+B)/cosAcosB

    積化和差

    sin(a)sin(b) = -1/2*[cos(a+b)-cos(a-b)]

    cos(a)cos(b) = 1/2*[cos(a+b)+cos(a-b)]

    sin(a)cos(b) = 1/2*[sin(a+b)+sin(a-b)]

    cos(a)sin(b) = 1/2*[sin(a+b)-sin(a-b)]

    誘導公式

    sin(-a) = -sin(a)

    cos(-a) = cos(a)

    sin(π/2-a) = cos(a)

    cos(π/2-a) = sin(a)

    sin(π/2+a) = cos(a)

    cos(π/2+a) = -sin(a)

    sin(π-a) = sin(a)

    cos(π-a) = -cos(a)

    sin(π+a) = -sin(a)

    cos(π+a) = -cos(a)

    tgA=tanA = sinA/cosA

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