高中三角函数所有公式 常用公式有哪些

    三角函数是高中数学学习的重点内容，那么，高中三角函数公式有哪些呢？下面小编整理了一些相关信息，供大家参考！

    两角和公式    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)

    半角公式    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)

    和差化积    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

    积化和差    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)]

    诱导公式    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

    万能公式    sin(a) = [2tan(a/2)] / {1+[tan(a/2)]^2}

    cos(a) = {1-[tan(a/2)]^2} / {1+[tan(a/2)]^2}

    tan(a) = [2tan(a/2)]/{1-[tan(a/2)]^2}

    其它公式    a?sin(a)+b?cos(a) = [√(a^2+b^2)]*sin(a+c) [其中，tan(c)=b/a]

    a?sin(a)-b?cos(a) = [√(a^2+b^2)]*cos(a-c) [其中，tan(c)=a/b]

    1+sin(a) = [sin(a/2)+cos(a/2)]^2;

    1-sin(a) = [sin(a/2)-cos(a/2)]^2;;

    其他非重点三角函数    csc(a) = 1/sin(a)

    sec(a) = 1/cos(a)