两角和公式
sin(A+B) = sinAcosB+cosAsinBsin(A-B) = sinAcosB-cosAsinBcos(A+B) = cosAcosB-sinAsinBcos(A-B) = cosAcosB+sinAsinB
tan(A+B) = (tanA+tanB)/(1-tanAtanB)tan(A-B) = (tanA-tanB)/(1+tanAtanB)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)}
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)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;;公式一:
设α为任意角,终边相同的角的同一三角函数的值相等:
sin(2kπ+α)= sinαcos(2kπ+α)= cosαtan(2kπ+α)= tanα公式二:
设α为任意角,π+α的三角函数值与α的三角函数值之间的关系:sin(π+α)= -sinαcos(π+α)= -cosαtan(π+α)= tanα公式三:
任意角α与 -α的三角函数值之间的关系:sin(-α)= -sinαcos(-α)= cosαtan(-α)= -tanα公式四:
利用公式二和公式三可以得到π-α与α的三角函数值之间的关系:sin(π-α)= sinαcos(π-α)= -cosαtan(π-α)= -tanα公式五:
利用公式-和公式三可以得到2π-α与α的三角函数值之间的关系:sin(2π-α)= -sinαcos(2π-α)= cosαtan(2π-α)= -tanα公式六:
π/2±α及3π/2±α与α的三角函数值之间的关系: sin(π/2+α)= cosαcos(π/2+α)= -sinαsin(π/2-α)= cosαcos(π/2-α)= sinαsin(3π/2+α)= -cosαcos(3π/2+α)= sinαsin(3π/2-α)= -cosαcos(3π/2-α)= -sinα