三角函数公式 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(asin(b = -1/2*[cos(a+b-cos(a-b] cos(acos(b = 1/2*[cos(a+b+cos(a-b] sin(acos(b = 1/2*[sin(a+b+sin(a-b] cos(asin(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 双曲函数
sinh(a = [e^a-e^(-a]/2 cosh(a = [e^a+e^(-a]/2 tg h(a = sin h(a/cos h(a 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 = sinα cos (2kπ+α = cosα
tan (2kπ+α = tanα cot (2kπ+α = cotα 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 = -sinα
cos (π+α = -cosα tan (π+α = tanα cot (π+α = cotα 公式三:
任意角 α与 -α的三角函数值之间的关系: sin (-α = -sinα cos (-α = cosα tan (-α = -tanα cot (-α = -cotα 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 = sinα
cos (π-α = -cosα tan (π-α = -tanα
cot (π-α = -cotα 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 = -sinα
cos (2π-α = cosα tan (2π-α = -tanα cot (2π-α = -cotα 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 = cosα cos (π/2+α = -sinα
