三角函数,反三角函数公式[宝典]

三角 函数 excel方差函数excelsd函数已知函数     2 f x m x mx m      2 1 4 2拉格朗日函数pdf函数公式下载 ,反三角函数公式[宝典] 第一部分,,,,,三角函数公式 ?两角和与差的三角函数,,,,, cos(α+β)=cosα?cosβ-sinα?sinβ,,,,, cos(α-β)=cosα?cosβ+sinα?sinβ,,,,, sin(α?β)=sinα?cosβ?cosα?sinβ,,,,, tan(α+β)=(tanα+tanβ)/(1-tanα?tanβ),,,,, tan(α-β)=(tanα-tanβ)/(1+tanα?tanβ),,,,, ?和差化积公式:,,,,, sinα+sinβ=2sin[(α+β)/2]cos[(α-β)/2],,,,, sinα-sinβ=2cos[(α+β)/2]sin[(α-β)/2],,,,, cosα+cosβ=2cos[(α+β)/2]cos[(α-β)/2],,,,, cosα-cosβ=-2sin[(α+β)/2]sin[(α-β)/2],,,,, ?积化和差公式:,,,,, sinα?cosβ=(1/2)[sin(α+β)+sin(α-β)],,,,, cosα?sinβ=(1/2)[sin(α+β)-sin(α-β)],,,,, cosα?cosβ=(1/2)[cos(α+β)+cos(α-β)],,,,, sinα?sinβ=-(1/2)[cos(α+β)-cos(α-β)],,,,, ?倍角公式:,,,,, sin(2α)=2sinα?cosα=2/(tanα+cotα),,,,, cos(2α)=(cosα)^2-(sinα)^2=2(cosα)^2-1=1-2(sinα)^2 ,,,,, tan(2α)=2tanα/(1-tan^2α),,,,, ?三倍角公式:,,,,, sin(3α),,,,,=,,,,,3sinα-4sin^3α,,,,,=,,,,,4sinα?sin(60?+α)sin(60?-α),,,,, cos(3α),,,,,=,,,,,4cos^3α-3cosα,,,,,=,,,,,4cosα?cos(60?+α)cos(60?-α),,,,, tan(3α),,,,,=,,,,,(3tanα-tan^3α)/(1-3tan^2α),,,,,=,,,,,tanαtan(π/3+α)tan(π/3-α),,,,, cot(3α)=(cot^3α-3cotα)/(3cot^2α-1),,,,, ?n倍角公式:,,,,, sin(nα)=ncos^(n-1)α?sinα-C(n,3)cos^(n-3)α?sin^3α+C(n,5)cos^(n-5)α?sin^5α-…,,,,, cos(nα)=cos^nα-C(n,2)cos^(n-2)α?sin^2α+C(n,4)cos^(n-4)α?sin^4α-…,,,,, ?半角公式:,,,,, sin(α/2)=??((1-cosα)/2),,,,, cos(α/2)=??((1+cosα)/2),,,,, tan(α/2)=??((1-cosα)/(1+cosα))=sinα/(1+cosα)=(1-cosα)/ sinα,,,,, cot(α/2)=??((1+cosα)/(1-cosα))=(1+cosα)/sinα=sinα/(1-cosα),,,,, sec(α/2)=??((2secα/(secα+1)),,,,, ?辅助角公式:,,,,, Asinα+Bcosα=?(A^2+B^2)sin(α+φ)(tanφ=B/A),,,,, Asinα+Bcosα=?(A^2+B^2)cos(α-φ)(tanφ=A/B),,,,, ?万能公式,,,,, sin(a)=,,,,,(2tan(a/2))/(1+tan^2(a/2)),,,,, cos(a)=,,,,,(1-tan^2(a/2))/(1+tan^2(a/2)),,,,, tan(a)=,,,,,(2tan(a/2))/(1-tan^2(a/2)),,,,, ?降幂公式,,,,, sin^2α=(1-cos(2α))/2=versin(2α)/2,,,,, cos^2α=(1+cos(2α))/2=covers(2α)/2,,,,, tan^2α=(1-cos(2α))/(1+cos(2α)),,,,, ?三角和的三角函数:,,,,, sin(α+β+γ)=sinα?cosβ?cosγ+cosα?sinβ?cosγ+cosα?cosβ?sinγ-sinα?sinβ?sinγ,,,,, cos(α+β+γ)=cosα?cosβ?cosγ-cosα?sinβ?sinγ-sinα?cosβ?sinγ-sinα?sinβ?cosγ,,,,, csc(α/2)=??((2secα/(secα-1)),,,,, tan(α+β+γ)=(tanα+tanβ+tanγ-tanα?tanβ?tanγ)/(1-tanα?tanβ-tanβ?tanγ-tanγ?tanα),,,,, ?其它公式,,,,, ?两角和与差的三角函数,,,,, cos(α+β)=cosα?cosβ-sinα?sinβ,,,,, cos(α-β)=cosα?cosβ+sinα?sinβ,,,,, sin(α?β)=sinα?cosβ?cosα?sinβ,,,,, tan(α+β)=(tanα+tanβ)/(1-tanα?tanβ),,,,, tan(α-β)=(tanα-tanβ)/(1+tanα?tanβ),,,,, ?和差化积公式:,,,,, sinα+sinβ=2sin[(α+β)/2]cos[(α-β)/2],,,,, sinα-sinβ=2cos[(α+β)/2]sin[(α-β)/2],,,,, cosα+cosβ=2cos[(α+β)/2]cos[(α-β)/2],,,,, cosα-cosβ=-2sin[(α+β)/2]sin[(α-β)/2],,,,, ?积化和差公式:,,,,, sinα?cosβ=(1/2)[sin(α+β)+sin(α-β)],,,,, cosα?sinβ=(1/2)[sin(α+β)-sin(α-β)],,,,, csinα?sinβ=-(1/2)[cos(α+β)-cos(α-β)],,,,, ?倍角公式:,,,,, sin(2α)=2sinα?cosα=2/(tanα+cotα),,,,, cos(2α)=(cosα)^2-(sinα)^2=2(cosα)^2-1=1-2(sinα)^2 ,,,,, tan(2α)=2tanα/(1-tan^2α),,,,, cot(2α)=(cot^2α-1)/(2cotα),,,,, sec(2α)=sec^2α/(1-tan^2α),,,,, csc(2α)=1/2*secα?cscα,,,,, ?三倍角公式:,,,,, sin(3α),,,,,=,,,,,3sinα-4sin^3α,,,,,=,,,,,4sinα?sin(60?+α)sin(60?-α),,,,, cos(3α),,,,,=,,,,,4cos^3α-3cosα,,,,,=,,,,,4cosα?cos(60?+α)cos(60?-α),,,,, tan(3α),,,,,=,,,,,(3tanα-tan^3α)/(1-3tan^2α),,,,,=,,,,,tanαtan(π/3+α)tan(π/3-α),,,,, cot(3α)=(cot^3α-3cotα)/(3cot^2α-1),,,,, ?n倍角公式:,,,,, sin(nα)=ncos^(n-1)α?sinα-C(n,3)cos^(n-3)α?sin^3α+C(n,5)cos^(n-5)α?sin^5α-…,,,,, cos(nα)=cos^nα-C(n,2)cos^(n-2)α?sin^2α+C(n,4)cos^(n-4)α?sin^4α-…,,,,, ?半角公式:,,,,, sin(α/2)=??((1-cosα)/2),,,,, cos(α/2)=??((1+cosα)/2),,,,,osα?cosβ=(1/2)[cos(α+β)+cos(α-β)] ?半角公式:,,,,, sin(α/2)=??((1-cosα)/2),,,,, cos(α/2)=??((1+cosα)/2),,,,, tan(α/2)=??((1-cosα)/(1+cosα))=sinα/(1+cosα)=(1-cosα)/sinα,,,,, cot(α/2)=??((1+cosα)/(1-cosα))=(1+cosα)/sinα=sinα/(1-cosα),,,,, sec(α/2)=??((2secα/(secα+1)),,,,, csc(α/2)=??((2secα/(secα-1)),,,,, ?辅助角公式:,,,,, Asinα+Bcosα=?(A^2+B^2)sin(α+φ)(tanφ=B/A),,,,, Asinα+Bcosα=?(A^2+B^2)cos(α-φ)(tanφ=A/B),,,,, ?万能公式,,,,, sin(a)=,,,,,(2tan(a/2))/(1+tan^2(a/2)),,,,, cos(a)=,,,,,(1-tan^2(a/2))/(1+tan^2(a/2)),,,,, tan(a)=,,,,,(2tan(a/2))/(1-tan^2(a/2)),,,,, ?降幂公式,,,,, sin^2α=(1-cos(2α))/2=versin(2α)/2,,,,, cos^2α=(1+cos(2α))/2=covers(2α)/2,,,,, tan^2α=(1-cos(2α))/(1+cos(2α)),,,,, ?三角和的三角函数:,,,,, sin(α+β+γ)=sinα?cosβ?cosγ+cosα?sinβ?cosγ+cosα?cosβ?sinγ-sinα?sinβ?sinγ,,,,, cos(α+β+γ)=cosα?cosβ?cosγ-cosα?sinβ?sinγ-sinα?cosβ?sinγ-sinα?sinβ?cosγ,,,,, tan(α+β+γ)=(tanα+tanβ+tanγ-tanα?tanβ?tanγ)/(1-tanα?tanβ-tanβ?tanγ-tanγ?tanα),,,,, ?其它公式,,,,, 1+sin(a)=(sin(a/2)+cos(a/2))^2,,,,,1-sin(a)=(sin(a/2)-c os(a/2))^2,,,,, csc(a)=1/sin(a),,,,,sec(a)=1/cos(a),,,,, cos30=sin60,,,,, sin30=cos60,,,,, ?推导公式,,,,, tanα+cotα=2/sin2α,,,,, tanα-cotα=-2cot2α,,,,, 1+cos2α=2cos^2α,,,,, 1-cos2α=2sin^2α,,,,, 1+sinα=[sin(α/2)+cos(α/2)]^2 1+sin(a)=(sin(a/2)+cos(a/2))^2,,,,,1-sin(a)=(sin(a/2)-cos( a/2))^2,,,,, csc(a)=1/sin(a),,,,,sec(a)=1/cos(a),,,,, cos30=sin60,,,,, sin30=cos60,,,,, ?推导公式,,,,, tanα+cotα=2/sin2α,,,,, tanα-cotα=-2cot2α,,,,, 1+cos2α=2cos^2α,,,,, 1-cos2α=2sin^2α,,,,, 1+sinα=[sin(α/2)+cos(α/2)]^2