What is the basic relationship between trigonometric functions and angles?
Reciprocal relationship: Relationship between businesses:? Square relation:?
tanα？ cotα= 1
sinα？ cscα= 1
cosα？ secα= 1？ sinα/cosα=tanα=secα/cscα
cosα/sinα=cotα=cscα/secα？ sin2α+cos2α= 1
1+tan2α=sec2α
1+cot2α=csc2α？
(Hexagon mnemonic method: the graphic structure is "upper chord cut, Zuo Zheng middle cut,1"; The product of two functions on the diagonal is1; The sum of squares of trigonometric function values of two vertices on the shadow triangle is equal to the square of trigonometric function value of the next vertex; The trigonometric function value of any vertex is equal to the product of the trigonometric function values of two adjacent vertices. " )
Inductive formula (formula: odd variable couple, sign according to quadrant. )?
Sine (-α) =-Sine α
cos(-α)=cosα？ tan(-α)=-tanα
cot(-α)=-cotα？
sin(π/2-α)=cosα
cos(π/2-α)=sinα
tan(π/2-α)=cotα
cot(π/2-α)=tanα
sin(π/2+α)=cosα
cos(π/2+α)=-sinα
tan(π/2+α)=-cotα
cot(π/2+α)=-tanα
Sine (π-α) = Sine α
cos(π-α)=-cosα
tan(π-α)=-tanα
cot(π-α)=-coα
Sine (π+α) =-Sine α
cos(π+α)=-cosα
tan(π+α)=tanα
cot(π+α)=cotα
sin(3π/2-α)=-cosα
cos(3π/2-α)=-sinα
tan(3π/2-α)=cotα
cot(3π/2-α)=tanα
sin(3π/2+α)=-cosα
cos(3π/2+α)=sinα
tan(3π/2+α)=-cotα
cot(3π/2+α)=-tanα
Sine (2π-α)=- Sine α
cos(2π-α)=cosα
tan(2π-α)=-tanα
Kurt (2π-α)=- Kurt α
sin(2kπ+α)=sinα
cos(2kπ+α)=cosα
tan(2kπ+α)=tanα
cot(2kπ+α)=cotα
(where k∈Z)?
Formulas of trigonometric functions of the sum and difference of two angles? Universal formula?
sin(α+β)=sinαcosβ+cosαsinβ
sin(α-β)=sinαcosβ-cosαsinβ
cos(α+β)=cosαcosβ-sinαsinβ
cos(α-β)=cosαcosβ+sinαsinβ
sin(A+B)=sinAcosB+cosAsinB
sin(A-B)=sinAcosB-sinBcosA
cos(A+B)=cosAcosB-sinAsinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/( 1-tanA tanB)
tan(A-B)=(tanA-tanB)/( 1+tanA tanB)
cot(A+B)=(cotA cotB- 1)/(cot B+cotA)
cot(A-B)=(cotA cotB+ 1)/(cot b-cotA)
Double angle formula
tan2A=2tanA/[ 1-(tanA)^2]
cos2a=(cosa)^2-(sina)^2=2(cosa)^2？ - 1= 1-2(sina)^2
sin2A=2sinA*cosA
Triple angle formula
sin3a=3sina-4(sina)^3
cos3a=4(cosa)^3-3cosa
tan3a = tana * tan(π/3+a)* tan(π/3-a)？
half-angle formula
sin(A/2)=√(( 1-cosA)/2)？ sin(A/2)=-√(( 1-cosA)/2)
cos(A/2)=√(( 1+cosA)/2)？ cos(A/2)=-√(( 1+cosA)/2)
tan(A/2)=√(( 1-cosA)/(( 1+cosA))？ tan(A/2)=-√(( 1-cosA)/(( 1+cosA))
cot(A/2)=√(( 1+cosA)/(( 1-cosA))？ cot(A/2)=-√(( 1+cosA)/(( 1-cosA))
Tan(A/2)=( 1-cosA)/ Sina = Sina /( 1+cosA)
Sum difference product
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)？ )
2cosAcosB=cos(A+B)+cos(A-B)
-2sinAsinB=cos(A+B)-cos(A-B)
sinA+sinB = 2 sin((A+B)/2)cos((A-B)/2
cosA+cosB = 2cos((A+B)/2)sin((A-B)/2)
tanA+tanB=sin(A+B)/cosAcosB
Product sum and difference formula
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)]
Inductive formula
sin(-a)=-sin(a)？
cos(-a)=cos(a)？
sin(pi/2-a)=cos(a)？
cos(pi/2-a)=sin(a)？
sin(pi/2+a)=cos(a)？
cos(pi/2+a)=-sin(a)？
sin(pi-a)=sin(a)？
cos(pi-a)=-cos(a)？
sin(pi+a)=-sin(a)？
cos(pi+a)=-cos(a)？
tgA=tanA=sinA/cosA
General formula of trigonometric function
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))
Other formulas
a*sin(a)+b*cos(a)=sqrt(a^2+b^2)sin(a+c)？ [where tan(c)=b/a]?
a*sin(a)-b*cos(a)=sqrt(a^2+b^2)cos(a-c)？ [where tan(c)=a/b]?
1+sin(a)=(sin(a/2)+cos(a/2))^2？
Double angle sine, cosine, tangent formula? Sine, cosine and tangent formulas of triple angle?
sin2α=2sinαcosα
cos 2α= cos 2α-sin 2α= 2 cos 2α- 1 = 1-2 sin 2α
2tanα
tan2α=———
1-tan2α
sin3α=3sinα-4sin3α
cos3α=4cos3α-3cosα
3tanα-tan3α
tan3α=————
1-3tan2α
Asinα？ Bcos α is the form of trigonometric function of an angle (formulas of trigonometric functions of auxiliary angle).
Auxiliary angle formula asinx+bcosx= radical sign (a 2+b 2) * sin (x+arctan? b/a)