High school mathematical formula theorem concentration
Formulas of trigonometric functions table
Basic relations of trigonometric functions with the same angle
Reciprocal relationship:
Relationship between businesses:
Square relation:
tanα
cotα= 1
sinα
cscα= 1
Coase α
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
Kurt (-α) =-Kurt α
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
Kurt (π-α) =-Kurt α
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 sum and difference of two angles.
General formula of trigonometric function
sin(α+β)=sinαcosβ+cosαsinβ
sin(α-β)=sinαcosβ-cosαsinβ
cos(α+β)=cosαcosβ-sinαsinβ
cos(α-β)=cosαcosβ+sinαsinβ
tanα+tanβ
tan(α+β)=———
1-tanα
tanβ
tanα-tanβ
tan(α-β)=———
1+tanα
tanβ
2 tons (α/2)
sinα=————
1+tan2(α/2)
1-tan2(α/2)
cosα=————
1+tan2(α/2)
2 tons (α/2)
tanα=————
1-tan2(α/2)
Sine, cosine and tangent formulas of half angle
Power drop formula of trigonometric function
Sine, cosine and tangent formulas of double angles
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
Sum and difference product formula of trigonometric function
Formula of product and difference of trigonometric function
α+β
α-β
sinα+sinβ=2sin——？ Because-
2
2
α+β
α-β
sinα-sinβ=2cos——？ Sin-
2
2
α+β
α-β
cosα+cosβ=2cos——？ Because-
2
2
α+β
α-β
cosα-cosβ=-2sin——？ Sin-
2
2
1
sinα
cosβ=-[sin(α+β)+sin(α-β)]
2
1
Coase α
sinβ=-[sin(α+β)-sin(α-β)]
2
1
Coase α
cosβ=-[cos(α+β)+cos(α-β)]
2
1
sinα
sinβ=—
-[cos(α+β)-cos(α-β)]
2
Chemical arsenic α
Bcos α is the form of trigonometric function of an angle (formulas of trigonometric functions of auxiliary angle