Definition of (1) function: let x and y be two variables, and d be a subset of real number set. If for every value x in D, the variable Y has a definite value corresponding to it according to certain rules, it is called a function of the variable X, and it is denoted as y=f(x).

(2) Inverse function: As far as relationship is concerned, it is generally bidirectional, and so is function. Let y = f (x) be a known function. If each y has a unique x∈X, let f (x) = y, this is a process of finding x from y, that is, x becomes a function of y, and is recorded as x =. F-1 is the inverse function of F. Traditionally, X is used to represent the independent variable, so this function is still recorded as y = f- 1 (x). For example, y = sinx and y = arcsinx are reciprocal functions. In the same coordinate system, the graphs of y = f (x) and y = f- 1 (x) are symmetrical about the straight line y = x.

(3) Implicit function: If the function equation f(x, y) = 0 can be used to determine that Y is a function y=f(x, that is, F(x, f(x))≡0, then Y is said to be an implicit function of X..

Thinking: Is implicit function a function? Because in the process of its reform, it is not satisfied with "one-on-one" and "many-on-one"

(5) The basic relationship of trigonometric functions with the same angle.

Reciprocal relation: quotient relation: square relation:

tanα cotα= 1

sinα cscα= 1

cosαsecα= 1 sinα/cosα= tanα= secα/CSCα

cosα/sinα= cotα= CSCα/secαsin 2α+cos 2α= 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

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)

General formula for sum and difference of formulas of trigonometric functions's two angles

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 reduction formula of trigonometric function

Sine, cosine and tangent formulas of double angles Sine, cosine and tangent formulas of triangle

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

α+β α-β

sinα+sinβ= 2 sin——cos——

2 2

α+β α-β

sinα-sinβ= 2cos——sin——

2 2

α+β α-β

cosα+cosβ= 2cos————cos———

2 2

α+β α-β

cosα-cosβ=-2 sin——sin——

2 2 1

sinα cosβ=-[sin(α+β)+sin(α-β)]

2

1

cosα sinβ=-[sin(α+β)-sin(α-β)]

2

1

cosα cosβ=-[cos(α+β)+cos(α-β)]

2

1

sinαsinβ=--[cos(α+β)-cos(α-β)]

2

Convert asinα bcosα into trigonometric function of angle (formulas of trigonometric functions of auxiliary angle).