1, the corresponding value of the function and the so-called monotonous interval are very useful in mathematics (junior high school is expanding, senior high school is very important, not to mention universities).

2, 1, as shown in the figure, in △ABC, ∠ c = 90.

(1) The ratio of the opposite side to the hypotenuse of acute angle A is called the sine of ∠A, and it is recorded as sinA, that is

(2) The ratio of the adjacent side to the hypotenuse of acute angle A is called cosine of ∠A, and it is recorded as cosA, that is

(3) The ratio of the opposite side to the adjacent side of acute angle A is called the tangent of ∠A, and it is written as tanA, that is

(4) The ratio of the adjacent side to the opposite side of acute angle A is called cotangent of ∠A and named cotA.

2. The concept of acute trigonometric function

The sine, cosine, tangent and cotangent of acute angle A are all called acute trigonometric functions of ∠ A..

3. Trigonometric function values of some special angles

4. The relationship between acute trigonometric functions.

(1) complementary relation

sinA=cos(90 —A)，cosA=sin(90 —A)

tanA=cot(90 —A)，cotA=tan(90 —A)

(2) Square relation

(3) Reciprocal relationship

tanA tan(90 —A)= 1

5. Increase or decrease of acute trigonometric function

When the angle varies between 0 and 90 degrees,

(1) The sine value increases (or decreases) with the increase (or decrease) of the angle.

(2) The cosine value decreases (or increases) with the increase (or decrease) of the angle.

(3) The tangent value increases (or decreases) with the increase (or decrease) of the angle.

(4) The cotangent value decreases (or increases) with the increase (or decrease) of the angle.

tanα？ cotα= 1

sinα？ cscα= 1

cosα？ secα= 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

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)

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

3.lim refers to the limit, which exists in high school and belongs to higher mathematics in universities.

limit

Limit is an important concept in higher mathematics.

Limit can be divided into sequence limit and function limit, which are defined as follows.

Sequence restriction:

Set it as a series, and a is a fixed number. For any positive number ε, there is always a positive integer n, so when n >: when n, there is.

| An-A | & lt； ε,

It is said that the sequence converges to a, and the fixed number A is called the limit of the sequence, which is recorded as

Lim An = A, or an->; A (n->∞),

When n tends to infinity, the limit of An equals to a or An tends to a.

Functional limitations:

Let f be a function defined on [a, +∞) and a be a definite number. If given ε >; 0, with a positive number m (> =a), so when x>m has:

| f(x)-A | & lt； ε,

Then let's say that the function F takes A as the limit when X tends to +∞, and it is recorded as

Lim f(x) = A or f (x)->; A (x->; +∞)

4、 4! Factorial of 4 = 1×2×3×4.

Factorial factor refers to the required number obtained by multiplying 1 by 2 times 3 times 4.

For example, if the required number is 4, the factorial formula is 1×2×3×4, and the product is 24, that is, the factorial of 4. For example, if the required number is 6, the factorial formula is 1× 2× 3×…× 6, and the product is 720, which is the factorial of 6. For example, if the required number is n, the factorial formula is 1× 2× 3× …× n, and the product obtained is X, that is, the factorial of n. ..