Senior High School Mathematics Compulsory Two Formulas Summary Daquan Senior High School Compulsory Two Mathematical Formulas Knowledge Summary Article 1
Formula 1:
Let α be an arbitrary angle, and the values of the same trigonometric function with the same angle of the terminal edge are equal:
sin(2kπ+α)=sinα
cos(2kπ+α)=cosα
tan(2kπ+α)=tanα
cot(2kπ+α)=cotα
Equation 2:
Let α be an arbitrary angle, and the relationship between the trigonometric function value of π+α and the trigonometric function value of α;
Sine (π+α) =-Sine α
cos(π+α)=-cosα
tan(π+α)=tanα
cot(π+α)=cotα
Formula 3:
The relationship between arbitrary angle α and the value of-α trigonometric function;
Sine (-α) =-Sine α
cos(-α)=cosα
tan(-α)=-tanα
Kurt (-α) =-Kurt α
Equation 4:
The relationship between π-α and the trigonometric function value of α can be obtained by Formula 2 and Formula 3:
Sine (π-α) = Sine α
cos(π-α)=-cosα
tan(π-α)=-tanα
cot(π-α)=-coα
Formula 5:
The relationship between 2π-α and the trigonometric function value of α can be obtained by formula 1 and formula 3:
Sine (2π-α)=- Sine α
cos(2π-α)=cosα
tan(2π-α)=-tanα
Kurt (2π-α)=- Kurt α
Equation 6:
The relationship between π/2 α and 3 π/2 α and the trigonometric function value of 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
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
Summarize regularly
The above inductive formula can be summarized as follows:
For the trigonometric function value of k π/2 α (k ∈ z),
① When k is an even number, the function value of α with the same name is obtained, that is, the function name is unchanged;
② When k is an odd number, the cofunction value corresponding to α is obtained, that is, sin→cos；; cos→sin； Tan → Kurt, Kurt → Tan.
(Odd and even numbers remain the same)
Then when α is regarded as an acute angle, the sign of the original function value is added.
(Symbols look at quadrants)
For example:
Sin (2π-α) = sin (4 π/2-α), and k=4 is an even number, so we take sinα.
When α is an acute angle, 2 π-α ∈ (270,360), sin (2π-α)
So sin(2π-α)=-sinα.
The above memory formula is:
Odd couples, symbols look at quadrants.
The symbols on the right side of the formula are angles k 360+α (k ∈ z),-α, 180 α, and when α is regarded as an acute angle, it is 360-α.
The sign of the original trigonometric function value in the quadrant can be memorized.
The name of horizontal induction remains unchanged; Symbols look at quadrants.
The second part of the compulsory second part of senior high school is a summary of mathematical formula knowledge.
Basic relations of trigonometric functions with the same angle
1. The basic relationship of trigonometric functions with the same angle.
Reciprocal relationship:
tanα cotα= 1
sinα cscα= 1
cosα secα= 1
Relationship between businesses:
sinα/cosα=tanα=secα/cscα
cosα/sinα=cotα=cscα/secα
Square relation:
sin^2(α)+cos^2(α)= 1
1+tan^2(α)=sec^2(α)
1+cot^2(α)=csc^2(α)
Hexagon memory method of equilateral trigonometric function relationship
Hexagonal mnemonics: (see pictures or links to resources)
The structure is "winding, cutting and cutting; Zuo Zheng, the right remainder and the regular hexagon of the middle 1 "are models.
(1) Reciprocal relation: The two functions on the diagonal are reciprocal;
(2) Quotient relation: the function value at any vertex of a hexagon is equal to the product of the function values at two adjacent vertices.
(Mainly the product of trigonometric function values at both ends of two dotted lines). From this, the quotient relation can be obtained.
(3) Square relation: In a triangle with hatched lines, the sum of squares of trigonometric function values on the top two vertices is equal to the square of trigonometric function values on the bottom vertex.
Two-angle sum and difference formula
2. The sum and difference of formulas of trigonometric functions.
sin(α+β)=sinαcosβ+cosαsinβ
sin(α-β)=sinαcosβ-cosαsinβ
cos(α+β)=cosαcosβ-sinαsinβ
cos(α-β)=cosαcosβ+sinαsinβ
Summary of Mathematics Formula Knowledge for Senior One and Senior Two Chapter III
Derivation of triple angle formula
Additional derivation:
tan3α=sin3α/cos3α
=(sin 2αcosα+cos 2αsinα)/(cos 2αcosα-sin 2αsinα)
=(2sinαcos^2(α)+cos^2(α)sinα-sin^3(α))/(cos^3(α)-cosαsin^2(α)-2sin^2(α)cosα)
Divided by COS 3 (α), we get:
tan3α=(3tanα-tan^3(α))/( 1-3tan^2(α))
sin 3α= sin(2α+α)= sin 2αcosα+cos 2αsinα
=2sinαcos^2(α)+( 1-2sin^2(α))sinα
=2sinα-2sin^3(α)+sinα-2sin^2(α)
=3sinα-4sin^3(α)
cos 3α= cos(2α+α)= cos 2αcosα-sin 2αsinα
=(2cos^2(α)- 1)cosα-2cosαsin^2(α)
=2cos^3(α)-cosα+(2cosα-2cos^3(α))
=4cos^3(α)-3cosα
that is
sin3α=3sinα-4sin^3(α)
cos3α=4cos^3(α)-3cosα
Extended reading: summary of compulsory English knowledge points in unit one of senior high school 1
1. Investigation and study
2. Stick to/insist on something/do it and do it resolutely.
3. belong to
4. Get/get lost; missing
5. do the treatment; deal with
6. looking for; Looking for it.
Get used to doing sth. Be used to doing sth.
Be used to doing sth. Be used to doing sth.
9. can be made ... is made;
Made of ... (raw materials are visible/invisible)
Do for ... ...
consist of
10.be+ abstract noun =be+ adjective of word
"be of+ noun (phrase)" indicates a certain shape or feature of the subject.
Belong to (n)/ the same "belong to, belong to"
Figure/weight/height/age/skin color/type …
1 1. amber artwork
12. As a gift of ... ...
13. In return
14. Become a part of ... ...
15. Play the role of ….
16. Add … to … Add … to …
17. Great miracle in the world.
18. In a state of war.
19. Less than
20. Undoubtedly
2 1. remains a mystery.
22. take it apart
23. It's better to say no than to compare.
to tell the truth
Pretend to do sth.
27. Give an example from your own life. Give an example from your life.
28. Highly value.
29. Looking for = looking for
Agree with sb. Agree with sb.
3 1. The modal verb (can/may/must/should)+has been done.
Express speculation, criticism, regret, etc about what happened in the past.
32. Have something. Done means "ask someone to do something" and "cause something (unfortunately) to happen"
2 unit
Join/join.
2 spirit, purpose and spirit of soul
be accustomed to
Find out
Every four years, every three years.
6 two sets of two sets
Allow sb. In (out) enter (out);
Allow sb. Do sth. Allow sb to do sth.
Allow to do sth. Allow to do sth.
10 be/ Get married (emphasize state) +to (cannot be used with ...) Get married. ...
1 1 one set.
12 Participate in ... compete in some way.
13 for ... competition ...
Compete with ... ...
Be allowed to do sth.
16 was admitted as …
17 standards reached, levels and standards reached. ...
Play an important role in … ...
19 and the same ...
Thank you for your time ...)
2 1 comes from the same root
Have (no) chance to do sth. Have (have) a chance to do it. ...
Accompanied by, accompanied by ...
Be associated with.
relate to ...
Violate ... confront ... ...
I heard that I heard that.
28 ensure
29 take turns
30 one by one
Make sure that clause is all right
Unit 3
1. Sounds simple.
2. Technological revolution. Technological revolution
3. Artificial intelligence
4. At first, it was ...
Step 5 solve the problem, solve the problem
6. A simple-minded person is a simple-minded person
7. Mathematical problems. Mathematical problems
8. It has been completely changed.
9. Share information with * * *
10. Serve mankind, serve mankind.
1 1. Common sense
12. Processing
13. In my opinion.
14. Public opinion; popular will
15 An analysis method
16. Share a room with … * * *
17. Contact with ... is related to ... ...
18. After (after) ...)
19. Make it effective.
20. Ordinary people
2 1. polymerization
22. After all, after all
With the help of ... ...
24. make up, make up
25. Personal letters. Personal letters
26. Guard guards and monitors
27. Have a good time.
28. Once a year is an annual event.
29. make a decision