超全超详细 人教版高中英语必修五各单元知识点总结

Book 5 Unit 1 Great Scientists

Part 1 课文知识点归纳

1. put forward 提出，将。。。提前

Several similar theories have been put forward over the years.

He put forward new peace proposals at the meeting.

The match has been put forward to 8:00 a.m.

Please inform them to put forward the sports meet for a week.

put off 推迟

The sports meet was put off because of the heavy rain.

Put aside 节省/储蓄，把。。。放到一边

He tries to put aside a little money every month.

They have put aside a lot of water for the dry season.

He took up a cigarette and then put it aside.

She put her work aside when the phone rang.

Let’s put aside this question for a moment.

Put away 放好/收起来(也有储存之意)

The old woman slowly put the cup of milk away and turned around. Please put those books away before leaving.

You should put some water/money away for tomorrow.

Put back 放回

Remember to put the chairs back after the meeting.

Put down 放下记下镇压

Tell him to put down the box for a while, it is really heavy.

I am putting down what my teacher said today in my notebook.

The riot was put down by the strong government very soon.

Put on 穿上上演

It is cold outside, don’t forget to put on your coat.

The famous movie will be put on again next week.

put into action/effect/practice实施/实行

We must put the plan into action/effect/practice as early as possible.

put up with 忍受

she never stops complaining, I can’t put up with her another day/any more.

Bear bear with 基本一样bear with多了理解、体谅的味儿。

I can’t bear this weather.

It is hard to bear criticism.

We should bear with his bad temper because he is unhappy these days.

Bear to do bear doing基本一样细微没做/做过

I left the room because I could n’t bear to listen any more.

He can’t bear to talk about it, even to me.

I can’t bear to see you like this.

I can’t bear being kept waiting.

2. attend to 照顾, 护理/专注于

The nurse is attending to a sick man.

You should attend to your studies.

3. cure sb. of sth 治愈某人某种疾病

As time goes on, doctors are now able to cure people of many diseases.

a cure for…治疗…法(药)

They have found a cure for the disease.

The cat is a good cure for mouse problem.

The traffic lights were proved to be a good cure for traffic problems.

4. challenge sb. to do sth. 向某人挑战做…

She challenged me to play a tennis game yesterday.

He is quite agile, do you dare to challenge him to climb the tree?

challenge sb. to sth. 就某事向某人挑战

Their school challenged ours to a basketball match.

Challenge for (sb)

Climbing a tree is a great challenge for that fat boy.

Challenge of (sth)

He is now facing a challenge of a speech.

Challenging

Teaching the children is a challenging job.

5. be absorbed in 全神贯注于= concentrate on

The children were absorbed in the cartoon at that time.

= The children were concentrating on the cartoon at that time.

The old scientist is always absorbed in his research.

= The old scientist always concentrates on his research.

Clever children usually absorb knowledge easily. 吸收

Be absorbed by…被。。。吸收/吞并

Aspirin is quickly absorbed by the body.

Several small countries were absorbed into the big one.

Absorb…into…吞并吸收

Can wild animals absorb this kind of food?

6. suspect sb. of sth 怀疑某人做某事

He was suspected of giving away government secrets to the enemy.

Why do you suspect her of taking the money?

suspect that…

The police suspected that it was the old man who stole the wallet.

We suspect that he is lost.

He is a political suspect.

The police are tracing a suspect.

7. blame sb. for sth. 为某事责怪某人

The teacher is blaming tom for breaking the window.

She is being blamed for her carelessness.

blame sth. on sb. 把某事归咎于某人

You shouldn’t blame the matter on him.

They decided to blame the accident on the driver.

be to blame for sth应受责备、对某事应负责任

The driver was not to blame for the traffic accident.

I feel it is your husband who is to blame for the spoiled child.

The mother didn’t know who to blame for the broken glass as it happened while she was out. bear/take/accept/get the blame for sth对某事承担责任

We should bear/take the blame for our failure.

lay/put the blame for sth on sb把某事归咎于某人

We shouldn’t l ay/put the blame for our failure on him.

8. link sth to/with 把…与…连接起来, 使…有联系

The wire is linked to/with the television.

The highway links Shanghai to/with Beijing.

Link up 连接/连接起来

A railway links up the two towns.

Be linked to…与。。。有关联/和。。。连接

Heart disease can be linked to smoking.

Theories should be linked to practice.

Link 做名词

Old friends are a link with the past.

9. instruct sb to do sth 命令某人做某事

The old general instructed his soldiers to cross the river.

I've been instructed to wait here until the lecturer arrives.

instruct sb in sth 在某方面教导某人

My job is to instruct her in English.

He instructed me in Kongfu every night those years.

10. be strict with sb. 对某人严格要求

The teacher is always strict with his students.

be strict in sth. 对某事严格要求

My parents are strict in my study.

11. lead to 导致/引向/通往

This may lead to difficulty in the furture.

All his calculations led to the same conclusion.

The road leads to the foot of the hill.

12. make sense 讲得通, 有意义，合理

It seems to make sense.

It seems to make sense to throw away old things.

Do such comparisons make sense?

make sense of 了解…的意义, 理解，搞清…的意思

Can you make sense of what he said?

I can’t make sense of what he said just now.

I can’t make sense of either Russian or Germany.

13. put sth. in order 按…顺序来整理，整理得整整齐齐，整理好When writing a story, you should put the things in order.

The girls always put her things in order.

Would you help me put things in order before we leave?

14. draw a conclusion 得出结论make a conclusion下结论

You can’t take just one day and draw a conclusion that the bear market is over.

Don’t make a conclusion before collecting enough data.

15. ease 减轻/消除，舒适/自在，减轻/消除某人的痛苦

These pills will ease the headache.

Her words gave ease to my distracted mind.

Walking helped to ease him of his pain.

at ease 放松自在安逸

With good social security, the old people can live at ease.

Be/feel at ease

I always don’t feel at ease in a strange place = I am always not at ease in a strange place. Put/set sb at one’s ease 使。。感到舒适、不拘束

The little is shy, we should try to put/set her at her ease.

With ease 容易地

Our football team won the match with ease.

16. expose… to 使显露, 暴露

Don’t expose yourself to the sun for too long a time.

He exposed the plan to the newpapers.

Never expose your soldiers to unnecessary risks.

Be exposed to…

It is very dangerous to be exposed to the viruses without any protection.

This medicine can’t be exposed to the sun.

17. apart from 除…之外= besides/except

Apart from his work, he has no interests.

Apart from English, he has a good command of Russian and French.

18. be cautious about / of …对…小心谨慎

The specialist reminds us to be cautious about/of online wills.

You should be cautious about/of making investments.

with caution 小心谨慎

You must always drive with caution.

It is dangerous, treat it with caution.

be careful about/of 对。。。注意

she is quite careful about/of her food/what she eats.

Be careful with…小心/注意处理

The vase is valuable, be careful with it.

Be careful not to do

The teacher is rather rigorous, be careful not to be late.

19. be severe with/on/upon sb. 对…严厉

Don’t be too severe with your children.

严重

The drought is becoming severe day by day.

表示“疾病严重”时，severe = serious

He suffered from a severe/serious illness those days.

表示“伤势、疼痛”只能用severe

I felt a severe pain in my chest. 剧烈的疼痛

He was severely injured in the accident.

20. lift up 举起提高

He is so strong that he can lift up the heavy case.

He lifted up his little son and mounted him on the horse.

To call back the boy from a distance, the father had to lift up his voice.

21. look into 调查

Take it easy please, the police are looking into the matter.

22. determine to do 决定做某事be determined to do sth 下决心做某事

Tom determined to have a trip the next weekend.

He is determined to get a high score/win the game next time.

I am determined to go to the countryside for my summer holiday for some time.(have determined错误，因determine to do表示动作，一时的决心，不与表示一段时间的时间状语连用)。

He has determined to give up smoking.

He is determined to stay here for a long time.

23. make investigations 进行调查

The reporter was often sent out to make investigations.

You should make full investigations before making a conclusion.

We often go out to make social investigations.

24. take in 吸收, 欺骗

The government plans to take in an investment of 1.6 billion.

The salesman found it easy to take in old ladies.

25. come to an end 结束

It hasn’t come to an end even after three years.

The long and boring meeting finally came to an end.

26. punish sb for sth. 因某事惩罚某人

The naughty boy was punished for breaking the window.

We should punish him for his carelessness.

27. at times 时而, 不时，时不时地

He is a real gentleman, but is a little pompous at times.

We play the badminton at times during the school days.

28. be for / against 支持/ 反对

We were all for/against his plan.

29. a link between…and…与…间的联系/关联

There is a definite link between the adult crime rate and the crime rate of youngsters.

30. point of view 观点(points of view)

Thanks for giving out your point of view.

Let’s take a different point of view to look at the problem.

31. hold discussions 进行讨论

The united nations is about to hold a discussion to reduce the danger of military confrontations. They are holding discussions about how to protect the animals in danger.

32. to one’s surprise 使某人感到惊奇的是

To my surprise, he passed the final exam.

33. believe in 信任, 信仰, 相信believe相信

I believe what said yesterday.

I always believe in him.

Some of his supporters have stopped believing in him.

34. stop/prevent sb (from) doing sth 阻止某人做某事keep sb from doing…不可省略

Be stopped/prevented/kept from doing…不可省略

35. in one’s honor / in honor of sb. 向…致敬，为纪念…

That year, the government set up a holiday in honor of the hero/in the hero’s honor.

They raised a flag in honor of the president.

We gave a dinner in honor of our guests.

Be/ feel honored to do …做…感到很荣幸

I am honored to speak on behalf of my group.

36. pass from传自于

Who used peas to show how physical characteristics are passed from parents to their children?

Pass to…传给

According to her will, the old lady’s money will pass to her grandson.

Pass from…to…从。。。传到。。。

The letter was passed from one to another until everyone had read it.

Pass sth to sb

The player passed the ball to his best teammate.

Pass to 转到

Now let me pass to the second phase.

37. exposed to…暴露于。。。

The soldiers in the open field are exposed to the enemy’s fire.

The boy was left exposed to the wind and rain.

He decided to help ordinary people exposed to cholera. Exposed过去分词做后置定语。

38, directly, immediately, instantly, the minute, the moment, the second 一。。。就。。。

She went to the crossing the moment she heard of the accident.

Each/every time 每当。。。

The boy asked his parents for money each/every time he went back home.

The last time 上次

The last time we met he said he needed another two days.

Next time 下次

Let’s talk about this matter next time we meet.

39, Advise sb to do...

He advises me to run for a while after school.

Advise doing = suggest doing

He advised/suggested taking a walk after dinner.

Advise/suggest that sb (should) do...

Uncle Wang advises/suggests that lilei (should) do morning exercises.

40, affected/moved

She was deeply affected/moved by my words.

41, be of great value/valuable(贵重的), priceless（无价的、价值连城的，意味强于valuable）Invaluable(无法估价的、无价的、珍贵的，不形容价值和金钱，重指品质)

Worthless（无价值的、无用的）valueless(无价值的)

The jewel is of great value, and it is priceless. 这珠宝很有价值，是无价之宝。

This ancient gold coin isn’t just valuable, it’s priceless.这枚古代金币不仅贵重，而且价值连城。Your advice is invaluable to us. 你的建议对我们来说是非常珍贵的。

The drawing is of no value, and it is worthless. 这画没有价值，它没有用。

It looks like gold, but in fact it is worthless/valueless. 这看起来像金子，其实毫无价值。

42, slow down （使）减速/慢下来

The bus is slowing down for the next stop.

The pills can slow down the development of the disease.

43, in addition = besides 但besides不能用于句尾

In addition, he suffered from a bad cold last month.

The man made him work 12 hours a day and beat him in addition.

In addition to… = besides/apart from

In addition to giving him some advice, I gave him thirty dollars.

He can get twenty dollars’ extra income every month in addition to his salary.

44, deliver sth to sb 交付/递送

Can you please help me deliver the letter to Mr.Wang?

45, be similar to 与。。。相似

My problems are similar to yours.

What I am going to say to you would be similar to what you are going to tell me.

be similar in 在。。方面相似

The two houses are similar in size.

The boys are similar in character.

46,

Conclude with/by doing…以。。。而结束

He concluded his speech with/by reading a poem.

Conclude from…从。。。推出结论

What do you conclude from these facts？

Conclude that…

The doctor concluded that the patient's disease was not serious.

To conclude/in conclusion 最后

To conclude/in conclusion, I wish you all good health and a long life.

Draw/arrive at/come to/reach a conclusion 得出结论

Did you draw a conclusion from what happened?

We can’t draw a conclusion that the bear market is over.

After a long discussion, they drew a conclusion in the end.

Jump to a conclusion 草率地得出结论

We can’t jump to a conclusion by now.

47,

Contribute 做贡献

Everyone should contribute what he or she can afford.

Contribute to 有助于、促成

Fresh air and exercise contribute to good health.

Contribute…to…捐赠、贡献

Everyone should contribute three dollars to the Red Cross.

I’ve been asked to contribute an article to the language magazine.

make a contribution to/towards…对。。。做贡献

He made an outstanding contribution to science last century.

48, 以only引导的短语作状语或状语从句放在句首时，为了加强语气，主句需要倒装。

Only by working hard can we succeed.

Only if you put the sun there did the movements of the other planets in the sky make sense.

make sense讲得通/有道理

What she said just now doesn’t make sense.

Your story doesn’t make sense to me.听不懂

Only if i get a job can I have enough money to continue my studies at college.

I wake up only if the alarm clock rings

If only “如果…就好了”, 后接虚拟条件句.

If only John were here with us!

If only he came back early.

49, rise raise arise

The sun rises from the east.

The father raised his son and put him on the horse.

That question did not arise.

Arise from/out of…由。。。而引起，从。。。中产生

Accidents usually arise from/out of carelessness.

The country's present difficulties arose from/out of the shortage of petroleum．

The trouble arose from/out of the radical policy.

50, have sth done 让。。。被。。。

I usually have my hair cut every 3 weeks.

We had the machine mended just now.

Please ask the patient to have his temperature taken.

A woman, who had moved away from Broad Street, liked the water from the pump so much that she had it delivered to her house every day.

51, with 的复合结构(with + 宾语+ 宾补)

He placed a fix sun at the center of the solar system with the planets going round it and only the moon still going round the earth.

with+n+adj

The boy often slept with his eyes open.

With+n+adv

We went back home with our work over.

With+n+介词短语

The teacher went into the classroom with a book in his right hand.

With+n+现分

The English class ended with all singing an English song.

With+n+过分

He stood there with his hands raised.

With+n+不定式

With something important to talk about with you, you must stay here.

With+n+条件、时间、原因

She didn’t go to work yesterday with her daughter being ill.

Please let me know with her coming.

Be enthusiastic about…对…热情/热心

People like coworkers who are enthusiastic about what they do.

Book 5 Unit 2 The United Kingdom

Part 1 课文知识点归纳

1. consist of = be made up of 由…组成

make up 组成, 编造, 化妆

The earth consists of/is made up of seven continents and four oceans.

Our class consists of/is made up of 60 students.

The girl makes up every morning before going to work.

The English teacher is good at making up nice sentences.

2. get all five questions right 五个问题全答对了

Did you get all the five questions right in today’s class.

I believe that she can get all the questions right.

3. divide… into…把…分成（把整体。。。分成）

The big house was divided into several parts.

The teacher plans to divide the students into 4 groups.

Please divide the cake into 6 parts.

Separate…into...（把连在一起的。。。分成）

The village is separated into 2 parts by the small river.

The woodworker separated the wooden board into 3 pieces.

separate…from 把…分离, 分开（非主观意愿，含被迫意味）

The kids were separated from their parents.

The civil war separated him from his family and sent him to Africa.

The war separated many families.

4. refer to 提到,涉及,参考,指的是

These books refer to Asian problems.

What he referred to in his new book is difficult to understand.

Want to know his phone number? You may refer to the phone directory.

The two words actually refer to the same meaning.

When they say so, they probably refer to what they will do next.

5. without conflict 没有纷争

You should find a way to assert yourself with conflict.

6. in the early / middle / late twentieth century

在二十世纪早期/ 中叶/ 后期

Many great scientists were born in the early / middle / late twentieth century.

7. break away (from) 脱离（含主观愿意意味）

He broke away from his country and joined an anti-war organization.

He broke away from the lawless group several years ago.

8. to one’s credit 为…带来荣誉/值得赞扬

To his credit, he admitted his mistakes.

To his credit, Mr. Bush himself has been learning how to do it.

To his credit, Graham never said that I was wrong.

9. for convenience 为了方便起见

Please pay in cash for convenience.

Please make it short for convenience.

For your convenience

For your convenience, I have gone through and summarized the entire story.

I will come as early as possible for your convenience.

At your convenience

Please send her the book at your convenience.

Still you have to do the work, but you can do it at your convenience.

At your earliest convenience

Please call her at your earliest convenience.

10. in the 1060s 在十一世纪六十年代

The great scientist was born in the 1060s.

They were all born in the 1980s.

11. find evidence of 找到…的证据

Researchers found evidence of brain rewiring through active learning.

Can you find more evidence of the dragon?

12. keep your eyes open 睁大眼睛，留意

Please keep your eyes open for a boy in a red cap and sweater.

13. make your trip enjoyable and worthwhile使得你的旅程有趣又值得

The summer holiday is coming, you should make a good plan and make your trip enjoyable and worthwhile.

14. leave out 省去, 遗漏, 不考虑

Keep what he said in your mind, leave out all the rest.

You have left out an important word in the sentence.

15. take the place/position of = take one’s place/position 取代…

16. break down 发生故障，毁坏，分解

Stop for a while, it may break down after a long-time work.

After many years, rocks broke down into dirt.

17. be unwilling to do…不乐意做…

He is always unwilling to help the old, you should teach him a lesson.

18. sb. be familiar with sth. 某人对…熟悉

sth. be familiar to sb. 某物对…是熟悉的

The teacher is familiar with all of his students.

He is a native here and is familiar with this city.

The famous singer is familiar to all of us.

19. a furnished house with all modern conveniences 一套有各种现代设施的配有家具的房子

Our foreign teacher wants to rent a furnished house with all modern conveniences nearby.

20. be alike in…在…方面类似

The two problems are alike in nature.

They are alike in character.

21. pick up

拾起，捡起

She picked up all the pieces on the floor when she left the classroom.

当她离开教室时，她把地上所有的碎片都捡了起来。

无意中/不费劲地学会

She soon picked up some French when she went to live in France.

收听，接收

My radio can pick up the BBC programs very clearly.

我的收音机能非常清楚地收听到英国广播公司的国际广播节目。

恢复健康，恢复体力

He soon picked up after a few days’ rest.他休息了几天，身体很快复原了。搭载；接某人

I’ll pick you up at 8 o’clock. 我会八点去接你。

接电话

I must pick up the phone whthin 5 seconds once it rings.

22. wear the four-hundred-year-old uniform穿着一件有四百年历史的制服Look! There is a man wearing the four-hundred-year-old uniform.

We will have a 3-week-long holiday next month.

Tom is a five-year-old boy.

They have a four-kilometer-long walk every day.

23. in memory of…为了纪念…

People built a large sculpture in memory of the hero.

I would like to take a picture of the old building in memory of my childhood.

24. just as…正当…的时候，正如…

The doorbell rang just as I was about to go to bed.

They won just as I expected.

25. have a photo taken (have sth. done) 拍照

I wish to have a photo taken with my friends.

26. on show/display 在展出

Some valuable paintings are on show/display today.

27. feel / be proud of 为…感到骄傲

We Chinese people are proud of our long history.

I must get a high score to make my parents feel proud of me!

28. leave …for…离开…前往…

When do you plan to leave home for the railway station?

He left his hometown for the big city that year.

29. fall asleep 睡着

She was so tired that she fell asleep very soon last night.

30. have problems in doing…做某事遇到麻烦

Do you often have problems in learning Russian?

The little girl always had problems in getting on with her schoolmates those years.

31. at one time 曾经，一度

They worked in the same company at one time.

32. break down 发生故障，毁坏，分解

Stop for a while, it may break down after a long-time work.

After many years, rocks broke down into dirt.

33. be delighted with 对…感到高兴

His family were delighted with his wise choice of profession.

34. take place （有计划地）发生,举行

A parade took place here in 1959.

Their wedding will take place next month.

35. at this / that time 在此时/ 在那时at the time of 在…的时候

We should avoid driving at this time of a day.

Was he cleaning the room at this time yesterday?

At that time, no one knew what had happened to the kids.

At the time of my birth, my family lived in Shanghai.

36. at war (with) 处于交战状态

They were at war with another country at that time.

37. be friendly to 对…友好

We should be friendly to the old people.

The girl is always friendly to small animals.

38. change one’s mind 改变主意

Are you sure that you will never change your mind?

Change one’s mind (not) to do….

He changed his mind not to go to hospital though he was badly injured.

Uncle Wang changed his mind to buy a new car instead.

39. be disappointed at 对…感到失望

The students were disappointed at their new school when they first saw it.

Are you disappointed at what he did yesterday?

40. come close to 接近

We can see them only when they come close to the earth.

41. took flight逃跑/逃之夭夭, 飞翔

Wolves took flight on hearing the gunshot.

How many times do you take flight in a year?

I will take flight 703. (乘坐703次航班)

42. start the fire 点火, 放火

Why did they start the fire in the fields?

43. make…into 把…制成, 使…转变为

We may make these old pieces of wood into a pretty desk.

句型: 1. How long does it take to fly from Beijing to London Heathrow Airport?

it takes sb. sometime to do sth. 花了某人多少时间做某事

2. These cities are not as large as those in China.

A 是B的三倍长: 1) _A is 3 times as long as B. ______

2) _A is 3 times the length of B.____

3) _A is 2 times longer than B._ ___

3. It’s a pity that the industrial cities built in the nineteenth century do not attract visitors.

built in the nineteenth century 过去分词短语作后置定语修饰cities

It’s a pity that…“遗憾的是…”常使用陈述语气; 若是跟虚拟语气, 常表示“竟然, 居然”等强烈的感情色彩.

[句型翻译]他错过了这次机会, 真是可惜

_It is a pity that he missed the chance.____

真可惜, 他竟然错过了这样好的一个机会.

高二英语Snow 南门Tel 83309000 _It is a pity that he should have missed such a good chance._____

4. Worried about the time available, Zhang Pingyu had made a list of the sites she wanted to

see in London.

Worried about the time available 过去分词短语作原因状语

5. This solid, square tower had remained standing for one thousand years.

remained standing 仍旧矗立着, remain 是一个系动词, 表示”一直保持着某种状态”

remain还可以作不及物动词, 意为”剩下, 保持”

Only several leaves remained on the tree.

The plane reamained on the ground for a long time because of the heavy rain.

6. There followed St. Paul’s Cathedral built after the terrible fire of London in 1666.

There followed…接下来的是

7. It seemed strange that the man who has developed communism should have lived and died

in London.

在主语从句中用来表示惊奇、惋惜、不满、理应如此等感情色彩时，谓语动词要用虚

拟语气“(should) +do”，常用的句型有：

It is necessary (important, natural, strange, etc.) that …

It is necessary that you (should) stay up late for the work tonight.

Book 5 Unit 3 Life in the future

make a deep / strong impression on sb.给某人留下深刻印象

The experience made a deep/strong impression on the children.

impress sb with sth = impress sth on sb 使某人记住某事（给…留下深刻印象）

Remember, never try to impress him with sexy clothes and make-ups.

= Remember, never try to impress sexy clothes and make-ups on him.

take up 拿起/拿出，接受，占据（时间/空间），开始从事

He insisted that we take up the matter on the meeting.

Don’t worry, I will take up my task.

Take up your courage and do what your heart tells you to do.

I hope that they will take up this challenge. 接受

Making up takes up a lot of her time.

Let’s move the piano out since it takes too much room.

He took up farming last year.

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（3）三角形中大边对大角，小边对小角； （4）正弦定理中,a =2R ·sin A , b =2R ·sin B , c =2R ·sin C ，其中R 是△ABC 外接圆半径. （5）在余弦定理中:2bc cos A =222a c b -+. （6）三角形的面积公式有:S = 21ah , S =21ab sin C=21bc sin A=2 1 ac sinB , S =))(()(c P b P a P P --?-其中，h 是BC 边上高，P 是半周长. 2、利用正、余弦定理及三角形面积公式等解任意三角形 （1）已知两角及一边，求其它边角，常选用正弦定理. （2）已知两边及其中一边的对角，求另一边的对角，常选用正弦定理. （3）已知三边，求三个角，常选用余弦定理. （4）已知两边和它们的夹角，求第三边和其他两个角，常选用余弦定理. （5）已知两边和其中一边的对角，求第三边和其他两个角，常选用正弦定理. 3、利用正、余弦定理判断三角形的形状 常用方法是：①化边为角；②化角为边. 4、三角形中的三角变换 （1）角的变换 因为在△ABC 中，A+B+C=π，所以sin(A+B)=sinC ；cos(A+B)=－cosC ；tan(A+B)=－tanC 。 2 sin 2cos ,2cos 2sin C B A C B A =+=+； （2）三角形边、角关系定理及面积公式，正弦定理，余弦定理。 r 为三角形内切圆半径，p 为周长之半 （3）在△ABC 中，熟记并会证明：∠A ，∠B ，∠C 成等差数列的充分必要条件是∠B=60°；△ABC 是正三角形的充分必要条件是∠A ，∠B ，∠C 成等差数列且a ，b ，c 成等比数列.

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