【作业手册PPT】课时作业(二十一)

课时作业(二十一) [第21讲 简单的三角恒等变换](时间：45分钟 分值：100分)基础热身1．cos75°cos15°－sin255°sin15°的值是( )A ．0 B.12C.32 D ．－122．已知cos ⎝⎛⎭⎫α－π4＝14，则sin2α的值为( ) A.3132 B ．－3132C ．－78 D.783．设－3π<α<－5π2，则化简1－cos （α－π）2的结果是( ) A ．sin α2 B ．cos α2C ．－cos α2D ．－sin α24．已知α，β为锐角，cos α＝45，tan(α－β)＝－13，则tan β的值为( ) A.13 B.139 C.1315 D.59能力提升5．[2012·陕西卷] 设向量a ＝(1，cos θ)与b ＝(－1，2cos θ)垂直，则cos2θ等于( )A.22B.12C ．0D ．－16．[2011·杭州二中仿真] 已知tan β＝43，sin(α＋β)＝513，其中α，β∈(0，π)，则sin α的值为( ) A.6365 B.3365C.1365D.6365或3365 7．[2012·北京四中期中] 若f (x )＝2tan x －2sin 2x 2－1sin x 2cos x 2，则f π12的值为( ) A ．4 3 B.833 C ．4 D ．88．[2012·台州中学模拟] 在△ABC 中，角A ，B ，C 所对的边分别为a ，b ，c ，满足：cos2A ＋52cos A ＝sin ⎝⎛⎭⎫π3＋B ·sin π3－B ＋sin 2B ，则A 等于( ) A.π6 B.π4 C.π3 D.π29．[2012·江西卷] 已知f (x )＝sin 2⎝⎛⎭⎫x ＋π4，若a ＝f (lg5)，b ＝f ⎝⎛⎭⎫lg 15，则( )A ．a ＋b ＝0B ．a －b ＝0C ．a ＋b ＝1D ．a －b ＝110．[2012·岳阳一中月考] 函数f (x )＝sin 22x －π4的最小正周期是________． 11．[2012·自贡诊断] 若f (x )是以4为周期的奇函数，f ⎝⎛⎭⎫12＝1，且sin α＝14，则f (4cos2α)＝________． 12．已知sin2α＋2sin 2α1＋tan α＝k ⎝⎛⎭⎫π4<α<π2，用k 表示sin α－cos α的值等于________． 13．[2012·哈尔滨一中期中] 若点P (cos α，sin α)在直线y ＝－2x 上，则sin2α＋2cos2α＝________．14．(10分)已知函数f (x )＝cos 2x －3sin x cos x ＋1.(1)求函数f (x )的单调递增区间；(2)若f (θ)＝56，θ∈⎝⎛⎭⎫π3，2π3，求sin2θ的值．15．(13分)[2013·浏阳一中月考] 已知函数f (x )＝2cos 2x 2－3sin x . (1)求函数f (x )的最小正周期和值域；(2)若α为第二象限角，且fα－π3＝13，求cos2α1＋cos2α－sin2α的值．难点突破16．(12分)[2013·山西大学附中月考] 已知A ，B ，C 为锐角△ABC 的三个内角，向量m ＝(2－2sin A ，cos A ＋sin A )，n ＝(1＋sin A ，cos A －sin A )，且m ⊥n .(1)求A 的大小；(2)求y ＝2sin 2B ＋cos 2π3－2B 取最大值时角B 的大小．课时作业(二十一)【基础热身】1．B [解析] 原式＝cos75°·cos15°＋sin75°sin15°＝cos(75°－15°)＝cos60°＝12. 2．C [解析] 方法一：sin2α＝cos ⎝⎛⎭⎫π2－2α＝2cos 2⎝⎛⎭⎫α－π4－1＝－78，故选C. 方法二：cos ⎝⎛⎭⎫α－π4＝22cos α＋22sin α＝14， 两边平方得，12＋12sin2α＝116， ∴sin2α＝－78，故选C. 3．C [解析] ∵－3π<α<－52π，∴－32π<α2<－54π， ∴cos α2<0， ∴原式＝1＋cos α2＝⎪⎪⎪⎪cos α2＝－cos α2. 4．B [解析] ∵α是锐角，cos α＝45，故sin α＝35，tan α＝34， ∴tan β＝tan[α－(α－β)]＝tan α－tan （α－β）1＋tan αtan （α－β）＝139. 【能力提升】5．C [解析] 由向量垂直的充要条件可知，要使两向量垂直，则有－1＋2cos 2θ＝0，则cos2θ＝2cos 2θ－1＝0.故选C.6．A [解析] 根据α，β∈(0，π)，求出sin β＝45，cos β＝35，判断角的范围，求出cos(α＋β)＝－1213， 所以sin α＝sin[(α＋β)－β]＝sin(α＋β)cos β－cos(α＋β)sin β＝6365. 7．D [解析] f (x )＝2tan x －2sin 2x 2－1sin x 2cos x 2＝2sin x cos x ＋1－2sin 2x 212sin x ＝2sin x cos x ＋2cos x sin x ＝2（sin 2x ＋cos 2x ）sin x cos x ＝4sin2x ， 所以f π12＝4sin π6＝8. 8．C [解析] 化简原式可得8cos 2A ＋10cos A －7＝0，求得cos A ＝12，得A ＝π3. 9．C [解析] 函数f (x )＝sin 2⎝⎛⎭⎫x ＋π4＝12⎣⎡⎦⎤1－cos2⎝⎛⎭⎫x ＋π4＝12＋12sin2x ，∵f (lg5)＋f (－lg5)＝1＋12[sin(2lg5)＋sin(－2lg5)]＝1＋12[sin(2lg5)－sin(2lg5)]＝1，∴a ＋b ＝1.故选C. 10.π2 [解析] 对解析式进行降幂扩角，转化为f (x )＝－12cos4x －π2＋12，可知其最小正周期为π2. 11．－1 [解析] 由sin α＝14可得4cos2α＝4(1－2sin 2α)＝4⎣⎡⎦⎤1－2×⎝⎛⎭⎫142＝72， 所以f (4cos2α)＝f ⎝⎛⎭⎫72＝f ⎝⎛⎭⎫－12＝－f ⎝⎛⎭⎫12＝－1. 12.1－k [解析] 由已知等式得2sin α（cos α＋sin α）cos αcos α＋sin αcos α＝k ，整理得2sin αcos α＝k . ∵π4<α<π2，∴sin α－cos α>0，得sin α－cos α＝1－2sin αcos α＝1－k . 13．－2 [解析] 由已知得sin α＝－2cos α，即tan α＝－2，所以sin2α＋2cos2α＝2sin αcos α＋2cos 2α－2sin 2α＝2sin αcos α＋2cos 2α－2sin 2αsin 2α＋cos 2α＝2tan α＋2－2tan 2αtan 2α＋1＝－2. 14．解：(1)f (x )＝cos 2x －3sin x cos x ＋1 ＝1＋cos2x 2－32sin2x ＋1＝cos ⎝⎛⎭⎫2x ＋π3＋32. 由2k π＋π≤2x ＋π3≤2k π＋2π(k ∈Z )，得k π＋π3≤x ≤k π＋5π6(k ∈Z )． ∴函数f (x )的单调递增区间是⎣⎡⎦⎤k π＋π3，k π＋5π6(k ∈Z )． (2)∵f (θ)＝56，∴cos ⎝⎛⎭⎫2θ＋π3＋32＝56， cos ⎝⎛⎭⎫2θ＋π3＝－23. ∵θ∈⎝⎛⎭⎫π3，2π3，∴2θ＋π3∈⎝⎛⎭⎫π，5π3， sin ⎝⎛⎭⎫2θ＋π3＝－1－cos 2⎝⎛⎭⎫2θ＋π3＝－53. ∴sin2θ＝sin ⎝⎛⎭⎫2θ＋π3－π3＝12sin ⎝⎛⎭⎫2θ＋π3－ 32cos ⎝⎛⎭⎫2θ＋π3＝23－56. 15．解：(1)∵f (x )＝1＋cos x －3sin x ＝1＋2cos x ＋π3， ∴函数f (x )的周期为2π，值域为[－1，3]．(2)∵fα－π3＝13，∴1＋2cos α＝13， 即cos α＝－13. cos2α1＋cos2α－sin2α＝cos 2α－sin 2α2cos 2α－2sin αcos α＝（cos α＋sin α）（cos α－sin α）2cos α（cos α－sin α）＝cos α＋sin α2cos α. 又∵α为第二象限角，∴sin α＝223， ∴原式＝cos α＋sin α2cos α＝1－222. 【难点突破】16．解：(1)∵m ⊥n ，∴m ·n ＝(2－2sin A )(1＋sin A )＋(cos A ＋sin A )(cos A －sin A )＝0，即2(1－sin 2A )＝sin 2A －cos 2A ，∴2cos 2A＝1－2cos 2A ⇒cos 2A ＝14. ∵△ABC 是锐角三角形，∴cos A ＝12，得A ＝π3. (2)△ABC 是锐角三角形，且A ＝π3， ∴π3<B <π2. ∴y ＝2sin 2B ＋cos 2π3－2B ＝1－cos2B －12cos2B ＋32sin2B ＝32sin2B －32cos2B ＋1＝3sin2B －π3＋1. 当y 取最大值时，2B －π3＝π2，即B ＝512π.。

毛额市鹌鹑阳光实验学校课时作业(二十一) [模块7 Unit 21 Human Biology](限时：40分钟)Ⅰ.单项填空1．If we sit near ________ front of the bus, we'll have ________ better view.A．/; the B．/; aC．the; a D．the; the2．The new movie ________ to be one of the biggest money­makers of all time.A．promises B．agreesC．pretends D．declines3．Do you agree or________ the plan? You have a say about this.A．oppose B．refuseC．object D．demand4．He didn't make________clear when and where the meeting would be held.A．these B．thisC．it D．that5．As time went on, those unpleasant events were gradually________ from his memory.A．wiped out B．stood outC．cleaned out D．put out6．If we________ other people's love and trust in us, we will be cast aside by others one day.A．hold B．takeC．abuse D．have7．Every classroom in this modern school is________ with a new TV set.A．equipped B．preparedC．fixed D．placed8．The passengers were robbed________all their money in broad daylight.A．of B．offC．from D．away9．In recent years travel companies have succeeded in selling us the idea that the further we go，________．A．our holiday will be betterB．our holiday will be the betterC．the better our holiday will beD．the better our holiday be10．________ thousands of people outside; it was too noisy.A．There seemed to beB．There seemed to haveC ．It seemed to beD ．It seemed to have Ⅱ.完形填空In a national spelling contest in America, an 11­year­old girl wasasked to spell a certain word.But with her __11__ voice the judges were not sure if she spelled the word with the letter “a” or “e”. They talked it over and __12__ decided to simply ask her what she had said.By now, the girl knew she had __13__ the word.But instead of lying, she told the truth that she had said the __14__ letter —so she lost the contest.As the girl walked off the __15__ , the entire audience stood to their feet clapping to applaud her __16__. Later, dozens of newspaper reporters wrote about this 11­year­old gi rl's honesty, even when it __17__ her the contest. But the fact is that she __18__ the biggest contest that day: the contest of her __19__．Probably the biggest test of our character is what we would do if we knew we would never get __20__. This young girl could easily have __21__ and nobody would have known it but herself. But that's just it: She would know she did wrong. It's been said, “If you __22__ , you make yourself cheap.” This young girl was strong and smart enough to prize her own __23__ and character rather than the prize from a spelling __24__. Her respect for herself was more important than any__25__ others might give her for winning a contest. She knew she would have to live with herself and the __26__ she made in that moment will have long­lasting influence.It's so true that the choices you make today __27__ what you aretomorrow. Our children will __28__ our behaviour much more than our advice. So if we want them to __29__ to be honest, we must show them the way by being honest ourselves. Remember, our kids are __30__ what we do and how we live even when we don't think they see or know. 11．A.high B ．sweet C ．tough D ．soft12．A.finally B ．kindly C ．secretly D ．totally13．A.forgotten B ．mispronouncedC ．misspelledD ．lost14．A.correct B ．wrong C ．different D ．same 15．A.stage B ．studio C ．test D ．classroom16．A.bravery B ．honestyC ．courageD ．cleverness 17．A.cancelled B ．cost C ．offered D ．wasted18．A.achieved B．brokeC．won D．defeated19．A.reputation B．knowledge C．life D．character20．A.paid B．awarded C．caught D．reported21．A.escaped B．lied C．changed D．answered22．A.accept B．fight C．cheat D．insist23．A.conscience B．feeling C．diligence D．modesty24．A.contest B．champion C．judge D．expert25．A.sense B．pride C．respect D．awareness26．A.plan B．conclusion C．discovery D．choice27．A.make B．change C．keep D．create28．A.give B．takeC．follow D．set29．A.grow up B．bring upC．take up D．come up30．A.recording B．inspectingC．correcting D．watchingⅢ.阅读理解AThe poor are very wonderful people. One evening we went out and we picked up four people from the street. And one of them was in a most terrible condition－and I told the sisters: You take care of the other three. I take care of this one who looks worse. So I did for her all that my love can do. I put her in bed, and there was such a beautiful smile on her face. She took hold of my hand as she said just the words “Thank you” and she died.I could not help but examine my conscience before her and I asked what I would say if I was in her place. And my answer was very simple.I would have tried to draw a little attention to myself. I would have said I am hungry, I am dying, I am cold, I am in pain, or something, but she gave me much more－she gave me her grateful love. And she died with a smile on her face. So did that man whom we picked up from the drain, half eaten with worms, and we brought him to the home. “I have lived like an animal in the street, but I am going to die like an angel, loved and cared for”， he said at the end. And it was so wonderful to see thegreatness of that man who could speak like that, who could die like that without blaming anybody, without cursing anybody, without comparing anything. Like an angel－this is the greatness of our people. And that is why we believe what Jesus has said: I was hungry, I was naked, I was homeless, I was unwanted, unloved, uncared for, and you did it to me.And with this prize that I received as a Prize of Peace, I am going to try to make the home for many people who have no home. Because I believe that love begins at home and if we can create a home for the poor I think that more and more love will spread. And we will be able through this understanding love to bring peace, the good news to the poor, the poor in our own family first, in our country and in the world. When I pick up a person from the street, hungry and I give him a plate of rice or a piece of bread, I have satisfied. I have removed that hunger. But to a person who is shut out, who feels unwanted, unloved, terrified, who has been thrown out from society, that poverty is so full of hurt and so unbearable… And so let us always meet each other with a smile, for the smile is the beginning of love, and once we begin to love each other naturally we want to do something.31. What can be learned from the second paragraph?A．The woman should have paid more attention to herself.B．The man couldn't blame anyone.C．The author is religious.D．The man died in the street.32．The purpose of this passage is ________．A．to appeal for more donation for the poorB．to call on the public to love each otherC．to tell the readers the poor are wonderfulD．to express how moved the author is to receive the prize33．Which of the following can NOT be inferred from the passage?A．The author has few supporters.B．The author was somewhat surprised at what the man said.C. The author is delighted to help others in trouble.D．The author may agree to solve social problems in soft ways.34. What's the best title of this passage?A．Have Sympathy for the PoorB．The Poor are WonderfulC．Smile and LoveD．Relieve PovertyBInformation has always been at the center of human communication.You may ask why.Well，communication between people contains giving and receiving information.The way we give and receive information today has experienced a revolution in the development of the mass media in the 20th century.The first truly mass communication medium was the newspaper.For the first time in history people could read about events in their country and from around the world every day. However there were two problems with newspapers of that time.Firstly，newspapers were available only in large cities，for getting newspapers to the countryside was a difficult and time­consuming(耗时的)task.Secondly, newspapers weren't always reliable, as there was a limited range of opinions.Nowadays，we can choose from a wide variety of sources to get information.Television and the Internet have given us the chance to be informed about everything the minute it rge numbers of radio and TV stations，satellite channels and millions of websites help people keep up with the latest news.People live in history and are part of it.The media have come a long way in the last century and there is no doubt that we now live in the information age. Whatever type of media we choose，it all comes down to the need for information.This will always be a basic need as long as communication is part of human nature.35．Information is considered the center of human communication because________．A．human communication means information exchangeB．human communication involves people's participationC．information is now experiencing a revolutionD．information helps people gather together36．What was the historical contribution of the newspaper as a source of information?A．It made the mass communication truly develop.B．It helped the mass communication develop in cities.C．It kept people timely informed about home and world events.D．It kept reliable information available in big cities.37．The third paragraph mainly tells us that technologyhelps________．A．make information easily availableB．people be part of historyC．inform everything timelyD．produce the latest news38．It can be concluded from the last paragraph that a basic need today is________．A．communicationB．informationC．high technologyD．media typesⅣ.短文改错Today I attended in the English Corner. It was the first time that an English Corner had held in our school. Many teachers, included some English teachers, went there. The Students' Union even invited Mr. Smith,a honored guest, to the English Corner. He introduces some western customs and also encouraged us student to learn to speak English freely. But when I had a chance to talk, I felt a bit nervously and was at a loss how to say. It took me some time to get used to speak fluent English.I was determined to take part in so wonderful activities as often as possible.参考答案课时作业(二十一)Ⅰ.1. C2. A 考查动词意义辨析。

课时作业(二十一)Ⅰ.[文章大意] 本文介绍了屠呦呦因发现青蒿素，研制出治疗疟疾的重要药物而获得诺贝尔生理学或医学奖，从而使人们更加关注中药的价值。

1．B细节理解题。

根据文章第一段第一句“…the Nobel Prize in Physiology(生理学) or Medicine…”以及第一段最后一句“…the Lasker-DeBakey Clinical Medical Research Award.”可知，本文提及屠呦呦所获的两个奖项。

故选B项。

2．D词义猜测题。

根据文章第二段画线词所在句“…reduced death rates among patients suffering from malaria.”中的death rate以及patient可知，malaria应为一种让病人死亡的“疾病(disease)”。

故选D项。

3．C细节理解题。

根据文章最后一段第二、三句“屠呦呦的成功会引发人们对中医的认可与尊重，西方国家应该学习欣赏中医的价值”可知，A项中的Easterners(东方人)错误，C项“全世界应更多地对中医价值进行研究”符合原文，故选C项。

B项的nothing以及D 项的only太绝对，排除B、D两项。

4．B主旨大意题。

全文主要描述屠呦呦所发现的青蒿素(一种中医药)让其获得诺贝尔生理学或医学奖，主要原因在于这种传统中药可有效用于治疗疟疾，从而引发人们对中医价值的重视。

由此可知，B项“诺贝尔奖得主屠呦呦强烈支持中医研究”符合文章主旨。

故选B项。

Ⅱ.[文章大意] 本文主要介绍了青少年和父母相处的问题。

1．A年轻人常觉得与父母在一起会感到不自在，空白处所在段均是年轻人的种种想法，故主语应该是they开头，且从空白处的下句也可得到暗示。

故选A项。

2．D根据本段第三、四句可知，成年人更容易担心，他们大多数都提前计划事情。

而第一、二句说的是年轻人的做法，故D项(年轻人喜欢不思考太多就行动)符合语境。