0高中数学诱导公式全集高三英语作文套题万能公式高考语文现(精)

1、高中数学诱导公式全集+高三英语作文套题万能公式+高考语文现代文规范答题模式 来源：马思超 schumi 的日志一、高中数学诱导公式全集：常用的诱导公式有以下几组：公式一：设a为任意角，终边相同的角的同一三角函数的值相等：sin(2kn+a)=sina (kZ)cos(2kn+a) =cosa(kZ)tan(2kn+ a) =tana(kZ)cot(2kn+ a) =cota( kZ)公式二：设a为任意角，n+的三角函数值与a的三角函数值之间的关系：sin( n+ a)=一 sinacos( n+ a)=一 cosatan( n+ a) tanacot( n+o) cota公式三： 任意角a与-

2、a的三角函数值之间的关系：sin(a) sinacos( a) COSatan( a) tanacot( a)cota公式四：利用公式二和公式三可以得到n a与a的三角函数值之间的关系：sin (n o) sinacos (n a) cosatan (n a)tanacot (n o) cota公式五：利用公式一和公式三可以得到2na与a的三角函数值之间的关系：sin (2n a sinacos (2n a)cosatan (2na tanacot (2n a) cota公式六：n/2 及%3n/2a a的三角函数值之间的关系：sin (n/+a) cosacos(n/+ a) sinatan

3、( n/+a) cotacot( n/+a) tanasin(n/ a) cosacos( n/ a) sinatan( n/ a) cotacot( n/2o) tanasin(3n/+ a cosacos(3n/+ a) sinatan(3n/2+ o) cotacot(3n/+a) tanasin(3n/ a) cosacos(3n/ a) sinatan(3n/ ) cotacot(3n/ ) tana(以 上 kZ注意：在做题时，将 a 看成锐角来做会比较好做。诱导公式记忆口诀规律总结上面这些诱导公式可以概括为：对于n/2*k ) Zk 的三角函数值， 当 k 是偶数时，得到a的同名

4、函数值，即函数名不改变；当 k 是奇数时，得到a相应的余函数值，即 sin cos;cos sin;tan cot,cot tan.(奇变偶不变)然后在前面加上把a看成锐角时原函数值的符号。(符号看象限)例如：sin(2 asin(4 /2, k 4 为偶数，所以取 sina当a是锐角时，2n a(270 360, sin(2naV0,符号为 ”。 所以 sin(2 兀a=sina上述的记忆口诀是：奇变偶不变，符号看象限。公式右边的符号为把a视为锐角时，角 k 360 +a(k Z), -a、180a360-a所在象限的原三角函数值的符号可记忆水平诱导名不变；符号看象限。#各种三角函数在四个象

5、限的符号如何判断，也可以记住口诀 一全正；二正弦(余割；三两切；四余弦(正割”.这十二字口诀的意思就是说：第一象限内任何一个角的四种三角函数值都是牛”； 第二象限内只有正弦是 牛”，其余全部是”；第三象限内切函数是牛”，弦函数是”；第四象限内只有余弦是 牛”，其余全部是”.上述记忆口诀，一全正,二正弦,三内切，四余弦#还有一种按照函数类型分象限定正负：函数类型 第一象限第二象限第三象限第四象限正弦.+.+. 余弦.+.+. 正切.+.+. 余 切.+.+.同角三角函数基本关系同角三角函数的基本关系式倒数关系：tana cotlasina csclacosa sda商的关系：sina/cos=t

6、anaseca/cscacosa/sin=eota=csca/seca平方关系：sinT(水 cosA2(a11 + tanA2(asecA2(a1 + cotA2(acscA2(同角三角函数关系六角形记忆法六角形记忆法：(参看图片或参考资料链接)构造以上弦、中切、下割；左正、右余、中间1的正六边形为模型。(1)倒数关系：对角线上两个函数互为倒数；(2)商数关系：六边形任意一顶点上的函数值等于与它相邻的两个顶点上函数值的乘积。(主要是两条虚线两端的三角函数值的乘积)。由此，可得商数关系式。(3)平方关系：在带有阴影线的三角形中，上面两个顶点上的三角函数值的平方 和等于下面顶点上的三角函数值的平

7、方。两角和差公式两角和与差的三角函数公式 sin (a+ B) asinaco+cosasinBsin (o = sinacos cosasinBcos( a+ B)acosacossinasinBcos( a B) acosaco 卅 sinasinBtan( a+ =(ta na+taj/(B-tanatanBtan( a =(ta natanB/ (1 + tana ta 二倍角公式二倍角的正弦、余弦和正切公式（升幕缩角公式）sin2a2sinaCOSacos2 斫 cosA2(彷 sinT(a2cosA2(卞1 = 1 2sinT(atan2a2tana/4tanT(a 半角公式半角的

8、正弦、余弦和正切公式(降幕扩角公式)sinA2(a/2(1COS/2 COsA2(a a(1+cos 2tan A2(a/2(1cos/(1+cosa另也有 tan(a/2= cosa/sina=sina/(1+万能公式万能公式sina=2tan(a/2/1+ta门八2(a/2sa=1a门八2(a/2/1+ta门八2(a/2tana=2tan(a-201八2(a/万能公式推导附推导：sin2a=2sinacosa=2sinacosa/(cosA2(a+sinA2(0因为.*cosA2(a+sinA2( ) =1再把*分式上下同除 cosA2(，可得 sin2a2tan /(1 +tanA2(a

9、然后用a/2 弋替a即可。同理可推导余弦的万能公式。正切的万能公式可通过正弦比余弦得到。 三倍角公式三倍角的正弦、余弦和正切公式sin3a3sin4sin八3(acos3a4cosA3(3cosatan3a3tanatanA3(/1 3ta门八2( 三倍角公式推导 附推导：tan3asin3a/cos3a=(sin2aco+ aos2asina/(cos2ainosasina =(2sinacosA2( cosA2(asi asinA3(a/(cosA cosasi门八2(2si门八2(acosa上下同除以 cosA3(a得：tan3a(3tantan八3(a-(1a门八2(asin3asin

10、(2+ aasin2aco+(cos2asina=2sinacosA2+12sin八2(asina =2sin(2sin八3(asin(2sin八3(a=3sin4sin八3(acos3acos(2+ a=cos2acossin2asina =(2cosA2(1cosa2cosaSinA2(a a2cosA3(acos+(2cosa2cosA3(a a4cosA3(a3cosa即 sin3a3sin 4sin八3(acos3a4cosA3( 3cos o 三倍角公式 联想记忆 记忆方法：谐音、联想正弦三倍角：3 元减 4 元 3 角(欠债了 (被减成负数，所以要 挣钱”音似正弦”)余弦三倍角：

11、4 元 3 角减 3 元(减完之后还有余”)注意函数名，即正弦的三倍角都用正弦表示，余弦的三倍角都用余弦表示。另外的记忆方法：正弦三倍角：山无司令(谐音为三无四立三指的是3 倍sina无指的是减号,四指的是4 倍，立指的是 sin(立方 余弦三倍角：司令无山与上同理和差化积公式三角函数的和差化积公二倍角的正弦、余弦和正切公式（升幕缩角公式）sin2a2sinaCOSa式 sin+sina2sin(+ B/2cos fW2sin(sina2cos(+ B/2sin(aB/2 cosO+ cosa2cos(+ B/2co B/2coscos3= 2sin(卅B/2 sir4(B a积化和差公式 二

12、角函数的积化和差公式sina eo0.5sin( +邮+ sin(-a B cosa Sr0.5sin(sin(立Bcosa co0.Bcos(-+B+ cos( B sina令0.5cos( + B cos(B和 差化积公式推导 附推导：首先，我们知道sin( a+b=s in a*cosb+cosa*s in b,s in( a-b=s in a*cosb-cosa*s inb我们把两式相加就得至 U sin(a+b+sin(a-b=2sina*cosb所以,sina*cosb=(sin(a+b+sin(a-b/2同理，若把两式相减，就得到 cosa*sinb=(sin(a+b-sin(a

13、-b/2同样的,我们还知道cos(a+b=cosa*cosb-sina*sinb,cos(a-b=cosa*cosb+sina*sinb所以,把两式相力卩，我们就可以得到 cos(a+b+cos(a-b=2cosa*cosb所以我们就得到,cosa*cosb=(cos(a+b+cos(a-b/2同理,两式相减我们就得到 sina*sinb=-(cos(a+b-cos(a-b/2这样,我们就得到了积化和差的四个公式：si na*cosb=(si n(a+b+si n(a-b/2cosa*si nb=(si n(a+b-s in (a-b/2cosa*cosb=(cos(a+b+cos(a-b/2

14、sin a*s in b=-(cos(a+b-cos(a-b/2 好，有了积化和差的四个公式以后，我们只需一个变形，就可以得到和差化积的四个公式. 我们把 上述四个公式中的 a+b设为 x,a-b 设为 y,那么 a=(x+y/2,b=(x-y/2 把 a,b 分别用 x,y 表示就可以得到和差化积的四个公式：sinx+si ny=2si n(x+y/2*cos(x-y/2sin x-si ny=2cos(x+y/2*si n( (x-y/2cosx+cosy=2cos(x+y/2*cos(x-y/2 cosx-cosy=-2si n(x+y/2*si n( (x-y/2 二、高考英语作文套题

15、万能公式：对比观点题型(1)要求论述两个对立的观点并给出自己的看法。1.有一些人认为2.另一些人认为.3. 我的看法. The topic of - (主题)is becoming moreand more popular rece ntly. There are two sides of opinions about it. Some people say A is their favorite.They hold their view for the reason of- (支持 A 的理由一) What is more,-理由二.Moreover,- (理由三.Whileothers t

16、hink that B is a better choice in the following three reasons. Firstly,-(支持 B 的理由一 .Secondly (besides-(理由二).Thirdly (finally,-(理由三.From my point of view, I think- (我的观点). The reason is that-(原因.As a matter of fact, there are some otherreasons to explain my choice. For me, the former is surely a wise

17、 choice ( 2) 给出一个观点，要求考生反对这一观点Some people believe tha-（观点一）.For example, they think - （举例说明）. And it will bring them -（为他们带来的好处.In my opin io n, I n ever thi nk this reason can be the point. For one thing-（我不同意该看法的理由一 .For an other thi ng,-（反对的理由之二.Form all what I have said, I agree to the thought t

18、ha-（我对文章所讨论主题的看法.阐述主题题型 要求从一句话或一个主题出发，按照提纲的要求进行论述.1.阐述名言或主题所蕴涵的意义.2.分析并举例使其 更充实. The good old proverb- （名言或谚语）reminds us that-（释义.In deed, we can leann many things form it. First of all,- （理由一.For example,-（举例说明.Secondly,- （理由二.Another case isthat- （举例说明.Furthermore ,-（理由三.In my opinion,-（我的观点.In sh

19、ort, whatever you do, please remember the say-A. If youun dersta nd it and apply it to your study or work, you” ll n ecessarily ben efit a lot fromit.解决方法题型 要求考生列举出解决问题的多种途径1.问题现状2.怎样解决（解决方案的优缺点In rece nt days, we have to face I problemA, which isbecomi ng more and more serious. First,-说明A的现状. Sec o

20、nd,-（举例进一步说明现状Confron ted with A, we should take a series of effectivemeasures to cope with the situation. For one thing,-解决方法一 .For another-（解决方法二.Fi nally,-（解决方法三.Person ally, I believe that （我的解决方法.Con seque ntly, I m con fide nt that a bright future is await ing us because （带来的好处.说明利弊题型这种题型往往要求先

21、说明一下现状，再对比事物本身的利弊，有时也会单从一个角度（利或弊）出发，最后往往要求考生表明自己的态度（或对事物前景提出预测）1.说明事物现状2.事物本身的优缺点（或一方面）3.你对现状（或前景）的看法 Nowadays ma ny peopleprefer A because it has a sig nifica nt role in our daily life. Gen erally, its adva ntages can be seen asfollows. First- （A的优点之一 .Besides-（A的优点之二）.But every coin has two sides.

22、 The negative aspects are also apparent. One of the(A的第一个缺点. To makematters worse,(A的第二个缺点.Through the above analysis, I believethat thepositive aspects overweigh the n egative on es. Therefore, I would like to- 我的看法.(From the comparis on betwee n these positive and n egative effects of A, we should

23、 take it reason ably and do it accord ing to the circumsta nces we are in. Only by this way,-(对前景的预测.议论文的框架(1 不同观点列举型(选择型) There is a widespread concern over the issue that 作文题目_. But it iswell known that the opinion concerning this hot topic varies from pers on to pers on. A majority of peoplethi n

24、k that _ 观点一_ .In their views there are 2 factorscon tribut ing to this attitude as follows: in the first place,_ 因一_ .Furthermore,in the sec ond place, _ 因二_ . So it goes without say ing that _ 点一_ .People, however, differ in their opinions on this matter. Some people hold the idea that点二.Intheir p

25、oint of view, on the one hand 原因一_ . On the other hand,_ 原因二_. Therefore, there is no doubt that_观点二_. As far as I am concerned, I firmly support the view that _观点一或二. It is not onlybecause_, but also because_The more_, the more_ . (2) 利弊型的议论文 Nowadays, there is awidespread concern over (the issue t

26、hat 作文题目_.In fact, there are bothadva ntages and disadva ntages in 题目议题_. Gen erally speak in g, it is widelybelieved there are several positive aspects as follows. Firstly, 优点一_ . Andimporta nt disadva ntages isthatsec on dly_ 点二_ . Just As a popular say ing goes, every coin has two sides,_讨论议题_is

27、no excepti on, and in ano ther word, it still has n egative aspects. Tobeg in with,_缺点一_.In additi on,_ 点二_ . To sum up, we shouldtry to bring the adva ntages of 讨论议题_ into full play, and reduce thedisadvantages to the minimum at the same time. In that case, we will definitely make a better use of t

28、he_ 论议题_ . ( 3 答题性议论文 Currently, there is a widespreadconcern over (the issue that 作文题目_ .It is really an important concern to every one of us. As aresult, we must spare no efforts to take some measures to solve this problem. As we know that there aremany steps which can be take n to undo this probl

29、em.First of all, _途径一_ .In additi on, ano ther way con tributi ng to success of thesolvi ng problem is_ 径二_ . Above all, to solve the problem of_ 乍文题目_, we should find a nu mber of various ways. But as far as I am concern ed, I would prefer to solvethe problem in this way, that is to say,_方法_ . ( 4

30、谚语警句性议论文 It is well know to us that the proverb: _ 谚语_ has a profoundsig nifica nee and value not only in our job but also in our study. It means_谚语的含义_ . The say ing can be illustrated through a series of examples as follows. ( alsotheoretically A case in point is_ 9 子一_. Therefore, it is goes with

31、out say ingthat it is of great of importa nee to practice the proverb _ 谚语_ . With the rapid developme nt of scie nee and tech no logy in Chi na, an increasingnumber of people come to realize that it is also of practical use to stick to the say ing: 谚语. Themore we are aware of the sig nifica nee of

32、this famous say ing,the more ben efits we will get in our daily study and job.图表作文的框架 as is shown/indicated/illustratedby the figure/percentage in the table(graph/picture/pie/chart,作文题目 的议题has been on rise/decrease(goesup/increases/drops/decreases,significantly/dramatically/steadily rising/decreasin

33、g frominto_ in_ . From the sharp/marked decli ne/ rise in thechart, it goes without saying that_ . There are at least two goodreasons accounting for_ . On the one hand,_ . On the otherhand, _ is due to the fact that_. In addition,_isresponsible for_. Maybe there are some other reasons to show_ . But

34、 it is gen erally believed that the above men ti oned reasons are commonly convincing. Asfar as I am concerned, I hold the point of view that. I am sure my opinion is both sound andwell-gro un ded.实用性写作(申请信 Your address Mon th, Date, year Receivers address Dear ., I amextremely pleased to hear from

35、you./ to see your advertiseme nt for the positi on in . And I would like towrite a letter to tell you that./ I am con fide nt that I am suitable for the ki nd of the job you are advertis ing. ./ I feel I am compete nt to meet the requireme nts you have listed. On the one han d, . On the otherhan d,

36、. I am en clos ing my resume for your kind con siderati on and refere nee. I shall be much obligedif you will offer me a precious opport unity to an in terview. I will greatly appreciate a resp onse from you atyour earliest convenien ce/ I am look ing forward to your replies at your earliest conveni

37、en ce. Bestregards for your health and success. Sin cerely yours, X XX 三、高考语文现代文规范答题模式：一、有关语言修辞的题型：描绘类 提问方式：某句话中某个词换成另一个行吗？为什么？或：文章的某个句子说成另一个句子好不好？为什么？答题模式：不行。因为该词生动具体（形象、准确）地写出了 +对象+效果，换了后就变成+不好的效果。或：不行，因为该词比另一 词的感情更强烈（或该词比另一词更切合对象的性格特征）。结构类 提问方式：某两个或三个词的顺序能否调换？为什么？答题模式：不能。因为（1）与人们认识事物的规律（由浅入深、由表入里

38、、由现象到本质）不一致（2）该词与上文是一一对应的关系（3）这些词是递进关系，环环相扣，表达了修辞类提问方式：这句话运用了什么修辞方法？这样写在表达上有什么好处？ 答题模式：确认修辞手法+修辞本身的作用+结合 句子语境 1.比喻、拟人：生动形象地写出了 +对象+特性。2.排比：有气势加强语气，一气呵成；层层铺开，逐步扩大，对点明主旨起强化作用等；强调 了 +对象+特性 3.对比：强调了突出了4.设问：引起读者对+对象 +特性的注意和思考 5.反问：强调，加强语气等； 6.反复：强调了 +加强语气二、有关布局谋篇的题型：提问方式：某句（段）话在文中有什么作用？ 答题模式：1.文首：开篇点题；照应

39、题目；总领全文；渲染气氛，埋下伏笔；设置悬念，为下文作辅垫。2.文中：承上启下；总领下文；总结上文；呼应前文。3.文末：点明中心；升华感情，深化主题；照应开头，结构严谨；画龙点睛；言有 尽而意无穷。三、有关表现手法的题型：艺术类提问方式：文章这样写有什么好处、效果、作用？答题模式：使用的方法+内容+效果（或作用） 人称类 提问方式：使用这种人称写的好处是什么？或：为什么要改变人称？答题模式： 第一人称：亲切、自然、真实，适于心理描写；第二人称：便于感情交 流，进行抒情，还能起拟人化的作用；第三人称：显得客观冷静，不受时空限制， 便于叙事和议论。四、有关归纳内容要点的题型：提问方式：请概括某一段（或全文）的内容要点。答题模式：分三步走，第一步划分本段的层次，第二步提取要点词语，第三步整合答案。五、有关鉴赏人物形象的题