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1、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：设为任意角，终边相同的角的同一三角函数的值相等：sin（2k）sin （kZ）cos（2k）cos （kZ）tan（2k）tan （kZ）cot（2k）cot （kZ）公式二：设为任意角，+的三角函数值与的三角函数值之间的关系：sin（）sincos（）costan（）tancot（）cot公式三：任意角与 -的三角函数值之间的关系：sin（）sincos（）costan（）tancot（）cot公式四：利用公式二和公式三可以得到-与的三角函数值之间的关系：sin（）sincos（）costan（）tancot（）cot公式五：利用公
2、式一和公式三可以得到2-与的三角函数值之间的关系：sin（2）sincos（2）costan（2）tancot（2）cot公式六：/2及3/2与的三角函数值之间的关系：sin（/2）coscos（/2）sintan（/2）cotcot（/2）tansin（/2）coscos（/2）sintan（/2）cotcot（/2）tansin（3/2）coscos（3/2）sintan（3/2）cotcot（3/2）tansin（3/2）coscos（3/2）sintan（3/2）cotcot（3/2）tan(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
3、可以概括为：对于/2*k (kZ)的三角函数值，当k是偶数时，得到的同名函数值，即函数名不改变；当k是奇数时，得到相应的余函数值，即sincos;cossin;tancot,cottan.（奇变偶不变）然后在前面加上把看成锐角时原函数值的符号。（符号看象限）例如：sin(2)sin(4/2)，k4为偶数，所以取sin。当是锐角时，2(270，360)，sin(2)0，符号为“”。所以sin(2)sin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视为锐角时，角k360+（kZ），-、180，360-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
4、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“”；第二象限内只有正弦是“”，其余全部是“”；第三象限内切函数是“”，弦函数是“”；第四象限内只有余弦是“”，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:tan cot1sin csc1cos sec1商的关系：sin/costansec/csccos/sincotc
5、sc/sec平方关系：sin2()cos2()11tan2()sec2()1cot2()csc2()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方。两角和差公式两角和与差的三角函数公式sin（）sincoscossinsin（
6、）sincoscossincos（）coscossinsincos（）coscossinsintan（）(tan+tan)(1-tantan)tan（）(tantan)(1tantan)二倍角公式二倍角的正弦、余弦和正切公式（升幂缩角公式）sin22sincoscos2cos2()sin2()2cos2()112sin2()tan22tan/1tan2()半角公式半角的正弦、余弦和正切公式（降幂扩角公式）sin2(/2)(1cos)2cos2(/2)(1cos)2tan2(/2)(1cos)(1cos)另也有tan(/2)=(1cos)/sin=sin/(1+cos)万能公式万能公式sin=2
7、tan(/2)/1+tan2(/2)cos=1-tan2(/2)/1+tan2(/2)tan=2tan(/2)/1-tan2(/2)万能公式推导附推导：sin2=2sincos=2sincos/(cos2()+sin2().*，（因为cos2()+sin2()=1）再把*分式上下同除cos2()，可得sin22tan/(1tan2()然后用/2代替即可。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sin33sin4sin3()cos34cos3()3costan33tantan3()13tan2()三倍角公式推导附推导：tan3sin3/
8、cos3(sin2coscos2sin)/(cos2cos-sin2sin)(2sincos2()cos2()sinsin3()/(cos3()cossin2()2sin2()cos)上下同除以cos3()，得：tan3(3tantan3()/(1-3tan2()sin3sin(2)sin2coscos2sin2sincos2()(12sin2()sin2sin2sin3()sin2sin3()3sin4sin3()cos3cos(2)cos2cossin2sin(2cos2()1)cos2cossin2()2cos3()cos(2cos2cos3()4cos3()3cos即sin33sin4
9、sin3()cos34cos3()3cos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：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sin, 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式sinsin2sin()/2cos()/2sinsin2cos()/2sin()/2coscos2cos()/2co
10、s()/2coscos2sin()/2sin()/2积化和差公式三角函数的积化和差公式sin cos0.5sin()sin()cos sin0.5sin()sin()cos cos0.5cos()cos()sin sin0.5cos()cos()和差化积公式推导附推导：首先,我们知道sin(a+b)=sina*cosb+cosa*sinb,sin(a-b)=sina*cosb-cosa*sinb我们把两式相加就得到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+
11、b)-sin(a-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,把两式相加,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:sina*cosb=(sin(a+b)+sin(a-b)/2cosa*sinb=(sin(a+b)-sin(a-b)/2cosa*cosb=(cos(a+
12、b)+cos(a-b)/2sina*sinb=-(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+siny=2sin(x+y)/2)*cos(x-y)/2)sinx-siny=2cos(x+y)/2)*sin(x-y)/2)cosx+cosy=2cos(x+y)/2)*cos(x-y)/2)cosx-cosy=-2sin(x+y)/2)*sin(x-y)/2)二、高考英语
13、作文套题万能公式：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 more and more popular recently. 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).While ot
14、hers think 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 other reasons to explain my choice. For me, the former is
15、 surely a wise choice .（2） 给出一个观点，要求考生反对这一观点Some people believe that -（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 opinion, I never think this reason can be the point. For one thing,-(我不同意该看法的理由一). For another thing, -(反对的理由之二) Form all what I have said, I agree to
16、 the thought that -(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 阐述名言或主题所蕴涵的意义 分析并举例使其更充实The good old proverb -（名言或谚语）reminds us that -(释义). Indeed, we can learn many things form it.First of all,-(理由一). For example, -(举例说明). Secondly,-(理由二). Another case is that -(举例说明). Furthermore , -(理由三)In my op
17、inion, -(我的观点). In short, whatever you do, please remember the say-A. If you understand it and apply it to your study or work, you”ll necessarily benefit a lot from it.解决方法题型要求考生列举出解决问题的多种途径 问题现状 怎样解决(解决方案的优缺点) In recent days, we have to face I problem-A, which is becoming more and more serious. Fir
18、st, -(说明的现状)Second, -(举例进一步说明现状) Confronted with A, we should take a series of effective measures to cope with the situation. For one thing, -(解决方法一). For another -(解决方法二). Finally, -(解决方法三).Personally, I believe that -(我的解决方法). Consequently, Im confident that a bright future is awaiting us because
19、-(带来的好处).说明利弊题型这种题型往往要求先说明一下现状，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） 说明事物现状 事物本身的优缺点（或一方面） 你对现状（或前景）的看法Nowadays many people prefer A because it has a significant role in our daily life. Generally, its advantages can be seen as follows. First -(的优点之一). Besides -（的优点之二）.But every co
20、in has two sides. The negative aspects are also apparent. One of the important disadvantages is that -(的第一个缺点)To make matters worse,-(的第二个缺点)Through the above analysis, I believe that the positive aspects overweigh the negative ones. Therefore, I would like to -(我的看法)(From the comparison between the
21、se positive and negative effects of A, we should take it reasonably and do it according to the circumstances 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 is well known that the opinion concerning this hot topic varies fr
22、om person to person. A majority of people think that _ 观点一_. In their views there are 2 factors contributing to this attitude as follows: in the first place, _原因一_.Furthermore, in the second place, _原因二_. So it goes without saying that _观点一_. People,however,differintheiropinionsonthismatter.Somepeop
23、lehold the idea that _观点二_. In their point of view, on the one hand， _原因一_. On the other hand, _原因二_. Therefore, thereis nodoubtthat _观点二_.As far as I am concerned, Ifirmlysupporttheviewthat _观点一或二_.Itis not only because _, but also because _. The more _, the more _. （2）利弊型的议论文Nowadays, there is a w
24、idespread concern over (the issue that)_作文题目_. In fact, there are both advantages and disadvantages in _题目议题_. Generally speaking, it is widely believed there are several positive aspects as follows. Firstly, _优点一_. And secondly _优点二_. Just As a popular saying goes, every coin has two sides, _讨论议题_
25、is no exception, and in another word, it still has negative aspects. To begin with, _缺点一_. In addition, _缺点二_. To sum up, we should try to bring the advantages of _讨论议题_ into full play, and reduce the disadvantages to the minimum at the same time. In that case, we will definitely make a better use o
26、f the _讨论议题_.( 3 ) 答题性议论文Currently, there is a widespread concern over (the issue that)_作文题目_ .It is really an important concern to every one of us. As a result, we must spare no efforts to take some measures to solve this problem.As we know that there are many steps which can be taken to undo this
27、problem. First of all, _途径一_. In addition, another way contributing to success of the solving problem is _途径二_.Above all, to solve the problem of _作文题目_, we should find a number of various ways. But as far as I am concerned, I would prefer to solve the problem in this way, that is to say, _方法_.( 4 )
28、 谚语警句性议论文It is well know to us that the proverb: _谚语_ has a profound significance and value not only in our job but also in our study. It means _谚语的含义_. The saying can be illustrated through a series of examples as follows. ( also theoretically )A case in point is _例子一_. Therefore, it is goes withou
29、t saying that it is of great of importance to practice the proverb _谚语_.With the rapid development of science and technology in China, an increasing number of people come to realize that it is also of practical use to stick to the saying: _谚语_. The more we are aware of the significance of this famou
30、s saying, the more benefits we will get in our daily study and job.图表作文的框架as is shown/indicated/illustrated by the figure/percentage inthetable(graph/picture/pie/chart), _作文题目的议题_ has been on rise/ decrease (goesup/increases/drops/decreases),significantly/dramatically/steadily rising/decreasing from
31、_ in _ to _ in _. From the sharp/marked decline/ rise in the chart, it goes without saying that _.Thereareatleasttwogoodreasons accounting for _. Ontheonehand, _. Onthe otherhand,_ isduetothefactthat _.Inaddition, _ isresponsiblefor _.Maybetherearesomeotherreasonstoshow _.Butitisgenerallybelievedtha
32、ttheabovementionedreasonsarecommonly convincing. AsfarasIamconcerned,I hold the point of view that _. Iamsuremyopinionisboth soundandwell-grounded. 实用性写作（申请信 )Your addressMonth, Date, yearReceivers addressDear .,I am extremely pleased to hear from you./ to see your advertisement for the position in
33、. And I would like to write a letter to tell you that./ I am confident that I am suitable for the kind of the job you are advertising./ I feel I am competent to meet the requirements you have listed. On the one hand, . On the other hand, . I am enclosing my resume for your kind consideration and ref
34、erence.I shall be much obliged if you will offer me a precious opportunity to an interview. I will greatly appreciate a response from you at your earliest convenience/ I am looking forward to your replies at your earliest convenience.Best regards for your health and success.Sincerely yours,X X X三、高考
35、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、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
36、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
37、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型:提问方式：请简要分析文中的
38、主人公的形象 答题模式：按总分（分总）来回答。先用一句话从整体上对该人物作出一个定性分析，然后再从几个方面作定量分析；也可以先从几个方面作定量分析，然后再用一句话作定性式的总括。二基本格式： 赏析“主题思想及其表现”的常用格式： a、本文通过记叙（描写），表达了作者的思想感情 b、是的主题 赏析艺术手法： 本文主要采用了的艺术手法，生动形象地表现了，具有很强的艺术感染力（手法表达效果） 构思技巧： a、是构思上最突出的特点 b、构思上最大的特点是 、主体部分 基本要求： 紧扣领起段提出的观点分析边叙边议 注意条理，适当运用序数词适当提段 、总结段基本要求： 再现观点 运用术语（如“总之”“综上所述”“总而言之”等） （一）主题思想：立意深刻独到，鞭辟入里；突破定势，标新立异；主旨深远，意韵丰富；言近旨远，耐人寻味；言有尽而意无穷；人无我有，人有我奇；意境深远 （二）构思技巧： 构思，是作者对自己将要动手写作的文章从内容到形式所作的总体设想。构思的外在表现形式为文章结构。文章的构思技巧主要从作品的立意、选材、结构安排、体裁、意境、表现手法等方面去判