1、三角函数的图像与性质一、 正弦函数、余弦函数的图像与性质函数ysin xycos x图象定义域RR值域1,11,1单调性递增区间：递减区间：递增区间：2k，2k (kZ)递减区间：2k，2k(kZ)最值x2k(kZ)时，ymax1；x2k(kZ)时，ymin1x2k(kZ)时，ymax1；x2k(kZ) 时，ymin1奇偶性奇函数偶函数对称性对称中心：(k，0)(kZ)（含原点）对称轴：xk，kZ对称中心：(k，0)(kZ)对称轴：xk，kZ（含y轴）最小正周期22二、正切函数的图象与性质定义域值域R单调性递增区间奇偶性奇函数对称性对称中心：（含原点）最小正周期三、三角函数图像的平移变换和伸缩
2、变换1. 由的图象得到()的图象方法一：先平移后伸缩方法二：先伸缩后平移操作向左平移个单位横坐标变为原来的倍结果操作横坐标变为原来的倍向左平移个单位结果操作纵坐标变为原来的A倍结果注意：平移变换或伸缩变换都是针对自变量x而言的，因此在用这样的变换法作图象时一定要注意平移与伸缩的先后顺序，否则会出现错误。2. ()的性质（1）定义域、值域、单调性、最值、对称性：将看作一个整体，与相应的简单三角函数比较得出；（2）奇偶性：只有当取特殊值时，这些复合函数才具备奇偶性：，当时为奇函数，当时为偶函数；（3）最小正周期：3. yAsin(x), x0,+) ()中各量的物理意义(1) A称为振幅；(2)称
3、为周期；(3)称为频率；(4)称为相位；(5)称为初相(6)称为圆频率.赠送以下资料英语万能作文(模板型）Along with the advance of the society more and more problems are brought to our attention, one of which is that.随着社会的不断发展，出现了越来越多的问题，其中之一便是_。As to whether it is a blessing or a curse, however, people take different attitudes.然而，对于此类问题，人们持不同的看法。(Ho
4、ld different attitudes 持不同的看;Come up with different attitudes 有不同的看法)As society develops, people are attaching much importance to.随着社会的发展，人们开始关注.People are attaching more and more importance to the interview during job hunting求职的过程中，人们慢慢意识到面试的重要性。As to whether it is worthwhile ., there is a long-run
5、ning controversial debate. It is quite natural that people from different backgrounds may have divergent attitudes towards it.关于是否值得_的问题，一直以来争论不休。当然，不同的人对此可能持不同的观点。In the process of modern urban development, we often find ourselves in a dilemma.在都市的发展中，我们往往会陷入困境。Recently the phenomenon has aroused w
6、ide concern, some people are in alarm that.最近，这种现象引起了人们的广泛关注，有人开始担心_。The human race has entered a completely new stage in its history, with the increasingly rapid economic globalization and urbanization, more problems are brought to our attention.人类进入了一个历史的崭新的阶段，经济全球化、都市化的速度不断加快，随之给我们带来了很多问题。. plays
7、 such an important role that it undeniably becomes the biggest concern of the present world, there comes a question, is it a blessing or a curse?_显得非常重要而成为当今世界所关注的最大的问题，这是无可厚非的。不过，问题是：我们该如何抉择?Now we are entering a new era, full of opportunities and challenges,现在我们正在进入一个充满机会和挑战的新时代。People from differ
8、ent backgrounds would put different interpretations on the same case.不同行业的人对同一种问题的解释不尽相同。The controversial issue is often brought into public focus. People from different backgrounds hold different attitudes towards the issue.这中极具争议性的话题往往很受社会的关注。不同的人对此问题的看法也不尽相同。When asked ., some people think. whil
9、e some prefer.说到_，有人认为_，而另一些人则认为_。Just as the saying goes: so many people, so many minds. It is quite understandable that views on this issue vary from person to person.俗话说，。不同的人对此有不同的看法是可以理解的。To this issue, different people come up with various attitudes.对于这个问题，不同的人持不同的观点。There is a good side and a
10、 bad side to everything, it goes without saying that.万事万物都有其两面性，所以，勿庸置疑，_。When it comes to ., most people believe that ., but other people regard .as .提到_问题，很多人认为_，不过，一些人则认为_是_.When faced with., quite a few people claim that ., but other people think as.提到_问题，仅少数人认为_，但另一些人则认为_。There is a public cont
11、roversy nowadays over the issue of . There who criticize .argue that ., they believe that .,but people who favor ., on the other hand, argue that.目前，_问题争议较大。批判_的人认为_，他们认为_，不过，另一方面，赞同_的人则认为_。Some people are of the opinion that. 有些人认为_。Many people claim that. 很多人认为_。A majority of 绝大多数A large number of
12、 很多人Some people contend that . has proved to bring many advantages (disadvantages)有些人认为_有很多有利之处(不利之处)。Those who argue for . say that .economic development of the cities.觉得_的人认为，_ 城市的经济发展。Some people advocate that .有些人在坚持认为_。They hold that . 他们认为_。People, who advocate that ., have their sound reasons
13、 (grounds)坚持认为_的人也有其说法(依据)。Those who have already benefited from practicing it sing high praise of it. 那些从中受益的人对此大家褒奖。Those who strongly approve of . have cogent reasons for it.强烈认同_的人有很多原因。Many people would claim that. 有人会认为_。People who support . give some or all of the following reasons.那些支持_观点的人列
14、出了如下原因：_。But others hold the view that .但是，另外一些人则认为_。观点的用词：Attitude, opinion, 与其搭配的动词以及词组：Take, have, come up with，set forth, put forward等。But on the other hand, there are also quite a few people who strongly advocate that.,.不过，另一方面，也有少部分人坚持认为_。But people who are ., on the other hand , maintain that
15、.不过，另一方面，_的人认为_。However, there are a large number of people who hold a different view concerning this case.然而，很多人对此有不同的看法。问题用词：Issue, phenomenon，后接介词, on, over等。However, some others argue that. 然而，另一些人则认为_。However, there are also some others who contend that.然而，也有人认为_。But other people set forth comp
16、letely totally different argument concerning this case.不过，对于此，另一些人则持完全不同的观点。Some people examine this issue from another angle.有的人用另一角度来看这一问题。On the other hand, there are also many opponents who strongly .另一方面，也有很多反对的人，他们认为_。According to my personality and fondness, I would prefer . rather than.根据我的个
17、性以及兴趣，我选择_而不会选择_。Personally, I side with the latter (former) opinion.就我个人而言，我支持后者(前者)_。Personally, I am in favor of the former point of view.就我个人而言，我较同意前一种看法。To my point of view 我认为To my mind, the advantages far overweigh the drawbacks(disadvantages, shortcomings)我认为，优点胜过缺点。For my part, I stand on s
18、ide of the latter opinion that.就我而言，我较赞同后一种观点_。As far as I am concerned, I am inclined to be on the side of the latter view.在我看来，我较同意后一种观点。After a thorough consideration, for my part, I am in favor of the latter view that. 经过深思熟虑，我较支持后一种看法，亦即_。If asked to make a decision, I would prefer.如果真的需要作出选择，我
19、宁愿_。展现问题篇问题的常用词：question, problem, issueRecently, the issue of . has been brought into public focus.近来，_的问题引起了社会的广泛关注。Now we are entering a brand new era full of opportunities and innovations, and great changes have taken place in peoples attitude towards some traditional practice.现在我们进入了一个充满机遇和创新的崭
20、新时代，很多人对某些传统的看法也发生了很大改变。Recently the issue of whether or not . has been in the limelight and has aroused wide concern in the public.近来，是否_的问题已经非常明确而且引起了社会的广泛关注。The issue whether it is good or not to . has aroused a heated discussion all over the country._的利与弊已在全国范围内引起热烈的讨论。At present, some people th
21、ink .while others claim .Both sides have their merits.目前，一些人认为_而另一些人则认为_。其实，两种观点都其可取之处。People rarely reach an absolute consensus on such a controversial issue.对于这种极具争议的话题，我们很难作出绝对的回答。People from different backgrounds would put different interpretations on the same case.不同行业的人对同一种问题的解释不尽相同。The contro
22、versial issue is often brought into public focus. People from different backgrounds hold different attitudes towards the issue.这中极具争议性的话题往往很受社会的关注。不同的人对此问题的看法也不尽相同。When asked ., some people think. while some prefer.说到_，有人认为_，而另一些人则认为_。Just as the saying goes: so many people, so many minds. It is qui
23、te understandable that views on this issue vary from person to person.俗话说，。不同的人对此有不同的看法是可以理解的。To this issue, different people come up with various attitudes.对于这个问题，不同的人持不同的观点。There is a good side and a bad side to everything, it goes without saying that.万事万物都有其两面性，所以，勿庸置疑，_。When it comes to ., most people believe that ., but other people regard .as .提到_问题，很多人认为_，不过，一些人则认为_是_.When faced with., quite a few people claim that ., but other people think as.提到_问题，仅少数人认为_，但另一些人则认为_.
