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《已知三角函数值求角》教案1

《已知三角函数值求角》教案1
《已知三角函数值求角》教案1

《已知三角函数值求角》教案1

一、教学目标

知识与技能

使学生理解符号arcsin x,arccos x,arctan x的意义。

过程与方法

1.会用符号arcsin x,arccos x,arctan x表示角。

2.当x为特殊的三角函数值时,会求符号arcsin x,arccos x,arctan x的值。

3.使学生更加深刻地认识函数与方程的关系。

4.培养学生运用数学结合的思想直观地解决数学问题。

情感态度与价值观

通过本节的学习,让学生认识到事物间是相互联系、相互依存的关系,抓住了事物间的内在联系,就能更加清楚地认识事物的有序结构。

二、教学重点、难点

本节的重点是已知三角函数的值求角,难点是符号arcsin a,arccos a,arctan a所表示的意义及利用其意义求它们的特殊值。

三、教学方法

利用数形结合思想,从特殊过渡到一般的方法,重点突破用如何arcsin a来表示角arcsin a的意义,再运用类比的思想,让学生自主探究符号arcsin a,arccos a,arctan a所表示角的意义

四、课时

1课时

五、教学过程:

教学内容师生互动设计意图

概念

的深化利用arcsin a所表示角的意义求值:

生:让学生练习课本P60练

习A组第3题(1)、(2)。

巩固符号

arcsin a所

表示角的意

应用例1、比较?

?

?

?

?

-

4

13

tan

π

与?

?

?

?

?

-

5

17

tan

π

的大

小。

解:tan

4

13

tan-

=

?

?

?

?

?

-

π

4

π

5

2

tan

5

17

tan

π

π

-

=

?

?

?

?

?

-,

又:?

?

?

?

?

=

<

<

2

,0

tan

,

5

2

4

π

π

π

x

y内单调

递增,

?

?

?

?

?

-

>

?

?

?

?

?

-

-

>

-

<

π

π

π

π

π

π

5

17

tan

4

13

tan

,

5

2

tan

4

tan

,

5

2

tan

4

tan

例2、谈论函数)

4

tan(

π

+

=x

y的性质

解析:

1.由函数x

y tan

=的定义域知,将

1、引导学生实

践,简单利用函

数的性质解决问

题;

学生通过自

己的实践,真

确地体会函

数的性质,强

化对新建构

的知识的理

解与掌握。

直接引入

师:我们知道,任意给定一个角,可以唯一地确定其正弦值;反之,我知道角的正弦值,能否确定角?

举例

4

π

+

x看作一个整体;

2.求函数x

y3

tan

=的定义域;(P71练

习3)

3.值域如何?在回答此问题之前先思考

函数x

y tan

=与函数)

4

tan(

π

+

=x

y的图

象之间的关系?(左右平移)——值域不变:

R;

4.周期呢?不变:π;

5.单调性如何?(整体来看:化复杂

()

4

tan(

π

+

=x

y)为简单(x

y tan

=))

6.奇偶性如何?由定义判断它是非奇非

偶函数;进一步:函数)

4

tan(

)

(

π

+

=x

x

f与

函数)

(x

f-有何关系?(倒数)

2、通过一个简单

的问题,探索整

个函数的各种性

质,让学生自主

的解决、评价等,

复习巩固刚学的

新知识。

概念

的深化利用arcsin a所表示角的意义求值:

生:让学生练习课本P60练

习A组第3题(1)、(2)。

巩固符号

arcsin a所

表示角的意

概念的形成1.教师给出例1:

已知

1

sin

2

x=,1)(0,)

2

x

π

∈,求x;

2)(0,2)

∈,求x;3)R,求x;

2.引导学生运用已学过的三角函数线和

三角函数图像求解,让学生讨论解决。

3.对于上例的3)问,教师利用几何画

板制作的课件演示函数

1

2

y=与

sin

y x

=图像交点,分析交点的结构,

并求出所有角。

生:教师给出实例,让学生

讨论解决。

引导学生运用已学过的三角

函数线和三角函数图像求解。

师:我们可以用正弦函数图

像来求角,也就是在函数

sin

y x

=图像上找出正弦值为

1

2

的点所对应的角,即求函数

1

2

y=与sin

y x

=图像交点横

坐标。

教师利用几何画板制作的

课件演示函数

1

2

y=与

sin

y x

=图像交点。

分析交点的结构:一个角

1

x在增区间[,]

22

ππ

-上,另一

个角

2

x在减区间

3

[,]

22

ππ

上;

3

[,]

22

ππ

-恰好为正弦函数

的一个周期长度,利用三角函

数的周期性,只要表示出两个

角,再在这两个角的基础上加

周期的整数倍,从而就能表示

出所有的角。而

12

,x x关于

2

x

π

=对称,所以

12

x xπ

+=,

因此只要表示出在增区间

[,]

22

ππ

-上的

1

x,就能表示出

2

x,所以只要求出了增区间

复习三角

函数线及

函数与方

程的关系;

培养学生

运用数形

结合的思

想方法解

决数学问

题;

概念的形成4.教师给出例2:

引出用反正弦符号表示角。

5.更一般地性况:sin([1,1])

x a a

=∈-

的解决,给出反正弦符号:arcsin a及

已知

1

sin

3

x=,x R

∈,求x;

[,]

22

ππ

-上的

1

x,就能求出

2

x,从而能求出所有的角。

此时

1

2

为特殊角的正弦

值,

16

x

π

=所以满足

1

sin()

2

x x R

=∈的所有角可

表示为2

6

x k

π

π

=+或

5

2

6

x k

π

π

=+

师:教师利用几何画板制作

的课件,移动直线,演示函数

1

3

y=与sin

y x

=图像交点。

学:让学生观察满足条件的

角的个数以及所有角的相互关

系,引导学生得出以下结论:

表示出了增区间[,]

22

ππ

-上的

1

x,利用对称性就能表示出

减区间

3

[,]

22

ππ

上的

2

x,再在

这两个角的基础上加周期的整

数倍,从而就能表示出所有的

角。

师:此时

1

3

为非特殊值,因

此所求角不为特殊角,那么此

时增区间[,]

22

ππ

-上的角

1

x该

如何表示呢?

我们用

1

arcsin

3

表示在增

由特殊到

一般的过

渡,让学生

更容易理

arcsin a 所表示角的意义:在[,]22ππ

-范围内,正弦值为a 的角。

区间[,]22

ππ

-上的角,那么满

足1

sin 3x =的角怎样用符号

1

arcsin 3

表示呢?

学:让学生用符号1

arcsin 3

示所有角。

师:一般性况下,该如何表示满足sin [1,1]x a a =∈-的角? 教师利用几何画板制作的课件,移动直线,演示函数

y a =与sin y x =图像交点。

师:设问:1)满足条件的角有多少个?2)这些角之间有什么关系?3)这些角中我们可以把哪个角作为关健的角? 4)你该如何表示这个关健的角? 生:学生回答以上问题,并表述符号arcsin a 的意义,并求

a 的范围。

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《新编商务英语精读》实践教学大纲 概论【具体教学内容】【教学目的要求】【实践内容】 概论 《新编商务英语精读》是一套将培养英语语言能力与学习商务知识相结合的新教材。加强实践练习,对于消化课文、使用词汇、训练口语和实战模拟,具有重要意义;是扩大学生商务英语词汇量、提高学生商务英语的听、说、读、写水平以及能够把所学知识运用于各种日常交际活动和商务活动的必要途径。 实践教学大纲名称:《新编商务英语精读》 学时与学分:电子商务和市场营销专业,18 / 36学时,1 / 2学分; 应用英语专业,64 / 128学时,4 / 8学分。 先修课程和实践内容:大学英语、综合英语、英语视听说 实践教学目标:通过本课程的学习,加强听、说、读、写等方面的训练,熟悉商务英语基本技能,接触真实语言材料,了解各种商务活动场景,积累相关的商务知识,系统掌握商务英语的基本词汇,提高商务英语语言水平和使用能力,实现毕业后在生活和对外商贸活动中进行正确的英语表达。 适用学科专业:电子商务、市场营销、应用英语 实践场地和器材:网络教室、下载视频资料、课本习题 教材及参考资料: 1、《新编商务英语精读》,(学生用书)张逸主编,高等教育出版社,2004年, ISBN7-04-015856-6。 2、《新编商务英语精读2》,(学生用书)张逸主编,高等教育出版社,2005年,

ISBN978-7-04-016242-4。 3、Lanwood.《新编剑桥商务英语》(第二版学生用书)及练习册(中级)经济科技出 版社 4、《新视野商务英语》外语教学与研究出版社 考核方式:考查,是平时成绩(50%)的重要参考内容。学生平时的出勤率(约占10%),平时作业情况(约占20%)课堂表现情况(约占20%)。 【具体教学内容】

教案-商务英语阅读-Unit 16-叶兴国

Unit 16 Teaching Objectives: 1. To remember and use new words and expressions; 2. To learn how a boss handle his men in the office to make business prosperous; 3. To learn how to help people with different cultures and languages in a community to overcome the difficulties in communication; 4. To learn the three steps of reading by evaluating; 5. To deal with the language points in Text A and Text B. Focuses: 2. To learn how a boss handle his men in the office to make business prosperous; 3. To learn how to help people with different cultures and languages in a community to overcome the difficulties in communication. Difficulties: How to do effective reading by evaluating. Teaching Time:2 periods. Teaching Procedures: Part I Pre-reading Questions It can be used as lead-in questions. For students, they can discuss with each other and will have free answers. Part II Extensive Reading In this part, there are two texts and their relevant exercises. By reading the texts in limited time, Teacher helps students understand the contents and the reading methods to build reading abilities gradually. Text A Handle Your Men In the Office a. Let the students read Text A as quickly as they can to find the answers to Exercise I; b. Check the answers to Exercise I &analyze the language points in the text: 1. That doesn’t mean that you ought to coddle idleness, or to be slack with viciousness, or even to carry on the pay-roll well-meaning incompetence. 那并不是说你应该纵容懒惰,或疏忽恶意,甚至给善良但不胜任的员工发放薪水。 2. For a fellow who mixes business and charity soon finds that he can’t make any money to give to charity; and in the end, instead of having helped others, he’s only added himself to the burden of others. 对一个把企业和慈善机构混淆起来的人来说,他很快就会发现赚不到任何钱捐给慈善机构了,并且最后他不但不能帮助别人,自己反而成了他人的负担。 3. …sits around waiting to be hunted up. ……坐等被人发现。 4. Indiscriminate blame is as bad as undiscriminating praise—it only makes a man tired. 不分青红皂白的指 责和不加区别的褒奖一样,是不可取的—只会使人感到厌烦。 5. Once you do, and it’s only a matter of time before you’ve got to place the remnants in the hands of a doctor as receiver. 一旦你这么做了,那么何时把你的余生交到医生手里就只是个时间问题了。 f. Assign Exercises II and III as their homework. Text B How to Make the Multicultural Work Force Work a. Several minutes for students to use some basic reading skills to read the text only once, then ask them to do Exercise I; b. Check the answers to Exercise I & point out some language points: 1. Immigrants will account for nearly two-thirds of the country’s population growth between now and 2050, according to the US Department of Labor. account for: (在数量方面)占。如:

教案-商务英语阅读-Unit 1- 叶兴国

Unit 1 Teaching Objectives: 1. To introduce the teaching contents and teaching plan; 2. To have a general idea of the New International Style of Management; 3. To be clear about the three main questions of business English reading; 4. To learn how to read business English passages effectively; 5. To learn to recognize and use some of the related words and expressions. Focuses: 1. To have a general idea of the New International Style of Management. 2. To learn how to read business English passages effectively. Difficulties: 1. How to read business English passages effectively. 2. How to remember business English words and expressions ASAP. Teaching Time:2 periods. Teaching Procedures: Part I Pre-reading Questions It can be used as lead-in questions. For students, they can discuss with each other and will have free answers. Part II Extensive Reading In this part, there are two texts and their relevant exercises. By reading the texts in limited time, Teacher helps students understand the contents and the reading methods to build reading abilities gradually. 1. Read Text A The New International Style of Management and do exercises; 2. Read Text B New Thinking for successful Entrepreneurs and do exercises; 3. Analyze the language points in the texts; 4. Check the answers to Exercises. Part III Reading Skills: Introduce the Basic Information about Business English Reading. Use three questions to lead students to deal with this part: 1. Why should we do Business English Reading? 2. What does Business English Reading mainly deal with? 3. How can we do the Business English Reading effectively? If students can not answer the questions, ask them to read through the passages in Reading Skill to get the details of how to do Business English Reading. Part IV Supplementary Reading: New Thinking for a New Financial Order For this part, ask students to finish it by reading first and summarizing it with no more than 50 words. Part V Test Yourself For this part, ask students to finish it by themselves. Questions for Discussion and Reflection: 1. Do you want to be a member of these multinational companies? Why? 2. What are the differences between these multinational companies and the local companies in China? Assignment: 1. Review Unit 1, to remember the contents learned. 2. Preview Unit 2, to find difficult points. References: 《商务英语阅读教程Ⅰ教师用书》《牛津英汉双解词典》

【K12学习】教案-商务英语阅读-Unit 6-叶兴国

教案-商务英语阅读-Unit 6-叶兴国 Unit 6 Teaching Objectives: 1. To remember and use new words and expressions; 2. To learn how managers get ideas from many people to make better decisions; 3. To learn how lessons you can learn from people who are even considered bad bosses; 4. To review some basic reading skills and learn some word formations; 5. To know about the word formations we often use in details; 6. To deal with the language points in Text A and Text B. Focuses: 1. To learn how managers get ideas from many people to make better decisions; 2. To learn how lessons you can learn from people who are even considered bad bosses; Difficulties: How to know more about the word formations we often use in details; Teaching Time: 2 periods. Teaching Procedures: Part I Pre-reading Questions It can be used as lead-in questions. For students,

商务英语精读句子翻译电子教案

U1 1. 飞机乘务员应对所有旅客的安全负责。be responsible for The crew of an airliner should be responsible for the safety of all the passengers. 2. 请尽快把这些英文报纸和杂志分送给每位订阅者。distribute to Please distribute these English newspapers and magazines to every subscriber as soon as possible. 3. 学院决定举办系列讲座,商务英语专业的学生必须出席。decide on The college has decided on a lecture series and Business English majors must be present. 4. 若需进一步的补充解释,请参阅教师参考书第58页。refer to For additional explanation, please refer to page 58 of the teacher’s reference book. 5. 大多数人都会关注与自己有关的事。relate to Most people will be interested in what relates to themselves. 6. 最近,下海经商的人越来越多。go into business Recently, more and more people have gone into business. 一个大批量出售货物的商人被称作批发商。in bulk 7. A businessman who sells goods in bulk is called a wholesaler. 8. 据报道,目前工资水平在某种程度上仍稍稍领先于物价水平。to a certain extent, ahead of It’s reported that nowadays wages are, to a certain extent, still one step ahead U2 1. 总经理将重要文件分发给部门经理。hand out The general manager handed out the important documents to the department managers. 2. 欺骗顾客和逃税构成了他们那个时期的商业政策。make up Cheating customers and evading taxes made up their business policy in those days. 3. 在英语中,数学可以简称作maths或math。for short Mathematics can be called maths or math for short in English. 4. 这座城市被认为是此经济合作区的龙头。be known as This city is known as leading the economic cooperative zone. 5. 虽然这对夫妇对所要买的家具的价格没有异议,但对式样意见不一。agree on Although the couple agreed on the price of the furniture they wanted to buy, they disagreed about the style. 6. 我上个月买了台笔记本电脑,不过花了大价钱。at a price I bought a laptop last month but only at a price. 7. 一个大a批量出售货物的商人被称作批发商。pay for The parents work hard to pay for their children’s tuition. 8. 你的不诚实是我最终与你断绝往来的原因。in the end Your dishonesty was the reason why I had to break off our relationship in the end. 9. 他叔父决意在乡下定居, 而不住在城里。choose to His uncle chose to settle in the countryside rather than in the city. 10. 经理在新闻发布会上分发了项目计划书,但大多数人都怀疑该项目的可行性。press conference, hand out, project, feasibility The manager handed out the project plan on the press conference, but most of the people doubted the feasibility of the project.

教案-商务英语阅读-Unit-8-叶兴国

Unit 8 Teaching Objectives: 1. To learn how to live and how to plan our life; 2. To learn how to beat retirement blues; 3. To know about the memorial methods to help students remember words; 4. To deal with the language points in Text A and Text B. 5. To remember and use new words and expressions; Focuses: 1. To learn how to live and how to plan our life; 2. To learn how to beat retirement blues; 3. To know about the memorial methods to help students remember words; Difficulties: How to help students remember words by knowing about the memorial methods. Teaching Time:2 periods. Teaching Procedures: Part I Pre-reading Questions It can be used as lead-in questions. For students, they can discuss with each other and will have free answers. Part II Extensive Reading In this part, there are two texts and their relevant exercises. By reading the texts in limited time, Teacher helps students understand the contents and the reading methods to build reading abilities gradually. Text A How Long Will You Live? a. Let the students read Text A as quickly as they can for the first time to get the general idea; b. Ask students to tell others the general idea of the text; c. Then use some basic reading skills to read through the text again to find the answers to Exercises I; d. Check the answers to Exercises I; e. Analyze the language points in the text: 1. 1-year-olds: 一岁的小孩。合成词变成复数,如果该合成词有主干词,则在主干词后面加-s: brother-in-law→brothers-in-law, looker-on→lookers-on; 如果该合成词没有主干词,则在最后一个词的词尾加-s:grow-up→grow-ups, forget-me-not→forget-me-nots; 若合成词中有man或woman的话,复数形式则要求其构成部分也要作相应变化:a woman doctor→women doctors, a man cook→men cooks。 2. hypothetical [or synthetic] cohort:假定或综合队列,实验样本的一种方式。cohort:在人口统计学、 统计学或市场调查中定义的一代人。如:The cohort of people aged 30 to 39 are more conservative. 年龄在30岁到39岁的一群人更加保守。 3. If your retirement plan assumes you’ll live to 81, you probably won’t hit it right on the button. 如果你 的养老金计划假设你将活到81岁,你可能计算得并不准确。 4. By the way, while the odds are heavily against his reaching 95, if he should happen to make it, he then faces a 22% chance of getting to 100. 顺便说说,虽然他活到95岁的可能性很小,但是如果他能的话,那么他就有22%的机会活到100岁。 5. Trouble is, the science behind them can be squishy. 麻烦在于这些做法的科学基础可能是脆弱的。 behind: 作为……的基础、支持。如:Behind your every action is self-interest. 你的每一个行动都是出于个人私利。 f. Assign Exercises II and III as their homework. Text B Plan Ahead to Beat Retirement Blues

教案-商务英语阅读-Unit 13-叶兴国

Unit 13 Teaching Objectives: 1. To remember and use new words and expressions; 2. To learn how to deal with marriage frictions; 3. To learn what is the difference between work with your head and work with your heart; 4. To deal with the language points in Text A and Text B. Focuses: 1. To learn how to deal with marriage frictions; 2. To learn what is the difference between work with your head and work with your heart; Difficulties: What is the difference between work with your head and work with your heart ? Teaching Time:2 periods. Teaching Procedures: Part I Pre-reading Questions It can be used as lead-in questions. For students, they can discuss with each other and will have free answers. Part II Extensive Reading In this part, there are two texts and their relevant exercises. By reading the texts in limited time, Teacher helps students understand the contents and the reading methods to build reading abilities gradually. Text A Married, with Money a. Let the students skim and scan Text A as quickly as possible to get the answers to Exercises I &II; b. then Check the answers to Exercises I &II; c. Analyze the language points in the text: 1. The husband wanted her to incorporate to reduce their income, thereby allowing the son to qualify for more aid. 丈夫要她把公司与别家合并以减少收入,这样一来就可让儿子有资格获得更多的经济援助。 2. get bogged down with: 由于……而陷入困境。如:You must not get bogged down with details. 你不 必纠缠于细节之中。 3. Think big and put it in buckets. 做大规划,并把你的梦想分门别类。 4. talk-show host: 访谈节目主持人。访谈节目是一档电视或广播节目,在该节目中,某些名人参加 讨论或被采访,并且经常会回答观众或听众提出的问题。 f. Assign Exercises II and III as their homework. Text B Positive Thinkers a. Several minutes for students to use some basic reading skills to read the text only once, then ask them to do Exercise I; b. Check the answers to Exercise I; c. Point out some language points: 1. Panda Express: “熊猫快餐”是著名的中式快餐连锁店,分店遍布美国各州。 2. After all, it’s hard to eat Chinese food while driving down the freeway. 毕竟在高速公路上开车时很 难享用中餐。 3. They also share a leadership philosophy that flies in the face of conventional management strategy. 他 们还在某一与传统经营策略背道而驰的领导哲学上取得共识。 fly in the face of: 敢于违抗,悍然不顾。如:Anyone who is tempted to fly in the face of discretion had better think twice. 任何想轻举妄动的人都要三思而行。

商务英语阅读(三)教学大纲与考试大纲

湖南应用技术学院商务英语阅读教程 教 学 大 纲 、 外国语学院

《商务英语阅读教程(三)》教学大纲 课程代码:02 开课学期:第二学年第一学期 适用专业:商务英语专业学时:32 编写教师:学分:2 审核:陈勇、郭俊兰、张霞辉审批:陈勇 第一部分说明 一、课程的性质、作用 本课程是为商务英语专业开设的必修课程。 本课程的作用在于传授学生有关的阅读与技巧,提升学生的商务英语阅读水平与理解能力,扩大阅读词汇,增加英语国家文化背景知识,为学生参加专业四、八级考试及其他形式的英语考试奠定良好的基础。学生通过有目的、较系统地阅读英语国家纸媒和网媒的精选文章,逐渐掌握泛读的基本技巧,了解一些英美国家的历史、文化、地理、政治、军事、法律、经济、金融、体育、经贸、环保、能源等方面的基本知识。从而为学生独立阅读各种商务英语文章打下良好的基础。 二、课程的任务与基本要求 本课程的任务是提高阅读速度,强调阅读速度与理解能力并重;掌握文章体裁、风格及相应的阅读方法;扩大词汇量,掌握基本句式,较能通顺的翻译句子和段落;较熟练地概括文章段落大意,培养较强的文章分就析归纳能力;较全面的了解英语国家政治、经济、文化、科技等方面的知识;增加英语国家背景知识,增强跨文化交际能力。 本课程重点讲述商务英语阅读的基本原理、阅读技巧和实践方法,侧重于英语学习者语言综合知识的运用。因而,在本课程的教学过程中,必须使学生真正透彻地领会诸如阅读的过程、图式理论、构词法、猜词技巧、句子与句子的关系、话题与话题句、要旨、推理与判断、文体与风格等阅读理论内涵;要注重阅读理论与阅读实践的紧密结合,处理好阅读速度与理解之间的关系,避免知识的重复和脱节,从而使学生能够得到比较系统而全面的英语阅读基本技能。 三、教学方法建议 针对阅读课教学的自身特点,课堂教学应贯穿以学生为主体、教师为主导的教学模式。在讲解阅读技巧的同时应辅以大量的阅读实践,在大量的阅读过程中体会并掌握各种阅读方法,达到逐渐提高阅读理解能力与阅读速度的目的。在加强训练的同时,采用启发式、讨论式、发现式和研究式的教学方法,充分调动学生学习的积极性,激发学生的学习动机,最大限度地让学生参与学习的全过程。指导学生利用现有图书资料和网上信息获取知识。课外阅读是阅读课教学必需的延伸与补充,更是培养和发展学生能力的重要途径。通过大量的课外阅读,涉猎题材广泛的各类读物,拓宽知识面,不断提高阅读能力并增强对文章的鉴赏力。 四、本课程与其它课程的关系 本门课程为商务英语专业基础必修阅读课程,要求学生在规定学期之内完成课程的修习,并逐步提高阅读水平,获得基本的英语语言知识和能力,形成基本的学习态度与策略,为后续的专业英语课程奠定基础。 五、本课程与专业核心技术、能力培养的关系及作用 本课程旨在培养学生的语言技能和丰富其语言知识,是通过大量阅读,使学习者不断积

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