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1、第第三三章章三三角角函函数数、解解三三角角形形第五第五节节两角两角和与和与差的差的正弦正弦、余、余弦和弦和正切正切公式公式抓抓 基基 础础明明 考考 向向提提 能能 力力教教 你你 一一 招招我我 来来 演演 练练Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd. 备考方向要明了备考方向要明了考考 什什 么么1.会用向量的数量积推导出两角差的余弦公式会用向量的数量积推导出两角差的余弦公式2.能利用两角差的余弦公式导出两
2、角差的正弦、正切公式能利用两角差的余弦公式导出两角差的正弦、正切公式3.能利用两角差的余弦公式导出两角和的正弦、余弦、正能利用两角差的余弦公式导出两角和的正弦、余弦、正 切公式，导出二倍角的正弦、余弦、正切公式，了解它切公式，导出二倍角的正弦、余弦、正切公式，了解它 们的内在联系们的内在联系.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.怎怎 么么 考考1.利用两角和与差的正弦、余弦、正切公式进行三角函数利用两角和
3、与差的正弦、余弦、正切公式进行三角函数 式的化简、求值是高考常考的点式的化简、求值是高考常考的点2.公式逆用、变形应用是高考热点公式逆用、变形应用是高考热点3.题型以选择题、解答题为主题型以选择题、解答题为主.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Co
4、pyright 2004-2011 Aspose Pty Ltd.一、两角和与差的三角函数公式一、两角和与差的三角函数公式sin() ；cos() ；tan() .coscos sinsinsincoscossinEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.其公式变形为：其公式变形为：tantan ；tantan ；tantan .tan()(1tantan)tan()(1tantan)Evaluation on
5、ly.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.二、二倍角公式二、二倍角公式sin2 ；cos2 ；tan2 .其公式变形为：其公式变形为：sin2 ；cos2 .2sincoscos2sin22cos2112sin2Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.
6、Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.答案：答案： DEvaluation only.Created with Aspose.Slides for .NET 3.5 Client P
7、rofile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.答案：答案： CEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation onl
8、y.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.答案：答案： AEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0
9、.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.1两角和与差的三角函数公式的理解两角和与差的三角函数公式的理解(1)正弦
10、公式概括为正弦公式概括为“正余，余正符号同正余，余正符号同”“符号同符号同”指的是前面是两角和，则后面中间为指的是前面是两角和，则后面中间为“”号；前面是两角差，则后面中间为号；前面是两角差，则后面中间为“”号号Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.(2)余弦公式概括为余弦公式概括为“余余，正正符号异余余，正正符号异”(3)二倍角公式实际就是由两角和公式中令二倍角公式实际就是由两角和公式中令所所 得特别地，
11、对于余弦：得特别地，对于余弦：cos 2cos2sin2 2cos2112sin2，这三个公式各有用处，同，这三个公式各有用处，同 等重要，特别是逆用即为等重要，特别是逆用即为“降幂公式降幂公式”，在考题中，在考题中常常 有体现有体现Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.2重视三角函数的重视三角函数的“三变三变”：“三变三变”是指是指“变角、变变角、变名、名、变式变式”；变角为：对角的分拆要尽可能化成同名、
12、同；变角为：对角的分拆要尽可能化成同名、同角、特殊角；变名：尽可能减少函数名称；变式：对角、特殊角；变名：尽可能减少函数名称；变式：对式子变形一般要尽可能有理化、整式化、降低次数等式子变形一般要尽可能有理化、整式化、降低次数等在解决求值、化简、证明问题时，一般是观察角度、在解决求值、化简、证明问题时，一般是观察角度、函数名、所求函数名、所求(或所证明或所证明)问题的整体形式中的差异，问题的整体形式中的差异，再选择适当的三角公式恒等变形再选择适当的三角公式恒等变形Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Prof
13、ile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created w
14、ith Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.巧练模拟巧练模拟(课堂突破保分题，分分必保！课堂突破保分题，分分必保！)Evaluation only.Created with Aspose.Slides for .NET 3.5 Clien
15、t Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.冲关锦囊冲关锦囊 两角和与差的三角函数
16、公式可看作是诱导公式的推两角和与差的三角函数公式可看作是诱导公式的推广，可用广，可用、的三角函数表示的三角函数表示的三角函数，在使用的三角函数，在使用两角和与差的三角函数公式时，特别要注意角与角之间两角和与差的三角函数公式时，特别要注意角与角之间的关系，完成统一角和角与角转换的目的的关系，完成统一角和角与角转换的目的.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created wi
17、th Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011
18、 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.答案：答案： AEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .
19、NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evalua
20、tion only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.冲关锦囊冲关锦囊(1)运用两角和与差的三角函数公式时，不但要熟练、准运用两角和与差的三角函数公式时，不但要熟练、准确，而且要熟悉公式的逆用及变形，如确，而且要熟悉公式的逆用及变形，如tan tan tan()(1tan tan )和二倍角的余弦公式的多和二倍角的余弦公式的多种变形等种变形等(2)应熟悉公式的逆用和变形应用，公式的正用是常见应熟悉公式的逆用和变形应用，公式的正用是常见
21、 的，但逆用和变形应用则往往容易被忽视，公式的逆的，但逆用和变形应用则往往容易被忽视，公式的逆 用和变形应用更能开拓思路，培养从正向思维向逆向用和变形应用更能开拓思路，培养从正向思维向逆向 思维转化的能力，只有熟悉了公式的逆用和变形应用思维转化的能力，只有熟悉了公式的逆用和变形应用 后，才能真正掌握公式的应用后，才能真正掌握公式的应用.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.C
22、reated with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.答案答案CEvaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyr
23、ight 2004-2011 Aspose Pty Ltd.巧练模拟巧练模拟(课堂突破保分题，分分必保！课堂突破保分题，分分必保！)Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evalua
24、tion only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.冲关锦囊冲关锦囊1当当“已知角已知角”有两个时，有两个时，“所求角所求角”一般表示为两个一般表示为两个“已已知角知角”的和或差的形式；的和或差的形式；2当当
25、“已知角已知角”有一个时，此时应着眼于有一个时，此时应着眼于“所求角所求角”与与“已已知角知角”的和或差的关系，然后应用诱导公式把的和或差的关系，然后应用诱导公式把“所求所求角角”变成变成“已知角已知角”Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyr
26、ight 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.易错矫正易错矫正 因扩大角的范围而致误因扩大角的范围而致误Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation on
27、ly.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyri
28、ght 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.点击此图进入点击此图进入Evaluation only.Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0.Copyright 2004-2011 Aspose Pty Ltd.
