2022年人教A版数学必修四1.2.1《任意角的三角函数》Word教案 .pdf

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1、名师精编优秀教案任意角的三角函数教学目的：知识目标：1.复习三角函数的定义、定义域与值域、符号、及诱导公式；2.利用三角函数线表示正弦、余弦、正切的三角函数值；3.利用三角函数线比较两个同名三角函数值的大小及表示角的范围。能力目标：掌握用单位圆中的线段表示三角函数值，从而使学生对三角函数的定义域、值域有更深的理解。德育目标：学习转化的思想，培养学生严谨治学、一丝不苟的科学精神；教学重点：正弦、余弦、正切线的概念。教学难点：正弦、余弦、正切线的利用。授课类型：新授课教学模式：讲练结合教具：多媒体、实物投影仪教学过程：一、复习引入：1三角函数的定义及定义域、值域：练习 1：已知角的终边上一点(3,

2、)Pm，且2sin4m，求cos,sin的值。解：由题设知3x，ym，所以2222|(3)rOPm，得23rm，从而2sin4m23mmrm，解得0m或216625mm当0m时，3,3rx，cos1,tan0 xyrx；当5m时，2 2,3rx，615cos,tan43xyrx；当5m时，2 2,3rx，615cos,tan43xyrx2三角函数的符号：练习 2：已知sin0且tan0，（1）求角的集合；（2）求角2终边所在的象限；（3）试判断tan,sincos222的符号。3诱导公式：练习 3：求下列三角函数的值：（1）9cos4，（2）11tan()6，（3）9sin2二、讲解新课：当角

3、的终边上一点(,)P x y的坐标满足221xy时，有三角函数正弦、余弦、正切值的几何表示三角函数线。名师精编优秀教案1单位圆：圆心在圆点O，半径等于单位长的圆叫做单位圆。2有向线段：坐标轴是规定了方向的直线，那么与之平行的线段亦可规定方向。规定：与坐标轴方向一致时为正，与坐标方向相反时为负。3三角函数线的定义：设任意角的顶点在原点O，始边与x轴非负半轴重合，终边与单位圆相交与点P(,)x y，过P作x轴的垂线，垂足为M；过点(1,0)A作单位圆的切线，它与角的终边或其反向延长线交与点T.由四个图看出：当角的终边不在坐标轴上时，有向线段,OMx MPy，于是有sin1yyyMPr，cos1xx

4、xOMr，tanyMPATATxOMOA我们就分别称有向线段,MP OM AT为正弦线、余弦线、正切线。说明：三条有向线段的位置：正弦线为的终边与单位圆的交点到x轴的垂直线段；余弦线在x轴上；正切线在过单位圆与x轴正方向的交点的切线上，三条有向线段中两条在单位oxyMTPAoxyMTPAxyoMTPAxyoMTPA（）（）（）（）文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2

5、Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8

6、M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1

7、F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4

8、L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI

9、8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H

10、10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档

11、编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3名师精编优秀教案圆内，一条在单位圆外。三条有向线段的方向：正弦线由垂足指向的终边与单位圆的交点；余弦线由原点指向垂足；正切线由切点指向与的终边的交点。三条有向线段的正负：三条有向线段凡与x轴或y轴同向的为正值，与x轴或y轴反向的为负值。三条有向线段的书写：有向线段的起点字母在前，终点字母在后面。4例题分析：例 1作出下列各角的正弦线、余弦线、正切线。（1）3；（2）56；（3）23；（4）136解：图略。例 2.利用三角函数线比较下

12、列各组数的大小：132sin与54sin 2tan32与 tan54 3cot32与 cot54解：如图可知：32sin54sintan32 tan54cot32cot54例 4利用单位圆写出符合下列条件的角x的范围。A B o T2 T1 S2S1 P2 P1 文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3

13、文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:C

14、P2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5

15、J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 H

16、P1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1

17、D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10

18、ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I

19、2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3名师精编优秀教案（1）1sin2x；（2）1cos2x；（3）10,sin2xx且1cos2x；（4）1|cos|2x；（5）1sin2x且tan1x答案：（1）71122,66kxkkZ；（2）22,66kxkkZ；（3）5,36xkZ；（4）,6262kxkkZ；（5）322,24kxkkZ三、巩固与练习四、小结：本节课学习了以下内容：1三角函数线的定义；2会画任意角的三角函数线；3利用单位圆比较三角函数值的大小，求角的范围。文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8

20、I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J

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24、HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R1D4L10 ZI8G8I2H10J3文档编码:CP2Z8F5J8M8 HP1F4R

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