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# å½æ° y=Asin( ï· x +ïª ) çå¾è±¡ä¸æ§è´¨æå­¦è®¾è®¡ [ è¯¾ é¢ ] å½æ° y=Asin(ï· x +ïª ) çå¾è±¡ï¼ç¬¬ä¸è - PowerPoint PPT Presentation

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[课 题]函数y=Asin(x+)的图象（第一课时）

[教学设计]

[教学目标]

1．会利用“五点”作图法作y=Asin(x+)简图。

2．理解振幅变换和周期变换的规律，会对函数y=sinx进行振幅和周期变换。

3．渗透数形结合，由简单到复杂，由特殊到一般的化归的数学思想，培养动与静的辨证关系，提高数学修养。

4. 能根据图像总结出函数的性质:最值,周期和定义域等.

[教学重点·难点]

1.“五点”作图法作y=Asin(x+)简图

2.理解振幅变换和周期变换的规律

3.熟练对y=sinx进行振幅、周期变换

4.掌握函数的性质,会求周期与最值.

[教具学具]PowerPoint串联几何画板

[教学过程]

[课后反思]

u = Um sin (ωt + )

y = sinx

2

0

x

R

y=sinx

0

1

0

-1

0

[ –1, 1 ]

T=2

y

y = sinx [ 0 , 2 ]

1

x

o

2

-1

1. y=Asinx和y=sinx图象之间的关系

（其中A>0且A≠ 1）（纵向伸缩）：

y=sinx

y=Asinx

[-A，A]

2. y=Asinx,x∈R(A>0)值域:

A

-A

y=Asinx的图象

y

y =2sinx

2

y =sinx

1

o

x

2

3

2

2

-1

2

R

[–A, A]

T=2

3. y=sinx和y=sinx图象之间的关系

(其中>0且≠1)（横向伸缩）：

y=sinx

y=sinx

y=sinx的图象

y

y = sin2x

1

o

x

2

2

3

4

3

2

1

y = sinx

R

[–1, 1]

4. y=sin(x+ )和y=sinx图象之间的关系(其中 ≠0)（平行移动）：

y=sinx

y=sin(x +)

y=sin(x+)的图象

y

1

o

x

4

9

4

3

2

3

2

5

3

2

–1

y = sinx

R

[–1, 1]

T=2

R

[-A,A]

A=2,ω=5, =

A=3,ω=1, =0

[ –3 , 3 ]

1.函数y = 3sinx的值域为；

A=1,ω=4, =0

2

[ –1, 1 ]

2.函数y = sin4x的值域为；

[-2,2]

3.函数y = 2sin(5x- )的值域为；