函数 Y=Asin( ω x+ φ) 的图像 - PowerPoint PPT Presentation

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复习提问：

1.画正、余弦函数图象的常用方法有那些？

2.“五点法”画正弦函数图象是指哪五个点呢？余弦呢？

0

0

1

0

-1

0

0

2

0

-2

0

0

0

0

y

2

o

x

-2

y=2sinx

y=sinx

1

y=0.5sinx

-1

y=2sinx,x∈R的值域是:

[-2,2]

-2

2

y

2

o

x

-2

y=2sinx

y=sinx

1

y=0.5sinx

-1

y=1/2sinx,x∈R的值域是:

[-1/2,1/2]

-1/2

1/2

y=2sinx

(横坐标不变)

y=1/2sinx

(横坐标不变)

y=Asinx

（A>0且A≠1)

1.A>1时,各点纵坐标伸长为原来的A倍

2.0<A<1时,各点纵坐标缩短为原来的A倍

(横坐标不变)

T=2π/2=π

T=2π/0.5=4π

y=sin2x的图像和y=sin(x/2)的

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

p

y

o

x

y=sinx

1

y=sin(0.5x)

-1

y=sin2x

y

o

x

y=sinx

1

y=sin(0.5x)

-1

y=sin2x

y=sin2x

(纵坐标不变)

y=sin(x/2)

(纵坐标不变)

1.ω>1时,各点横坐标缩短为原来的1/ω倍

y=sinωx

（ω>0且ω≠1)

2.0<ω<1时,各点横坐标伸长为原来的1/ω倍

(纵坐标不变)

y=sin(x-3π/4)

Y

1

X

-1

y=sin(x+π/4)

y=sin(x+π/4)的图象可以看作是把y=sinx 的图象上所有的点向左平行移动π/4个单位而得到的。

y=sin(x-3π/4)的图象可以看作是把y=sinx的图象上所有的点向右平行移动3π/4个单位而得到的。

|φ|个单位而得到的。

函数y=Asin(ωx+φ) (A>0, ω>0)的图象可以用下面的方法得到：

Y=sinx

Y=sin(x+φ)

|φ|个单位

Y=sin(ωx+φ )

Y=Ａsin(ωx+φ )

(1) y=4sinx

(2) y=sin(4x)

(3) y=sin(x+3)

(4) y=2sin(3x+2)

1.函数y=Asin( x+ )的图象可由变换得到，

２.作图时请注意X轴是实数轴，坐标刻度角一律用弧度制．