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# 正弦、余弦函数的图象 - PowerPoint PPT Presentation

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## 正弦、余弦函数的图象

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y

x

x

-1

O

sin=MP

cos=OM

tan=AT

T

P

A(1,0)

M

A(1,0)

y

o

x

T

P(x,y)

1

M

-1

1

- 1

R

[-1,1]

R

[-1,1]

R

2.设实数x对应的角的正弦值为y，则对应关系y=sinx就是一个函数，称为正弦函数；同样y= cosx也是一个函数，称为余弦函数.其定义域都是实数集R

C( , )

y

x

O

P

1

M

-1

y

1

O1

O

x

-1

B

A

y=sinx xR

y=sinx x[0,2]

y

1

o

x

-1

y=sinx x[0,2]

y=sinx xR

y

1

o

-

4

3

2

5

-4

-3

-2

6

x

-1

y

1

o

( ,1)

( ,1)

( ,1)

( ,1)

( ,1)

( ,1)

( ,1)

( ,1)

( ,1)

x

-1

( 2 ,0)

( ,0)

(0,0)

( ,0)

( 2 ,0)

(0,0)

( ,0)

( 2 ,0)

( ,-1)

( ,-1)

( ,1)

( ,1)

( ,-1)

( ,1)

( ,-1)

( ,-1)

( ,1)

(0,0)

( ,0)

( 2 ,0)

( ,0)

( 2 ,0)

(0,0)

(0,0)

( ,0)

( 2 ,0)

(0,0)

( 2 ,0)

( ,0)

(0,0)

( 2 ,0)

( ,0)

(0,0)

( ,0)

( 2 ,0)

(0,0)

( ,0)

y=cosx=sin(x+ ), xR

y

y

( ,0)

1

1

o

o

-

-

4

4

3

3

2

2

5

5

-4

-4

-3

-3

-2

-2

6

6

x

x

-1

-1

(0,1)

( 2 ,1)

( ,-1)

y

x

0

1

0

0

-1

1 2 1 0 1

1.列表

2.描点

3.连线

2

y=1+sinx，x[0, 2]

1

o

y=sinx，x[0, 2]

-1

y

1

0  2

o

x

-1

1

0

1

-1

0

-1 0 1 0 -1

y=cosx，x[0, 2]

y= - cosx，x[0, 2]

y= sinx，x[0, 2] 和 y= cosx，x[ , ]的简图：

0  2

0 

0

-1

1

1

0

y

2

1

o

x

-1

y= cosx，x[ , ]

0

0

-1

1

0

y=sinx，x[0, 2]

？思考

(1)sinx ≥

(2)cosx ＜(0＜x＜4)

y

1

o

x

-1

1. 正弦曲线、余弦曲线

2.注意与诱导公式、三角函数线等知识的联系

y=cosx，x[0, 2]

y=sinx，x[0, 2]

（必做）三维设计19页 跟踪演练1

（选作）做出下列函数的图像

（1）

（2）