Question

如图所示为函数y=Asin(wx+φ）+c（A>0,w>0,φ＞0）图像的一部分（1求T及值max与min（2求此图象关

Answer 1

A=3,c=1,

3T/4=12-3=9

T=12

max=4,min=-2

2.f(x)=3sin(wx+φ)+1

2π/w=12,w=π/6,又（3,1),(12,4),所以

1=3sin(π/6X3+φ)+1

4=3sin(π/6X12+φ)+1

φ=π/2+2kπ,k∈N

f(x)=3cosπ/6x+1

设所求图象任一点坐标为(x,y),关于x=2对称的点为(4-x,y)在f(x)的图象上,则

y=3cos[π/6·(4-x)]+1 =3cos(2π/3-π/6·x)+1=-3cos(π/6·x+π/3)+1