已知函數(shù)fx=Asin(wx+φ),其中w>0.
1)當(dāng)A=w=2,φ=π/6時,函數(shù)g(x)=f(x)-m在[0,π/2]上有兩個零點(diǎn),求m的范圍.
2)當(dāng)A=1,φ=π/6時,若函數(shù)fx圖像的相鄰兩條對稱軸之間的距離等于π/2,求函數(shù)fx的解析式；并求最小實(shí)數(shù)n,使得函數(shù)fx的圖像向左平移n個單位所對應(yīng)的函數(shù)是奇函數(shù).
(1)解析：∵f(x)=Asin(wx+φ)(w>0).
令A(yù)=w=2,φ=π/6==>f(x)=2sin(2x+π/6)
f(0)=1,f(π/2)=2sin(π+π/6)=-1
∵g(x)=2sin(2x+π/6)-m在[0,π/2]上有兩個零點(diǎn)
g(0)=1-m<=0==>m>=1
∴1<=m<2
(2)解析：令A(yù)=1,φ=π/6==> f(x)=sin(wx+π/6)
∵函數(shù)fx圖像的相鄰兩條對稱軸之間的距離等于π/2
T/2=π/2==>T=π==>w=2
f(x)=sin(2x+π/6)
∵函數(shù)fx的圖像向左平移n個單位所對應(yīng)的函數(shù)是奇函數(shù)
f(x+n)=sin(2x+2n+π/6)=±sin2x
2n+π/6=π==>n=5π/12
2n+π/6=2π==>n=11π/12
∴最小實(shí)數(shù)n為5π/12