∵f(π/6)=f(π/2)
且f(x)在区间(π/6,π/2)有最大值,无最小值,
∴对称轴x=(π/6+π/2)/2=π/3
∴f(π/3)=sin(w*π/3+π/3)=1
w*π/3+π/3=2kπ+π/2,k是整数
w=6k+1/2
又w>0
∴w=6n+1/2,n是自然数
∵f(π/6)=f(π/2)
且f(x)在区间(π/6,π/2)有最大值,无最小值,
∴对称轴x=(π/6+π/2)/2=π/3
∴f(π/3)=sin(w*π/3+π/3)=1
w*π/3+π/3=2kπ+π/2,k是整数
w=6k+1/2
又w>0
∴w=6n+1/2,n是自然数