已知f(x)最小正周期为π,则
2π/ω=π,所以 ω=2.
f(x)在x=π/8出取得最大值,则
(π/8)*2+α=2kπ+π/2,k为整数
所以,α=2kπ+π/4,根据|α|<π/2,即-π/2<2kπ+π/4<π/2
由k为整数,得k=0,α=π/4
f(x)=2sin(2x+π/4）.