函数fx=Asin(wx+ω (A>0,ω>0,-π/2

题目

函数fx=Asin(wx+ω (A>0,ω>0,-π/2

答案

f(x)的周期为1/4即T/4=2π/3-π/6=π/2
∴T=2π,那么2π/w=2π,w=1
而且最大值为1,故A=1
∴f(x)=sin(x+φ)
将(π/6,1)代入得,
π/6+φ=2kπ+π/2,k∈Z
∴φ=2kπ+π/3,k∈Z
∵-π/2