函數(shù)f(x)=sin(ωx+φ)（ω＞0,0≤φ≤π）是R上的偶函數(shù),
所以當x=0時,sinφ=1或sinφ=-1,
又0≤φ≤π,所以φ=π/2,所以f(x)=sin(ωx+π/2),
圖象關(guān)于M(3π/4,0)對稱,則f(3π/4)=sin(ω(3π/4)+π/2)=0
所以 sin(ω(3π/4)+π/2)=cosω(3π/4)=0,ω(3π/4)=π/2+kπ,k∈Z,
ω=2/3+4k/3,k∈Z,
又因為f(x)在[0,π/2]上是單調(diào)函數(shù),所以函數(shù)的周期T=π,
即 2π/ω=2π/(2/3+4k/3)=π,得k=1,ω=2
故 f(x)=sin(2x+π/2)
其實也可以是 f(x)=cos(2x)