You can refer to this problem and know that the function f (x) = sin (ω x+φ) (w >; 0,0 ≤φ≤π) is an even function on R, its image is symmetric about point m (3 π/4,0), and it is a monotonic function in the interval [0,π/2]. Find the values of ω and φ.

∵ function f (x) = sin (ω x+φ) (w >; 0,0 ≤φ≤π) is an even function ∴ f (-x) = f (x) → sin (-wx+φ) = sin (wx+φ) →-sin ω xcos φ = sin ω xcos φ.

∫sinωx is not necessarily equal to 0,∴cosφ=0, 0 ≤φ≤π→φ = π/2.

If the image is symmetric about the point (3/4π, 0), ω * 3 π/4+π/2 = kπ (k ∈ z) → ω = (4k-2)/3 (k ∈ z).

And ∵f(x) is the smallest positive period of the monotone function f(x) in the interval [0, π/2] ∴, which can be obtained by drawing a schematic diagram.

That is, 2π/ω≥π, and ω >; 0→0 & lt； ω≤2.

∴ω=2 or 2/3?