直線x=π/3,x=π/2都是函數(shù)f(x)=sin(wx+φ)(w>0,-π<φ≤π)的對稱軸,
且函數(shù)f(x)在區(qū)間[π/3,π/2]上單調(diào)遞減
那么直線x=π/3,x=π/2是相鄰對稱軸,相距半周期
即T/2=π/2-π/3=π/6,T=π/3
由2π/w=π/3
得w=6
又x=π/3為最大值點(diǎn),
∴sin(6*π/3+φ)=1
∴sin(2π+φ)=1
∴sinφ=1,φ=2kπ+π/2,k∈Z
∵-π<φ≤π
∴φ=π/2