函数f(x)=Asin(ωx+φ)在当x=π/9时取得最大值1/2,当x=4π/9时取得最小值-1/2,且x属于(π/9,4π/9)时都有-1/2

问题描述:

函数f(x)=Asin(ωx+φ)在当x=π/9时取得最大值1/2,当x=4π/9时取得最小值-1/2,且x属于(π/9,4π/9)时都有-1/2

由题可得,若A>0,则A=1/2,若A0时,φ=π/6,此时,当x属于(π/9,4π/9)时,ωx+φ属于(π/2,3π/2),满足-1/2