y=sin(ωx+φ)+cos(ωx+φ)的最小正周期是π,且f(-x)=f(x)则

2个回答

  • (A)y=f(x)在(0,π/2)单调递减(B)y=f(x)在(π/4,3π/4)单调递减(C)y=f(x)在(0,π/2)单调递增(D)y=f(x)在(π/4,3π/4)单调递增

    解析:∵函数f(x)=sin(wx 十φ) 十cos(wx十 φ)(|φ|0)的最小正周期为π,且f(-x)=f(x)

    ∴f(x)=sin(wx十 φ)十 cos(wx十 φ)=√2sin(wx 十φ 十π/4)

    ∴f(x)=2sin(2x十 φ 十π/4)

    ∵f(-x)=f(x)

    ∴φ π/4=π/2==>φ=π/4===>f(x)=√2cos(2x)

    ∴f(x)在(0,π/2)单调递减,A正确

    选择A