已知函数fx=4cosωxsin(ωx+π/4)(ω>0)的最小正周期为π.

问题描述:

已知函数fx=4cosωxsin(ωx+π/4)(ω>0)的最小正周期为π.
(Ⅰ)求ω的值;
(Ⅱ)讨论fx在区间[0,π/2]上的单调性.

(1)∵函数fx=4cosωxsin(ωx+π/4)(α>0)的最小正周期为π∴f(x)=2sin(2ωx+π/4)-2sin(-π/4)= 2sin(2ωx+π/4)+√2=2sin(2x+π/4)+ √2∴ω=1(2)∵f(x)=2sin(2x+π/4)+ √2∴函数f(x)初相为π/4,其图像离Y轴...