高一数学题 已知f(x)=cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)(x∈R)

问题描述:

高一数学题 已知f(x)=cos(2x-π/3)+2sin(x-π/4)cos(x-π/4)(x∈R)
求: 函数最小正周期;函数在区间[-π/12,π/2]上的值域

f(x)=cos(2x-π/3)+sin(2x-π/2)=(1/2)cos2x+(√3/2)sin2x-cos2x=(√3/2)sin2x-(1/2)cos2x=sin(2x-π/6)则函数f(x)的最小正周期是2π/2=π,当x∈[-π/12,π/2]时,2x-π/6∈[-π/3,5π/6],此时sin(2x-π/6...