Question

函数f(x)=cosx+cos(x+π/3)的最小正周期为

Answer 1

问：函数f(x)=cosx+cos(x+π/3)的最小正周期为

答：(x)=cos[cos(x+π/3)]∵-1≤cos(x)≤1,且从-1→1的周期为π又∵cos(x)是偶函数，|±1|<π/2∴cos[cos(x)]恒大于0∴cos[cos(x)]的最小正周期是π（最小值=cos1，最大值=1）f(x)=cos[cos(x+π/3)]的周期与cos[cos(x)]一致，只是函数图像平移而已。∴f(x)=cos[cos(x+π/3)]的最小正周期是π