设函数f(X)=cos(2x+π/3)+sin方x.求函数f(x)的最大值和最小正周期

问题描述:

设函数f(X)=cos(2x+π/3)+sin方x.求函数f(x)的最大值和最小正周期

∵f(x)=cos2xcos(π/3)-sin2xsin(π/3)+(sinx)^2
=(1/2)cos2x-(√3/2)sin2x+(sinx)^2
=(1/2)[1-2(sinx)^2]-(√3/2)sin2x+(sinx)^2
=1/2-(sinx)^2-(√3/2)sin2x+(sinx)^2
=1/2-(√3/2)sin2x.
∴当sin2x=-1时,f(x)有最大值为1/2+√3/2. f(x)的最小正周期=2π/2=π.