设函数f(x)=cos(2x+π/3)+sin^2 X

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/10 14:32:08

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

f(x)=cos2x*1/2-√3*sin2x+(1-cos2x)/2
=cos2x-√3sin2x+1/2
=2cos(2x+π/3)+1/2
所以最小正周期T=2π/2=π
当cos（2x+π/3）=1
取最大值
为5/2

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