已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期

来源:学生作业帮助网 编辑:作业帮 时间:2024/07/21 11:31:54
已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期
x){}K}6uCFQqf^Br~qY QγM gsnvӉ+͙oTO v6pn]`i[X(rAX,q鄪 h" bqP<;l2]d&$g/xv ۟؅~

已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期
已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期

已知函数f(x)=2sinx cosx+√3 cos2x,求f(x)最小正周期
f(x)=2sinx cosx+√3 cos2x
=sin2x+√3 cos2x
=2(sin2xcosπ/3+cos2xsinπ/3)
=2sin(2x+π/3)
f(x)最小正周期=2π/2=π

f(x)=2sinx cosx+√3 cos2x
=sin2x+√3 cos2x
=2sin(2x+π/3)
因此f(x)最小正周期为2π/2=π