f(x)=3sin²x+2√3sinxcosx+5cos²x
=3+2cos^2x+√3sin2x
=4+cos2x+√3sin2x
=4+2(1/2cos2x+√3/2sin2x)
=4+2sin(π/6＋2x)
所以其周期是2π/2=π
最大值当sin(π/6＋2x)＝1时有f(x)=6