y=sin^x+2sinxcosx
=1/2-cos2x/2+sin2x
=根号下(5/4)*[2sin2x/根号5-cos2x/根号5]+1/2
设cosa=2/根号5,sina=-1/根号5
上式=根号下(5/4)*sin(2x+a)+1/2
因此周期=2派/2=派