问题
填空题
y=sin2x+2sinxcosx的周期是______．
答案
∵y=sin2x+2sinxcosx
=
+sin2x1-cos2x 2
=sin2x-
cos2x+1 2 1 2
=
sin（2x+φ）+5 2
，（tanφ=-1 2
）1 2
∴其周期T=
=π．2π 2
故答案为：π．
搜题请搜索小程序“爱下问搜题”
y=sin2x+2sinxcosx的周期是______．
∵y=sin2x+2sinxcosx
=
+sin2x1-cos2x 2
=sin2x-
cos2x+1 2 1 2
=
sin（2x+φ）+5 2
，（tanφ=-1 2
）1 2
∴其周期T=
=π．2π 2
故答案为：π．