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.
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.