求下列函数的周期：(1)y=sin^2+2sinxcosx.(2)y=sin^4x+cos^4x.
问题描述：
求下列函数的周期：(1)y=sin^2+2sinxcosx.(2)y=sin^4x+cos^4x.
答
(1)y=sin^2+2sinxcosx=(1-cos2x)/2 + sin2x
=Asin(2x+ψ)+1/2 T=2π/2=π
(2)y=sin^4x+cos^4x.=（sin²x+cos²x)²-2sin²x*cos²x
=1-2sin²x*cos²x=1 - (1/2)sin²2x=1-(1/4)(1-cos4x)
=1/4cos4x -3/4
T=2π/4=π/2
答
(1)π(2)π/2