函数y=sin^4+cos^4的周期是?
问题描述：
函数y=sin^4+cos^4的周期是?
答
y=(sinx)^4+(cosx)^4
=[(sinx)^2+(cosx)^2]^2-2(sinx)^2(cosx)^2
=1-2(sinx)^2(cosx)^2
=1-4(sinx)^2(cosx)^2/2
=1-(sin2x)^2/2
=(cos4x+3)/4
所以周期是π/2