函数y=sin(4次方)x+cos(4次方)x的最小正周期是?

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函数y=sin(4次方)x+cos(4次方)x的最小正周期是?

函数y=sin(4次方)x+cos(4次方)x的最小正周期是?
函数y=sin(4次方)x+cos(4次方)x的最小正周期是?

函数y=sin(4次方)x+cos(4次方)x的最小正周期是?
y=(sinx)^4+(cosx)^4
=[(sinx)^2+(cosx)^2]^2-2(sinx)^2(cosx)^2
=1-(1/2)[sin(2x)]^2
=1-(1/4)2[sin(2x)]^2
=1/4-(1/4)2[sin(2x)]^2+3/4
=(1/4){1-2[sin(2x)]^2}+3/4
=(1/4)cos(4x)+3/4
则最小正周期T=2π/4=π/2.