求函数fx=sin^4x+cos^4x+sin^2xcos^2x/2-2sinxcosx的最小正周期,最大值和最小值
求函数fx=sin^4x+cos^4x+sin^2xcos^2x/2-2sinxcosx的最小正周期,最大值和最小值
数学人气:930 ℃时间:2019-09-29 06:16:40
优质解答
f(x)=sin^4x+cos^4x+sin^2xcos^2x/2-2sinxcosx=(sin²x+cos²x)²-3sin²xcos²x/2-2sinxcosx=1-3sin²2x/8-sin2x=-(3/8)(sin2x+4/3)²+5/3,显然,最小正周期为2π/2=π.当sin2x= -1时,f...
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