y=sin6次方x+cos6次方x的最小正周期,并求函数的最大值和最小值
问题描述:
y=sin6次方x+cos6次方x的最小正周期,并求函数的最大值和最小值
答
y=sin^6x+cos^6=(sin^2x+cos^2x)(sin^4x-sin^2xcos^2x+cos^4x) =sin^4x-sin^2xcos^2x+cos^4x=sin^4x+2sin^2xcos^2x+cos^4x-3sin^2cos^2 =(sin^2+cos^2)^2-3/4(2sinxcosx)^2 =-3/4*sin^2(2x)+1 =-3/8*2...