来自程晓的问题
sinX的6次方+cosX的6次方的周期怎么算?
sinX的6次方+cosX的6次方的周期怎么算?
1回答
2020-06-16 01:10
sinX的6次方+cosX的6次方的周期怎么算?
sinX的6次方+cosX的6次方的周期怎么算?
y=sin^6x+cos^6x
=(sin^2x+cos^2x)*(sin^4x+cos^4x-
sin^2x*cos^2x)
=sin^4x+cos^4x+2sin^2x*cos^2x-3sin^2x*cos^2x
=(sin^2x+cos^2x)^2-3*sin^2x*cos^2x
=1-3*sin^2x*cos^2x
=-3*[(1-cos2x)/2]*[(1+cos2x)/2]+1
=-3*[(1-cos^22x)/4]+1
=-3/4*sin^22x+1
=-3/4*[(1-cos4x)/2]+1
=-3/8*(1-cos4x)+1
=3/8*cos4x+5/8
则T=2兀/4=兀/2