cosX的6次方+sinX的6次方 求周期?

cosX的6次方+sinX的6次方 求周期?
cosX的6次方+sinX的6次方 求周期?

cosX的6次方+sinX的6次方 求周期?
sin(x)^6+cos(x)^6
＝【sin(x)^2+cos(x)^2】*【sin(x)^4-sin(x)^2*cos(x)^2+cos(x)^4】
＝sin(x)^4+2*sin(x)^2*cos(x)^2+cos(x)^4-3*sin(x)^2*cos(x)^2
＝【sin(x)^2+cos(x)^2】^2-3*sin(x)^2*cos(x)^2
=1-3*sin(x)^2*cos(x)^2
=5/8+3/8*cos(4*x) 【注：sin(x)^2再化简就简单了,
cos(4*x)的周期是pi/2.

F(x)=sin^6(x)+cos^6(x)
=[sin^2(x)+cos^2(x)][sin^4(x)-sin^2(x)cos^2(x)+cos^4(x)]
=[sin^2(x)+cos^2(x)]^2-3sin^2(x)cos^2(x)
=1-3sin^2(x)cos^2(x)
=1-3*[2sinxcosx]^2/4
=1-3*sin^2(2x)/4
sin^2(2x)的周期是pi/2，所以这个函数的周期的pi/2
加分