f(x)=sin^4(x)+2*根号3sinxco - 知识问答

f(x)=sin^4(x)+2*根号3sinxcosx-cos^4(x) (1)求函数的最小正周期和最小值 (2)f(x

2个回答

f(x)=sin^4(x)+2*√3sinxcosx-cos^4(x)
=[sin^2(x)+cos^2(x)][sin^2(x)-cos^2(x)]+2*√3sinxcosx
=sin^2(x)+2*√3sinxcosx-cos^2(x)
=0.5(1-cos2x)+√3sin2x-0.5(1+cos2x)
=-cos2x+√3sin2x
=2sin(2x-0.25π)
(1)所以最小正周期是π,最小值是-2
(2)

相关问题