已知向量m=(sinx,1),n=(根号3cosx,1⼀2)

...函数f(x)=(m+n)*m
2025-05-24 10:14:05
推荐回答(2个)
回答1:

m+n=(sinx+√3cosx,3/2)
m=(sinx,1)
f(x)=sinx(sinx+√3cosx)+3/2
=sin²x+√3sinxcosx+3/2
=(1-cos2x)/2+(√3/2)sin2x+3/2
=sin2x*cos(π/6)-cos2x*sin(π/6)+2
=sin(2x-π/6)+2

回答2:

向量m+n=(sinx+√3cosx,3/2)
f(x)=(sinx+ √3cosx)sinx+3/2=(sinx)^2+√3sinxcosx+3/2
=(√3/2)sin2x-(1/2)cos2x+2=sin(2x-π/6)+2