f(x)=sin^3·x·cosx+cos^3·x·sinx+√3sin²x.求T
问题描述：
f(x)=sin^3·x·cosx+cos^3·x·sinx+√3sin²x.求T
答
f(x)=sinxcosx(sin²x+cos²x)+√3sin²x =sinxcosx+√3sin²x =1/2sin2x+√3/2*(1-cos2x) =1/2sin2x-√3/2cos2x+√3/2 =√[(1/2)²+(√3/2)²]*sin(2x-z)+√3/2 =sin(2x-z)+√3/2 其中tanz=(√3/2)/(1/2)=√3 z=π/3 f(x)=sin(2x-π/3)+1/2 T=2π/2=π