y=2sinθ+√3cosθsinφ-cosθcosφ
=2sinθ+2cosθ(√3sinφ/2-cosφ/2)
=2sinθ+2cosθsin(φ-30)
=2sinθ+2cosθsina
=√(4+4sin^2a)sin(θ+m)
上式中a=φ-30,m=tan^(-1)sina
所以max{y}=√(4+4sin^2a)=2√2,此處a=90+180k1 k1為整數(shù),θ+m=90+360k2 k2為整數(shù)
或當φ=120+180k1 k1為整數(shù),并且θ=-tan^(-1)sin(φ-30)+90+360k2 k2為整數(shù)時,max{y}=2√2
當φ=120+180k1 k1為整數(shù),并且θ=-tan^(-1)sin(φ-30)-90+360k2 k2為整數(shù)時,min{y}=-2√2