3sinθ+3cosθ=3根号下2×根号下2/2(sinθ+cosθ)
=3根号下2×sin(θ+π)
由题意知0≤sin(θ+π)≤1
∴0≤根号下3sinθ+3cosθ≤根号下（3根号下2）是 根号下3sinθ+3cosθ3sinθ+3cosθ=3×根号下2×根号下2/2×(sinθ+cosθ)=3×根号下2×sin(θ+π/4)由题意知0≤sin(θ+π/4)≤1∴0≤根号下3sinθ+3cosθ≤根号下（3根号下2)