已知sinx+√3cosx=y,则实数y取值范围是

已知sinx+√3cosx=y,则实数y取值范围是
已知sinx+√3cosx=y,则实数y取值范围是

已知sinx+√3cosx=y,则实数y取值范围是
解
sinx+√3cosx
=2(1/2sinx+√3/2cosx)
=2(sinxcosπ/3+cosxsinπ/3)
=2sin(x+π/3)
∵sin(x+π/3)∈[-1,1]
∴y∈[-2,2]