Question

已知函数f(x)=2COS2x+2倍根三sinxcosx.求函数在[负六分之派,三分之派上的值域]

Answer 1

f(x)=2COS²x+2√3sinxcosx

=(1+cos2x)+√3sin2x

=√3sin2x+cos2x+1

=2sin(2x+π/6)+1,

X∈[-π/6,π/3],2x+π/6∈[-π/6,5π/6],

∴sin(2x+π/6) ∈[-1/2,1],

2sin(2x+π/6)+1∈[0,3],

函数值域为[0,3].