(1)f(x)=(sinx+√3cosx, 3/2)*(sinx, 1)=sin²x+√3sinxcosx+3/2=(1-cos2x)/2+√3/2sin2x+3/2
=√3/2sin2x-1/2cos2x+1=sin(2x-30°)+1
∴最小正周期::T=2π/2=π
单调增区间:2x-π/6∈[2kπ-π/2,2kπ+π/2]即x∈[kπ-π/6,kπ+π/3]
(1)f(x)=(sinx+√3cosx, 3/2)*(sinx, 1)=sin²x+√3sinxcosx+3/2=(1-cos2x)/2+√3/2sin2x+3/2
=√3/2sin2x-1/2cos2x+1=sin(2x-30°)+1
∴最小正周期::T=2π/2=π
单调增区间:2x-π/6∈[2kπ-π/2,2kπ+π/2]即x∈[kπ-π/6,kπ+π/3]