(1)
∵向量a=( sin(1/2)x,(√3)/2 ),向量b=( 1/2,cos(1/2)x )
∴f(x)=向量a·向量b=(1/2)sin(1/2)x+[(√3)/2 ]cos(1/2)x =sin(x/2+π/3)
∴函數(shù)y=f(x)的最小正周期T=2π/(1/2)=4π.
當(dāng)且僅當(dāng)x/2+π/3=π/2+2kπ(k∈Z),即x=π/3+4kπ(k∈Z)時(shí),f(x)取得最大值1.
(2)
令-π/2+2kπ≤x/2+π/3≤π/2+2kπ(k∈Z),即-5π/3+4kπ≤x≤π/3+4kπ(k∈Z).
則函數(shù)y=f(x)的單調(diào)遞增區(qū)間為-5π/3+4kπ≤x≤π/3+4kπ(k∈Z).