已知向量a=(sinx,cos²x-1/2),向量b=(cosx,負(fù)根號3)其中x∈R,函數(shù)f(x)=5向量a·向量b-3（1）求函數(shù)的最小正周期；（2）確定函數(shù)f(x)的單調(diào)區(qū)間；（3）函數(shù)f(x)的圖像可以由y=5sin2x的圖像經(jīng)過怎樣的變化而得到
(1)解析：∵向量a=(sinx,cos²x-1/2),向量b=(cosx,負(fù)根號3),函數(shù)f(x)=5向量a·向量b-3
向量a·向量b=sinxcosx-√3( cos²x-1/2)=1/2sin2x-√3/2cos2x=sin(2x-π/3)
∴f(x)=5sin(2x-π/3)-3
∴函數(shù)的最小正周期為π
(2)解析：2kπ-π/2<=2x-π/3<=2kπ+π/2==>kπ-π/12<=x<=kπ+5π/12,單調(diào)增；kπ+5π/12<=x<=kπ+11π/12,單調(diào)減；
(3)解析：由y=5sin2x的圖像右移π/6,下移3個(gè)單位,得到函數(shù)f(x)的圖像