1、f(x)的最小正周期為2π/2=π
2、令2kπ-π/2≤2x+π/3≤2kπ+π/2,以求f(x)的單調(diào)增區(qū)間,得
kπ-5π/12≤x≤kπ+π/12,（k∈Z）
令2kπ+π/2≤2x+π/3≤2kπ+3π/2,以求f(x)的單調(diào)減區(qū)間,得
kπ+π/12≤x≤kπ+7π/12,（k∈Z）
3、f(x)=sin(2x+π/3)對(duì)應(yīng)的奇函數(shù)為±sin2x
f(x)=sin(2x+π/3)= sin[2(x+π/6)]
f(x)向左平移π/3得f(x+π/3)=sin[2(x+π/3+π/6)]= -sin2x,是奇函數(shù).
繼續(xù)向左平移周期的整數(shù)倍,得f(x+π/3+kπ)=sin[2(x+π/3+kπ+π/6)]= -sin2x,仍是奇函數(shù).
f(x)向右平移π/6得f(x-π/6)=sin[2(x-π/6+π/6)]=sin2x,是奇函數(shù).
繼續(xù)向右平移周期的整數(shù)倍,得f(x-π/6-kπ)=sin[2(x-π/6-kπ+π/6)]=sin2x,仍是奇函數(shù).
綜上所述,
f(x)向左kπ+π/3,或向右平移kπ-π/6,（k∈Z）,仍是奇函數(shù).