由题意3-4sin^2x＞0且9-x^2≥0
∴-√3/2＜sin2x＜√3/2且-3≤x≤3
∴2kπ-π/3＜2x＜2kπ+4π/3
∴kπ-π/6＜x＜kπ+2π/3,又-3≤x≤3
∴k只能取-1、0和1
∴定义域为[-3,-π/3)∪（-π/6,2π/3）∪(5π/6,3]