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江西省2025届八年级《学业测评》分段训练（二）数学.考卷答案试卷答案
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分析由同角三角函数基本关系，结合诱导公式，整体计算可得．
解答解：∵α∈（$\frac{π}{3}$，$\frac{5π}{6}$），∴α+$\frac{π}{6}$∈（$\frac{π}{2}$，π），
∵sin（α+$\frac{π}{6}$）=$\frac{1}{3}$，∴cos（α+$\frac{π}{6}$）=-$\frac{2\sqrt{2}}{3}$，
∴sin（$\frac{π}{3}$-α）=sin[$\frac{π}{2}$-（α+$\frac{π}{6}$）]=cos（α+$\frac{π}{6}$）=-$\frac{2\sqrt{2}}{3}$，
故答案为：-$\frac{2\sqrt{2}}{3}$
点评本题考查诱导公式，涉及同角三角函数基本关系，属基础题．
