单选题
第 10 / 223 题
若 $\sin\alpha = \frac{3}{5}$，$\alpha \in (\frac{\pi}{2}, \pi)$，则 $\sin(\frac{\pi}{4} - \alpha) =$（ ）
📖 解析
由 $\sin\alpha=\frac{3}{5}$，$\alpha$ 在第二象限得 $\cos\alpha=-\frac{4}{5}$。$\sin(\frac{\pi}{4}-\alpha) = \sin\frac{\pi}{4}\cos\alpha - \cos\frac{\pi}{4}\sin\alpha = \frac{\sqrt{2}}{2}\times(-\frac{4}{5}) - \frac{\sqrt{2}}{2}\times\frac{3}{5} = -\frac{7\sqrt{2}}{10}$。注意选项C是 $-\frac{7\sqrt{2}}{10}$，D是 $-\frac{\sqrt{2}}{10}$，我算错？重新计算：$\frac{\sqrt{2}}{2} \times (-\frac{4}{5}) = -\frac{4\sqrt{2}}{10}$，减去 $\frac{\sqrt{2}}{2}\times\frac{3}{5} = \frac{3\sqrt{2}}{10}$，结果为 $-\frac{4\sqrt{2}}{10} - \frac{3\sqrt{2}}{10} = -\frac{7\sqrt{2}}{10}$，所以选C。