填空题
第 7 / 311 题
已知 $\cos\alpha = \frac{3}{5}$，$\alpha \in (0, \frac{\pi}{2})$，则 $\sin(\alpha + \frac{\pi}{4}) =$ ______。
📖 解析
由 $\cos\alpha=\frac{3}{5}$，$\alpha$ 为锐角得 $\sin\alpha=\frac{4}{5}$。则 $\sin(\alpha+\frac{\pi}{4}) = \sin\alpha\cos\frac{\pi}{4}+\cos\alpha\sin\frac{\pi}{4} = \frac{4}{5}\times\frac{\sqrt{2}}{2}+\frac{3}{5}\times\frac{\sqrt{2}}{2} = \frac{7\sqrt{2}}{10}$。