24.26. Дано: \(\sin\left(\frac{\pi}{4}-\alpha\right)=-\frac{\sqrt2}{10}\), \(\pi<\alpha<\frac{3\pi}{2}\). Найдите \(\sin\alpha\).

Обозначим \(x=\frac{\pi}{4}-\alpha\). Тогда \(-\frac{5\pi}{4}

\(\cos x=-\sqrt{1-\sin^2x}=-\sqrt{1-\frac{2}{100}}=-\frac{7\sqrt2}{10}.\)

Поскольку \(\alpha=\frac{\pi}{4}-x\),

\(\sin\alpha=\frac{\sqrt2}{2}(\cos x-\sin x)=\frac{\sqrt2}{2}\left(-\frac{7\sqrt2}{10}+\frac{\sqrt2}{10}\right)=-\frac35.\)

Ответ: \(-\frac35\).