Question

Знайти sin á, якщо cos á=-2/3, π/2<á<π.​

Answer 1

$\sf \sin {}^{2} \alpha + \cos {}^{2} \alpha = 1 \to \sin \alpha = 1 - \cos {}^{2} \alpha \to \sin \alpha = \sqrt{1 - \cos {}^{2} \alpha } \to \sin \alpha = \sqrt{1 - ( - \frac{2}{3} ) {}^{2} } = \sqrt{1 - \frac{4}{9} } = \sqrt{ \frac{5}{9} } = \frac{ \sqrt{5} }{3} .$