Question

Письменно решите задание. Найдите значение cos⁡α, если sin α = √2/3 и 0 < α < π/2

Answer 1

$sin\alpha = \frac{\sqrt{2}}{3} => sin^2\alpha = \frac{2}{9} => cos^2\alpha = 1 - sin^2\alpha = \frac{7}{9} => |cos\alpha| = \frac{\sqrt{7}}{9} => (0 < \alpha < \frac{\pi}{2}) => cos\alpha = \frac{\sqrt{7}}{9}\\Answer: cos\alpha = \frac{\sqrt{7}}{9}$