15. Найдите tg а если sin a = √26 и а є (0,5л; л).

Разбираемся:

• Шаг 1: Находим cos α, зная sin α.

sin² α + cos² α = 1 cos² α = 1 - sin² α = 1 - (\(\frac{\sqrt{2}}{6}\))^2 = 1 - \(\frac{2}{36}\) = 1 - \(\frac{1}{18}\) = \(\frac{17}{18}\) cos α = ± \(\sqrt{\frac{17}{18}}\) = ± \(\frac{\sqrt{34}}{6}\)

Так как α ∈ (0.5π; π), то cos α < 0, значит cos α = - \(\frac{\sqrt{34}}{6}\)

• Шаг 2: Находим tg α.

tg α = \(\frac{sin α}{cos α}\) = \(\frac{\frac{\sqrt{2}}{6}}{-\frac{\sqrt{34}}{6}}\) = \(\frac{\sqrt{2}}{-\sqrt{34}}\) = -\(\sqrt{\frac{2}{34}}\) = -\(\sqrt{\frac{1}{17}}\) = -\(\frac{1}{\sqrt{17}}\) = -\(\frac{\sqrt{17}}{17}\)

Ответ: -\(\frac{\sqrt{17}}{17}\)