и) sin A, tg A, если cos A=\frac{\sqrt{19}}{10}.

и) Дано: $$cos A = \frac{\sqrt{19}}{10}$$

Найти: $$sin A, tg A$$

Основное тригонометрическое тождество: $$sin^2 A + cos^2 A = 1$$

$$sin^2 A = 1 - cos^2 A = 1 - (\frac{\sqrt{19}}{10})^2 = 1 - \frac{19}{100} = \frac{81}{100}$$

$$sin A = \sqrt{\frac{81}{100}} = \frac{9}{10}$$

$$tg A = \frac{sin A}{cos A} = \frac{\frac{9}{10}}{\frac{\sqrt{19}}{10}} = \frac{9}{\sqrt{19}} = \frac{9\sqrt{19}}{19}$$

Ответ: $$sin A = \frac{9}{10}, tg A = \frac{9\sqrt{19}}{19}$$