e)sin A, tg A, если cos A=\frac{4}{25}.

e) Дано: $$cos A = \frac{4}{25}$$

Найти: $$sin A, tg A$$

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

$$sin^2 A = 1 - cos^2 A = 1 - (\frac{4}{25})^2 = 1 - \frac{16}{625} = \frac{625-16}{625} = \frac{609}{625}$$

$$sin A = \sqrt{\frac{609}{625}} = \frac{\sqrt{609}}{25}$$

$$tg A = \frac{sin A}{cos A} = \frac{\frac{\sqrt{609}}{25}}{\frac{4}{25}} = \frac{\sqrt{609}}{4}$$

Ответ: $$sin A = \frac{\sqrt{609}}{25}, tg A = \frac{\sqrt{609}}{4}$$