8.Найти значение cos a, tg a, ctg a , если sin a=3, 0 < a < 90°

Дано: $$\sin \alpha = \frac{3}{5}$$, $$0 < \alpha < 90^\circ$$.

Найти: $$\cos \alpha$$, $$\tan \alpha$$, $$\cot \alpha$$.

1) $$\cos^2 \alpha + \sin^2 \alpha = 1$$

$$\cos^2 \alpha = 1 - \sin^2 \alpha = 1 - (\frac{3}{5})^2 = 1 - \frac{9}{25} = \frac{16}{25}$$.

$$\cos \alpha = \sqrt{\frac{16}{25}} = \frac{4}{5}$$ (т.к. 0 < α < 90°, косинус положителен).

2) $$\tan \alpha = \frac{\sin \alpha}{\cos \alpha} = \frac{3/5}{4/5} = \frac{3}{4}$$.

3) $$\cot \alpha = \frac{1}{\tan \alpha} = \frac{4}{3}$$.

Ответ: $$\cos \alpha = \frac{4}{5}$$, $$\tan \alpha = \frac{3}{4}$$, $$\cot \alpha = \frac{4}{3}$$.