588. Найдите cos B, tg B и ctg B, если sin β = \frac{4}{5}.

sin β = $$\frac{4}{5}$$

sin²β + cos²β = 1

cos²β = 1 - sin²β = 1 - $$\left( \frac{4}{5} \right)^2$$ = 1 - $$\frac{16}{25} = \frac{9}{25}$$

cos β = $$\sqrt{\frac{9}{25}} = \frac{3}{5}$$

tg β = $$\frac{sin β}{cos β} = \frac{\frac{4}{5}}{\frac{3}{5}} = \frac{4}{5} \cdot \frac{5}{3} = \frac{4}{3}$$

ctg β = $$\frac{1}{tg β} = \frac{1}{\frac{4}{3}} = \frac{3}{4}$$

Ответ: cos β = $$\frac{3}{5}$$, tg β = $$\frac{4}{3}$$, ctg β = $$\frac{3}{4}$$