587. Найдите sin a, tg a и ctg a, если cos a = \frac{1}{3}.

cos a = $$\frac{1}{3}$$

sin²a + cos²a = 1

sin²a = 1 - cos²a = 1 - $$\left( \frac{1}{3} \right)^2$$ = 1 - $$\frac{1}{9} = \frac{8}{9}$$

sin a = $$\sqrt{\frac{8}{9}} = \frac{2\sqrt{2}}{3}$$

tg a = $$\frac{sin a}{cos a} = \frac{\frac{2\sqrt{2}}{3}}{\frac{1}{3}} = \frac{2\sqrt{2}}{3} \cdot \frac{3}{1} = 2\sqrt{2}$$

ctg a = $$\frac{1}{tg a} = \frac{1}{2\sqrt{2}} = \frac{\sqrt{2}}{4}$$

Ответ: sin a = $$\frac{2\sqrt{2}}{3}$$, tg a = $$2\sqrt{2}$$, ctg a = $$\frac{\sqrt{2}}{4}$$