Упр.992 ГДЗ Колягин Ткачёва 10 класс (Алгебра)

1) sin a, tga и ctga, если cosa =-3/5 и пи/2 < а < пи; 2) cosa, tga и ctga, если sin а = —2/5 ипи < а < 3пи/2.

1. Если $$\cos a=-\frac{3}{5}$$ и $$\frac{\pi}{2}0.$$

   $$\sin a=\sqrt{1-\cos^2 a}=\sqrt{1-\frac{9}{25}}=\sqrt{\frac{16}{25}}=\frac{4}{5}.$$

   $$\tg a=\frac{\sin a}{\cos a}=\frac{4/5}{-3/5}=-\frac{4}{3}.$$

   $$\ctg a=\frac{1}{\tg a}=-\frac{3}{4}.$$

2. Если $$\sin a=-\frac{2}{5}$$ и $$\pi

   $$\cos a=-\sqrt{1-\sin^2 a}=-\sqrt{1-\frac{4}{25}}=-\sqrt{\frac{21}{25}}=-\frac{\sqrt{21}}{5}.$$

   $$\tg a=\frac{\sin a}{\cos a}=\frac{-2/5}{-\sqrt{21}/5}=\frac{2}{\sqrt{21}}=\frac{2\sqrt{21}}{21}.$$

   $$\ctg a=\frac{1}{\tg a}=\frac{\sqrt{21}}{2}.$$

Ответ

1) $$\sin a=\frac{4}{5},\ \tg a=-\frac{4}{3},\ \ctg a=-\frac{3}{4};$$
2) $$\cos a=-\frac{\sqrt{21}}{5},\ \tg a=\frac{2\sqrt{21}}{21},\ \ctg a=\frac{\sqrt{21}}{2}.$$