Упр.77 ГДЗ Колягин Ткачёва 11 класс (Алгебра)

1) x = 5пи/6;
2) x = 3пи/4;
3) x = -пи/6;
4) x = -2пи/3.

1. $$x=\frac{5\pi}{6}$$

   $$y=\frac{1}{|\tg x|}=\frac{1}{\left|\tg \frac{5\pi}{6}\right|}=\frac{1}{\left|-\tg \frac{\pi}{6}\right|}=\frac{1}{\left|-\frac{1}{\sqrt{3}}\right|}=\sqrt{3}.$$

2. $$x=\frac{3\pi}{4}$$

   $$y=\frac{1}{\left|\tg \frac{3\pi}{4}\right|}=\frac{1}{|-1|}=1.$$

3. $$x=-\frac{\pi}{6}$$

   $$y=\frac{1}{\left|\tg\left(-\frac{\pi}{6}\right)\right|}=\frac{1}{\left|-\tg \frac{\pi}{6}\right|}=\frac{1}{\left|-\frac{1}{\sqrt{3}}\right|}=\sqrt{3}.$$

4. $$x=-\frac{2\pi}{3}$$

   $$y=\frac{1}{\left|\tg\left(-\frac{2\pi}{3}\right)\right|}=\frac{1}{\left|-\tg \frac{2\pi}{3}\right|}=\frac{1}{|\sqrt{3}|}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}.$$

Ответ

1) $$\sqrt{3}$$; 2) $$1$$; 3) $$\sqrt{3}$$; 4) $$\frac{\sqrt{3}}{3}$$.