Упр.29 ГДЗ Колмогоров 10-11 класс (Алгебра)

На единичной окружности координаты точки $$P_\alpha$$ равны $$\bigl(\cos \alpha;\sin \alpha\bigr).$$

1. $$\alpha=\frac{\pi}{2},\ \frac{\pi}{4},\ -\pi$$

   $$P_{\pi/2}(0;1),\quad P_{\pi/4}\left(\frac{\sqrt2}{2};\frac{\sqrt2}{2}\right),\quad P_{-\pi}(-1;0).$$

2. $$\alpha=-\frac{\pi}{6},\ \frac{2\pi}{3},\ \frac{3\pi}{2}$$

   $$P_{-\pi/6}\left(\frac{\sqrt3}{2};-\frac12\right),\quad P_{2\pi/3}\left(-\frac12;\frac{\sqrt3}{2}\right),\quad P_{3\pi/2}(0;-1).$$

3. $$\alpha=-\frac{\pi}{2},\ \frac{\pi}{3},\ 3\pi$$

   $$P_{-\pi/2}(0;-1),\quad P_{\pi/3}\left(\frac12;\frac{\sqrt3}{2}\right),\quad P_{3\pi}(-1;0).$$

4. $$\alpha=\frac{3\pi}{4},\ -\frac{\pi}{3},\ \frac{5\pi}{2}$$

   $$P_{3\pi/4}\left(-\frac{\sqrt2}{2};\frac{\sqrt2}{2}\right),\quad P_{-\pi/3}\left(\frac12;-\frac{\sqrt3}{2}\right),\quad P_{5\pi/2}(0;1).$$