Упр.28 ГДЗ Колмогоров 10-11 класс (Алгебра)

На единичной окружности точка $$P_\alpha$$ имеет координаты $$\bigl(\cos \alpha,\ \sin \alpha\bigr).$$

1. $$\alpha=\frac{\pi}{6},\ \alpha=\frac{\pi}{2},\ \alpha=\frac{3\pi}{4}.$$

   Точки:

   • $$P_{\pi/6}\left(\frac{\sqrt3}{2},\frac12\right);$$
   • $$P_{\pi/2}(0,1);$$
   • $$P_{3\pi/4}\left(-\frac{\sqrt2}{2},\frac{\sqrt2}{2}\right).$$

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

   Точки:

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

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

   Точки:

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

4. $$\alpha=-\frac{\pi}{6},\ \alpha=2\pi,\ \alpha=\frac{5\pi}{4}.$$

   Точки:

   • $$P_{-\pi/6}\left(\frac{\sqrt3}{2},-\frac12\right);$$
   • $$P_{2\pi}(1,0);$$
   • $$P_{5\pi/4}\left(-\frac{\sqrt2}{2},-\frac{\sqrt2}{2}\right).$$