1. Выразите в радианной мере величины углов. 1.1. 10°, 135°, -60°; 1.2. 18°, 150°, -90°; 1.3. 30°, 144, 130°; 1.4. 54°, 135°, -36°; 1.5. 15°, 120°, -180°; 1.6. 20°, 125°, -36°; 1.7. 40°, 225°, -30°; 1.8. 45°, 240°, -18°; 1.9. 36°, 150°, -210°; 1.10. 60°, 72°, -252°; 1.11. 72°, 108°, 270°; 1.12. 120°, 135°, -144°; 1.15. 45°, 160°, -75°; 1.16. 216°, 15°, -60°; 1.17. 130°, 72°-180°; 1.18. 54°, 120°, -150°; 1.19. 18°, 1080, -30°; 1.20. 252°, 45°,-240°; 1.21. 210°, 15°, -60°; 1.22. 50°, 144°, -120°; 1.23. 108°, 135°, -300°; 1.24. 30°, 315°, -36°; 1.25. 10°, 216°, -18°; 1.26. 55°, 150°,-135°;

Решение:

Привет! Давай вместе переведем углы из градусов в радианы. Напоминаю, что для перевода из градусов в радианы используется формула:

\[ \text{радианы} = \text{градусы} \times \frac{\pi}{180} \]

Давай разберем по порядку:

1.1.

• 10°: \[ 10 \times \frac{\pi}{180} = \frac{\pi}{18} \]
• 135°: \[ 135 \times \frac{\pi}{180} = \frac{3\pi}{4} \]
• -60°: \[ -60 \times \frac{\pi}{180} = -\frac{\pi}{3} \]

1.2.

• 18°: \[ 18 \times \frac{\pi}{180} = \frac{\pi}{10} \]
• 150°: \[ 150 \times \frac{\pi}{180} = \frac{5\pi}{6} \]
• -90°: \[ -90 \times \frac{\pi}{180} = -\frac{\pi}{2} \]

1.3.

• 30°: \[ 30 \times \frac{\pi}{180} = \frac{\pi}{6} \]
• 144°: \[ 144 \times \frac{\pi}{180} = \frac{4\pi}{5} \]
• 130°: \[ 130 \times \frac{\pi}{180} = \frac{13\pi}{18} \]

1.4.

• 54°: \[ 54 \times \frac{\pi}{180} = \frac{3\pi}{10} \]
• 135°: \[ 135 \times \frac{\pi}{180} = \frac{3\pi}{4} \]
• -36°: \[ -36 \times \frac{\pi}{180} = -\frac{\pi}{5} \]

1.5.

• 15°: \[ 15 \times \frac{\pi}{180} = \frac{\pi}{12} \]
• 120°: \[ 120 \times \frac{\pi}{180} = \frac{2\pi}{3} \]
• -180°: \[ -180 \times \frac{\pi}{180} = -\pi \]

1.6.

• 20°: \[ 20 \times \frac{\pi}{180} = \frac{\pi}{9} \]
• 125°: \[ 125 \times \frac{\pi}{180} = \frac{25\pi}{36} \]
• -36°: \[ -36 \times \frac{\pi}{180} = -\frac{\pi}{5} \]

1.7.

• 40°: \[ 40 \times \frac{\pi}{180} = \frac{2\pi}{9} \]
• 225°: \[ 225 \times \frac{\pi}{180} = \frac{5\pi}{4} \]
• -30°: \[ -30 \times \frac{\pi}{180} = -\frac{\pi}{6} \]

1.8.

• 45°: \[ 45 \times \frac{\pi}{180} = \frac{\pi}{4} \]
• 240°: \[ 240 \times \frac{\pi}{180} = \frac{4\pi}{3} \]
• -18°: \[ -18 \times \frac{\pi}{180} = -\frac{\pi}{10} \]

1.9.

• 36°: \[ 36 \times \frac{\pi}{180} = \frac{\pi}{5} \]
• 150°: \[ 150 \times \frac{\pi}{180} = \frac{5\pi}{6} \]
• -210°: \[ -210 \times \frac{\pi}{180} = -\frac{7\pi}{6} \]

1.10.

• 60°: \[ 60 \times \frac{\pi}{180} = \frac{\pi}{3} \]
• 72°: \[ 72 \times \frac{\pi}{180} = \frac{2\pi}{5} \]
• -252°: \[ -252 \times \frac{\pi}{180} = -\frac{7\pi}{5} \]

1.11.

• 72°: \[ 72 \times \frac{\pi}{180} = \frac{2\pi}{5} \]
• 108°: \[ 108 \times \frac{\pi}{180} = \frac{3\pi}{5} \]
• 270°: \[ 270 \times \frac{\pi}{180} = \frac{3\pi}{2} \]

1.12.

• 120°: \[ 120 \times \frac{\pi}{180} = \frac{2\pi}{3} \]
• 135°: \[ 135 \times \frac{\pi}{180} = \frac{3\pi}{4} \]
• -144°: \[ -144 \times \frac{\pi}{180} = -\frac{4\pi}{5} \]

1.15.

• 45°: \[ 45 \times \frac{\pi}{180} = \frac{\pi}{4} \]
• 160°: \[ 160 \times \frac{\pi}{180} = \frac{8\pi}{9} \]
• -75°: \[ -75 \times \frac{\pi}{180} = -\frac{5\pi}{12} \]

1.16.

• 216°: \[ 216 \times \frac{\pi}{180} = \frac{6\pi}{5} \]
• 15°: \[ 15 \times \frac{\pi}{180} = \frac{\pi}{12} \]
• -60°: \[ -60 \times \frac{\pi}{180} = -\frac{\pi}{3} \]

1.17.

• 130°: \[ 130 \times \frac{\pi}{180} = \frac{13\pi}{18} \]
• 72°: \[ 72 \times \frac{\pi}{180} = \frac{2\pi}{5} \]
• -180°: \[ -180 \times \frac{\pi}{180} = -\pi \]

1.18.

• 54°: \[ 54 \times \frac{\pi}{180} = \frac{3\pi}{10} \]
• 120°: \[ 120 \times \frac{\pi}{180} = \frac{2\pi}{3} \]
• -150°: \[ -150 \times \frac{\pi}{180} = -\frac{5\pi}{6} \]

1.19.

• 18°: \[ 18 \times \frac{\pi}{180} = \frac{\pi}{10} \]
• 108°: \[ 108 \times \frac{\pi}{180} = \frac{3\pi}{5} \]
• -30°: \[ -30 \times \frac{\pi}{180} = -\frac{\pi}{6} \]

1.20.

• 252°: \[ 252 \times \frac{\pi}{180} = \frac{7\pi}{5} \]
• 45°: \[ 45 \times \frac{\pi}{180} = \frac{\pi}{4} \]
• -240°: \[ -240 \times \frac{\pi}{180} = -\frac{4\pi}{3} \]

1.21.

• 210°: \[ 210 \times \frac{\pi}{180} = \frac{7\pi}{6} \]
• 15°: \[ 15 \times \frac{\pi}{180} = \frac{\pi}{12} \]
• -60°: \[ -60 \times \frac{\pi}{180} = -\frac{\pi}{3} \]

1.22.

• 50°: \[ 50 \times \frac{\pi}{180} = \frac{5\pi}{18} \]
• 144°: \[ 144 \times \frac{\pi}{180} = \frac{4\pi}{5} \]
• -120°: \[ -120 \times \frac{\pi}{180} = -\frac{2\pi}{3} \]

1.23.

• 108°: \[ 108 \times \frac{\pi}{180} = \frac{3\pi}{5} \]
• 135°: \[ 135 \times \frac{\pi}{180} = \frac{3\pi}{4} \]
• -300°: \[ -300 \times \frac{\pi}{180} = -\frac{5\pi}{3} \]

1.24.

• 30°: \[ 30 \times \frac{\pi}{180} = \frac{\pi}{6} \]
• 315°: \[ 315 \times \frac{\pi}{180} = \frac{7\pi}{4} \]
• -36°: \[ -36 \times \frac{\pi}{180} = -\frac{\pi}{5} \]

1.25.

• 10°: \[ 10 \times \frac{\pi}{180} = \frac{\pi}{18} \]
• 216°: \[ 216 \times \frac{\pi}{180} = \frac{6\pi}{5} \]
• -18°: \[ -18 \times \frac{\pi}{180} = -\frac{\pi}{10} \]

1.26.

• 55°: \[ 55 \times \frac{\pi}{180} = \frac{11\pi}{36} \]
• 150°: \[ 150 \times \frac{\pi}{180} = \frac{5\pi}{6} \]
• -135°: \[ -135 \times \frac{\pi}{180} = -\frac{3\pi}{4} \]

Ответ: Все углы переведены в радианы, как ты и просил!

Ты отлично справляешься! Продолжай в том же духе, и у тебя все получится!