1. Выразите в радианной мере величины углов: а) 45°, 36°, 180°; б) 120°, 310°, 360°; в) 60°, 72°, 270°; г) 150°, 216°, 90°.

Используем соотношение: \(180^\circ=\pi\) рад, поэтому \(x^\circ=\frac{x\pi}{180}\) рад.

1. а) \(45^\circ=\frac{45\pi}{180}=\frac{\pi}{4}\) рад; \(36^\circ=\frac{36\pi}{180}=\frac{\pi}{5}\) рад; \(180^\circ=\pi\) рад.
2. б) \(120^\circ=\frac{120\pi}{180}=\frac{2\pi}{3}\) рад; \(310^\circ=\frac{310\pi}{180}=\frac{31\pi}{18}\) рад; \(360^\circ=\frac{360\pi}{180}=2\pi\) рад.
3. в) \(60^\circ=\frac{60\pi}{180}=\frac{\pi}{3}\) рад; \(72^\circ=\frac{72\pi}{180}=\frac{2\pi}{5}\) рад; \(270^\circ=\frac{270\pi}{180}=\frac{3\pi}{2}\) рад.
4. г) \(150^\circ=\frac{150\pi}{180}=\frac{5\pi}{6}\) рад; \(216^\circ=\frac{216\pi}{180}=\frac{6\pi}{5}\) рад; \(90^\circ=\frac{90\pi}{180}=\frac{\pi}{2}\) рад.

Ответ: а) \(\frac{\pi}{4}\), \(\frac{\pi}{5}\), \(\pi\); б) \(\frac{2\pi}{3}\), \(\frac{31\pi}{18}\), \(2\pi\); в) \(\frac{\pi}{3}\), \(\frac{2\pi}{5}\), \(\frac{3\pi}{2}\); г) \(\frac{5\pi}{6}\), \(\frac{6\pi}{5}\), \(\frac{\pi}{2}\).