Вычислить (1143—1144). 1143. 1) arccos 0; 2) arccos 1; 3) arccos(√2/2); 4) arccos(1/2); 5) arccos(-√3/2); 6) arccos(-√2/2). 1144. 1) 2 arccos0+3 arccos 1; 2) 3 arccos(-1) - 2 arccos 0; 3) 12arccos(√3/2) - 3arccos(-1/2); 4) 4arccos(-√2/2) + 6arccos(-√3/2).

1143

• 1) \(\arccos 0 = \frac{\pi}{2}\)
• 2) \(\arccos 1 = 0\)
• 3) \(\arccos \frac{\sqrt{2}}{2} = \frac{\pi}{4}\)
• 4) \(\arccos \frac{1}{2} = \frac{\pi}{3}\)
• 5) \(\arccos \left(-\frac{\sqrt{3}}{2}\right) = \frac{5\pi}{6}\)
• 6) \(\arccos \left(-\frac{\sqrt{2}}{2}\right) = \frac{3\pi}{4}\)

1144

• 1) \(2 \arccos 0 + 3 \arccos 1 = 2 \cdot \frac{\pi}{2} + 3 \cdot 0 = \pi + 0 = \pi\)
• 2) \(3 \arccos(-1) - 2 \arccos 0 = 3 \cdot \pi - 2 \cdot \frac{\pi}{2} = 3\pi - \pi = 2\pi\)
• 3) \(12 \arccos \frac{\sqrt{3}}{2} - 3 \arccos \left(-\frac{1}{2}\right) = 12 \cdot \frac{\pi}{6} - 3 \cdot \frac{2\pi}{3} = 2\pi - 2\pi = 0\)
• 4) \(4 \arccos \left(-\frac{\sqrt{2}}{2}\right) + 6 \arccos \left(-\frac{\sqrt{3}}{2}\right) = 4 \cdot \frac{3\pi}{4} + 6 \cdot \frac{5\pi}{6} = 3\pi + 5\pi = 8\pi\)