Основано на упр. 1, стр. 20

Выбери правильные ответы

Найди область определения каждой функции.

\(y = \arcsin (2 \cos x)\) ;

• \(- \cfrac{\pi}{4} \le x \le \cfrac{\pi}{4}\) .
• \(- \cfrac{\pi}{3} \le x \le \cfrac{\pi}{3}\) .
• \(\cfrac{\pi}{3} \le x \le \cfrac{2\pi}{3}\) .
• \(- \cfrac{\pi}{6} \le x \le \cfrac{\pi}{6}\) .

\(y = \arccos (2 \sin x)\) ;

• \(- \cfrac{\pi}{4} \le x \le \cfrac{\pi}{4}\) .
• \(- \cfrac{\pi}{3} \le x \le \cfrac{\pi}{3}\) .
• \(- \cfrac{\pi}{6} \le x \le \cfrac{\pi}{6}\) .
• \(- \arccos \cfrac{2}{\pi} \le x \le \arccos \cfrac{2}{\pi}\) .

\(y = \arcsin (\sqrt{2} \sin x)\) ;

• \(- \cfrac{\pi}{4} \le x \le \cfrac{\pi}{4}\) .
• \(- \cfrac{\pi}{3} \le x \le \cfrac{\pi}{3}\) .
• \(- \cfrac{\pi}{6} \le x \le \cfrac{\pi}{6}\) .
• \(- \arccos \cfrac{2}{\pi} \le x \le \arccos \cfrac{2}{\pi}\) .

\(y = \arccos \left( \cfrac{\pi}{2} \cos x \right)\) ;

• \(- \cfrac{\pi}{4} \le x \le \cfrac{\pi}{4}\) .
• \(- \arccos \cfrac{2}{\pi} \le x \le \arccos \cfrac{2}{\pi}\) .
• \(- \cfrac{\pi}{6} \le x \le \cfrac{\pi}{6}\) .
• \(\pi - \arccos \cfrac{2}{\pi} \le x \le \arccos \cfrac{2}{\pi}\) .

\(y = \arcsin ( \tg x)\) ;

• \(- \cfrac{\pi}{4} \le x \le \cfrac{\pi}{4}\) .
• \(- \cfrac{\pi}{3} \le x \le \cfrac{\pi}{3}\) .
• \(- \cfrac{\pi}{6} \le x \le \cfrac{\pi}{6}\) .
• \(- \arccos \cfrac{2}{\pi} \le x \le \arccos \cfrac{2}{\pi}\) .

\(y = \arccos (\tg x)\) ;

• \(- \cfrac{\pi}{3} \le x \le \cfrac{\pi}{3}\) .
• \(- \cfrac{\pi}{6} \le x \le \cfrac{\pi}{6}\) .
• \(- \arccos \cfrac{2}{\pi} \le x \le \arccos \cfrac{2}{\pi}\) .
• \(- \cfrac{\pi}{4} \le x \le \cfrac{\pi}{4}\) .