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Пример.

\(\cos x=-\dfrac{1}{2}\) .

Решение.

По формуле \(x=\pm \arccos \left(-\dfrac{1}{2}\right) +2\pi n\) , \(n\in \Z\) :

\(\arccos\left(-\dfrac{1}{2}\right)=\pi-\arccos\dfrac{1}{2}=\pi-\dfrac{\pi}{3}=\dfrac{2\pi}{3}\) ,

\(x=\pm \dfrac{2\pi}{3}+2\pi n\) , \(n\in \Z\) .

Ответ: \(x=\pm \dfrac{2\pi}{3}+2\pi n\) , \(n\in \Z\) .

Реши уравнения.

• \(\pm \dfrac{3\pi}{4}\)
• \(2\pi k\)
• \(\pm \dfrac{5\pi}{6}\)
• \(2\pi n\)
• \(\pm \dfrac{\pi}{4}\)
• \(\pm \dfrac{\pi}{6}\)
• \(\pi k\)
• \(\pi n\)

1. \(\cos x=-\dfrac{\sqrt{2}}{2}\) .

   \(x=\) [ ] \(+\) [ ], \(k\in \Z\) .

2. \(\cos x=-\dfrac{\sqrt{3}}{2}\) .

   \(x=\) [ ] \(+\) [ ], \(n\in \Z\) .