Задание 15.4

Question

$^{\circ}$ Решите уравнение:
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1) $\cos 2 x=\frac{1}{2}$; 2) $\cos \frac{x}{5}=-\frac{\sqrt{3}}{2}$; 3) $\cos \frac{3 x}{4}=-1$.

Gimli · Accepted Answer

1. $$\cos 2 x=\frac{1}{2} \qquad 2 \cos ^{2} x-1=\frac{1}{2} \qquad 2 \cos ^{2} x=\frac{3}{2} \qquad \cos ^{2} x=\frac{3}{4}\qquad \cos x=\frac{\sqrt{3}}{2} \qquad x=\pm \arccos \frac{\sqrt{3}}{2} +2\pi n\quad x=\pm\frac{\pi}{6} + 2\pi n, \quad n \in \mathbb{Z}$$
2. $$\cos \frac{x}{5}=-\frac{\sqrt{3}}{2} \qquad \frac{x}{5}=\pm \arccos \left(-\frac{\sqrt{3}}{2}\right) + 2\pi n \qquad  \frac{x}{5}=\pm\frac{5\pi}{6} +2\pi n\qquad x=\pm\frac{25\pi}{6} + 10\pi n, \quad n \in \mathbb{Z}
$$
3. $$\cos \frac{3 x}{4}=-1 \qquad \frac{3 x}{4}=\pm\arccos (-1) +2\pi n\qquad \frac{3 x}{4}=\pi +2\pi n\qquad 3x=4 \pi +8\pi n\qquad x=\frac{4 \pi}{3} + \frac{8}{3}\pi n, \quad n \in \mathbb{Z}$$

Задание 15.4

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Задание 15.4

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