018.1. a) sin 2x = \(\frac{\sqrt{2}}{2}\); 6) cos \(\frac{x}{3}\) = -\(\frac{1}{2}\); B) sin \(\frac{x}{4}\) = \(\frac{1}{2}\); r) cos 4x = 0.

Ответ: a) x = \(\frac{\pi}{8}\) + \(\frac{\pi k}{2}\), x = \(\frac{3\pi}{8}\) + \(\frac{\pi k}{2}\); б) x = ±2π + 6πk; в) x = \(\frac{2\pi}{3}\) + 8πk, x = \(\frac{10\pi}{3}\) + 8πk; г) x = \(\frac{\pi}{8}\) + \(\frac{\pi k}{4}\)

a) sin 2x = \(\frac{\sqrt{2}}{2}\)

2x = \(\frac{\pi}{4}\) + 2\(\pi k\), 2x = \(\frac{3\pi}{4}\) + 2\(\pi k\)

x = \(\frac{\pi}{8}\) + \(\pi k\), x = \(\frac{3\pi}{8}\) + \(\pi k\)

б) cos \(\frac{x}{3}\) = -\(\frac{1}{2}\)

\(\frac{x}{3}\) = ±\(\frac{2\pi}{3}\) + 2\(\pi k\)

x = ±2\(\pi\) + 6\(\pi k\)

в) sin \(\frac{x}{4}\) = \(\frac{1}{2}\)

\(\frac{x}{4}\) = \(\frac{\pi}{6}\) + 2\(\pi k\), \(\frac{x}{4}\) = \(\frac{5\pi}{6}\) + 2\(\pi k\)

x = \(\frac{2\pi}{3}\) + 8\(\pi k\), x = \(\frac{10\pi}{3}\) + 8\(\pi k\)

г) cos 4x = 0

4x = \(\frac{\pi}{2}\) + \(\pi k\)

x = \(\frac{\pi}{8}\) + \(\frac{\pi k}{4}\)

Ответ: a) x = \(\frac{\pi}{8}\) + \(\frac{\pi k}{2}\), x = \(\frac{3\pi}{8}\) + \(\frac{\pi k}{2}\); б) x = ±2π + 6πk; в) x = \(\frac{2\pi}{3}\) + 8πk, x = \(\frac{10\pi}{3}\) + 8πk; г) x = \(\frac{\pi}{8}\) + \(\frac{\pi k}{4}\)