28. 4 cos x/2 = √3/2 , [−4π; 4π].

$$cos(\frac{x}{2}) = \frac{\sqrt{3}}{2}$$

$$\frac{x}{2} = \pm \frac{\pi}{6} + 2\pi n, n \in Z$$

$$x = \pm \frac{\pi}{3} + 4\pi n, n \in Z$$

Отберем корни, принадлежащие отрезку $$[-4\pi, 4\pi]$$

$$x = \frac{\pi}{3} + 4\pi \cdot (-1) = \frac{\pi}{3} - \frac{12\pi}{3} = -\frac{11\pi}{3}$$

$$x = \frac{\pi}{3} + 4\pi \cdot 0 = \frac{\pi}{3}$$

$$x = \frac{\pi}{3} + 4\pi \cdot 1 = \frac{\pi}{3} + \frac{12\pi}{3} = \frac{13\pi}{3}$$

$$x = -\frac{\pi}{3} + 4\pi \cdot (-1) = -\frac{\pi}{3} - \frac{12\pi}{3} = -\frac{13\pi}{3}$$

$$x = -\frac{\pi}{3} + 4\pi \cdot 0 = -\frac{\pi}{3}$$

$$x = -\frac{\pi}{3} + 4\pi \cdot 1 = -\frac{\pi}{3} + \frac{12\pi}{3} = \frac{11\pi}{3}$$

Ответ: $$x = \pm \frac{\pi}{3}, x = \pm \frac{11\pi}{3}, x = \pm \frac{13\pi}{3}$$