Ответ:

решение смотри на фотографии

[tex]\displaystyle\bf\\Sin\frac{x}{2} =-\frac{1}{2} \\\\\\\frac{x}{2} =\Big(-1\Big)^{n} arcSin\Big(-\frac{1}{2} \Big)+\pi n,n\in Z\\\\\\\frac{x}{2} =\Big(-1\Big)^{n+1} arc Sin\frac{1}{2} +\pi n,n\in Z\\\\\\\frac{x}{2} =\Big(-1\Big)^{n+1} \frac{\pi }{6} +\pi n,n\in Z\\\\\\\boxed{x=\Big(-1\Big)^{n+1}\frac{\pi }{3} +2\pi n,n\in Z}[/tex]