Сумма корней в промежутке [0; 4π] [latex] \left \{ {{sinx\ \textless \ 0} \atop {cosx= \frac{1}{2} }} \right. [/latex]

[latex] \left \{ {{sinx\ \textless \ 0} \atop {cosx=\frac{1}{2}}} \right. \; \left \{ {{-\frac{\pi}{2}+2\pi n\ \textless \ x\ \textless \ 2\pi n} \atop {x=\pm \frac{\pi}{3}+2\pi k}} \right. ;x=-\frac{\pi}{3}+2\pin\\\\x\in [\, 0;4\pi ]\; :\; \; x=\frac{5\pi}{3}\; ,\; \frac{11\pi}{3}\; .\\\\\frac{5\pi}{3}+\frac{11\pi }{3}=\frac{16\pi}{3}[/latex]