[m]cos(5\pi-3x)=\frac{-\sqrt{2}}{2}[/m]
[m]cos(4\pi + \pi -3x)=\frac{-\sqrt{2}}{2}[/m]
[m]cos( \pi -3x)=\frac{-\sqrt{2}}{2}[/m]
[m]cos( \pi -3x)=cos(3x- \pi )[/m]
[m] 3x-\pi =(\pi -arccos\frac{-\sqrt{2}}{2})+2\pi n, n \in Z[/m]
[m] 3x-\pi =\pm\frac{3\pi}{4}+2\pi n, n \in Z[/m]
[m] 3x=\pi \pm\frac{3\pi}{4}+2\pi n, n \in Z[/m]
[m] x=\frac{\pi}{3} \pm\frac{\pi}{4}+\frac{2 \pi }{3}n, n \in Z[/m]
[m] x=\frac{\pi}{3}-\frac{\pi}{4}+\frac{2 \pi}{3} n, n \in Z[/m]или [m] x=\frac{\pi}{3} +\frac{\pi}{4}+\frac{2 \pi }{3}m, m \in Z[/m]
[m] x=\frac{\pi}{12}+\frac{2\pi}{3}n, n \in Z[/m]или [m] x=\frac{7\pi}{12} +\frac{2\pi }{3} m, m \in Z[/m]
Наибольший отрицательный : [m] x=\frac{7\pi}{12} -\frac{2 \pi}{3}=\frac{7\pi}{12} -\frac{8 \pi}{12}=-\frac{ \pi}{12}[/m]