-\frac{\sqrt{3}}{2}\\3x\in(arcsin(-\frac{\sqrt{3}}{2})+2\pi*n;\pi-\arcsin(-\frac{\sqrt{3}}{2})+2\pi*n),n\in Z\\3x\in(-arcsin\frac{\sqrt{3}}{2}+2\pi*n;\pi+\arcsin\frac{\sqrt{3}}{2}+2\pi*n),n\in Z\\3x\in(-\frac{\pi}{3}+2\pi*n;\frac{4\pi}{3}+2\pi*n),n\in Z\\x\in(-\frac{\pi}{9}+\frac{2\pi*n}{3};\frac{4\pi}{9}+\frac{2\pi*n}{3}),n\in Z" alt="sin(3x)>-\frac{\sqrt{3}}{2}\\3x\in(arcsin(-\frac{\sqrt{3}}{2})+2\pi*n;\pi-\arcsin(-\frac{\sqrt{3}}{2})+2\pi*n),n\in Z\\3x\in(-arcsin\frac{\sqrt{3}}{2}+2\pi*n;\pi+\arcsin\frac{\sqrt{3}}{2}+2\pi*n),n\in Z\\3x\in(-\frac{\pi}{3}+2\pi*n;\frac{4\pi}{3}+2\pi*n),n\in Z\\x\in(-\frac{\pi}{9}+\frac{2\pi*n}{3};\frac{4\pi}{9}+\frac{2\pi*n}{3}),n\in Z" align="absmiddle" class="latex-formula">
-\frac{\sqrt{2}}{2}\\\frac{x}{2}\in(-arccos(-\frac{\sqrt{2}}{2})+2\pi*n;arccos(-\frac{\sqrt{2}}{2})+2\pi*n),n\in Z\\\frac{x}{2}\in(-\frac{3\pi}{4}+2\pi*n;\frac{3\pi}{4}+2\pi*n),n\in Z\\x\in(-\frac{3\pi}{2};+4\pi*n;\frac{3\pi}{2}+4\pi*n),n\in Z" alt="cos(\frac{x}{2})>-\frac{\sqrt{2}}{2}\\\frac{x}{2}\in(-arccos(-\frac{\sqrt{2}}{2})+2\pi*n;arccos(-\frac{\sqrt{2}}{2})+2\pi*n),n\in Z\\\frac{x}{2}\in(-\frac{3\pi}{4}+2\pi*n;\frac{3\pi}{4}+2\pi*n),n\in Z\\x\in(-\frac{3\pi}{2};+4\pi*n;\frac{3\pi}{2}+4\pi*n),n\in Z" align="absmiddle" class="latex-formula">
![cos(3x-\frac{\pi}{4})\geq-\frac{1}{2}\\(3x-\frac{\pi}{4})\in[-arccos(-\frac{1}{2})+2\pi*n;arccos(-\frac{1}{2})+2\pi*n],n\in Z\\(3x-\frac{\pi}{4})\in[-\frac{2\pi}{3}+2\pi*n;\frac{2\pi}{3}+2\pi*n],n\in Z\\3x\in[-\frac{2\pi}{3}+\frac{\pi}{4}+2\pi*n;\frac{2\pi}{3}+\frac{\pi}{4}+2\pi*n],n\in Z\\3x\in[-\frac{5\pi}{12}+2\pi*n;\frac{11\pi}{12}+2\pi*n],n\in Z\\x\in[-\frac{5\pi}{36}+\frac{2\pi*n}{3};\frac{11\pi}{36}+\frac{2\pi*n}{3}],n\in Z](https://tex.z-dn.net/?f=cos%283x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Cgeq-%5Cfrac%7B1%7D%7B2%7D%5C%5C%283x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Cin%5B-arccos%28-%5Cfrac%7B1%7D%7B2%7D%29%2B2%5Cpi%2An%3Barccos%28-%5Cfrac%7B1%7D%7B2%7D%29%2B2%5Cpi%2An%5D%2Cn%5Cin+Z%5C%5C%283x-%5Cfrac%7B%5Cpi%7D%7B4%7D%29%5Cin%5B-%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%2An%3B%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B2%5Cpi%2An%5D%2Cn%5Cin+Z%5C%5C3x%5Cin%5B-%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B%5Cfrac%7B%5Cpi%7D%7B4%7D%2B2%5Cpi%2An%3B%5Cfrac%7B2%5Cpi%7D%7B3%7D%2B%5Cfrac%7B%5Cpi%7D%7B4%7D%2B2%5Cpi%2An%5D%2Cn%5Cin+Z%5C%5C3x%5Cin%5B-%5Cfrac%7B5%5Cpi%7D%7B12%7D%2B2%5Cpi%2An%3B%5Cfrac%7B11%5Cpi%7D%7B12%7D%2B2%5Cpi%2An%5D%2Cn%5Cin+Z%5C%5Cx%5Cin%5B-%5Cfrac%7B5%5Cpi%7D%7B36%7D%2B%5Cfrac%7B2%5Cpi%2An%7D%7B3%7D%3B%5Cfrac%7B11%5Cpi%7D%7B36%7D%2B%5Cfrac%7B2%5Cpi%2An%7D%7B3%7D%5D%2Cn%5Cin+Z "cos(3x-\frac{\pi}{4})\geq-\frac{1}{2}\\(3x-\frac{\pi}{4})\in[-arccos(-\frac{1}{2})+2\pi*n;arccos(-\frac{1}{2})+2\pi*n],n\in Z\\(3x-\frac{\pi}{4})\in[-\frac{2\pi}{3}+2\pi*n;\frac{2\pi}{3}+2\pi*n],n\in Z\\3x\in[-\frac{2\pi}{3}+\frac{\pi}{4}+2\pi*n;\frac{2\pi}{3}+\frac{\pi}{4}+2\pi*n],n\in Z\\3x\in[-\frac{5\pi}{12}+2\pi*n;\frac{11\pi}{12}+2\pi*n],n\in Z\\x\in[-\frac{5\pi}{36}+\frac{2\pi*n}{3};\frac{11\pi}{36}+\frac{2\pi*n}{3}],n\in Z")
в 3 не знаю что перед косинусом стоит