Question

Срочно на картинке!!!

Answer 1

$1)Sinx\leq \frac{\sqrt{2} }{2}\\\\-\pi -arcSin\frac{\sqrt{2} }{2} +2\pi n\leq x \leq arcSin\frac{\sqrt{2}}{2} +2\pi n,n\in Z\\\\-\pi -\frac{\pi }{4}+2\pi n\leq x\leq\frac{\pi }{4}+2\pi n,n\in Z\\\\ -\frac{5\pi }{4}+2\pi n\leq x\leq\frac{\pi }{4}+2\pi n,n\in Z\\\\Otvet:\boxed{x\in[ -\frac{5\pi }{4}+2\pi n;\frac{\pi }{4}+2\pi n],n\in Z}\\\\\\2)Cosx\leq\frac{\sqrt{3} }{2}\\\\arcCos\frac{\sqrt{3} }{2}+2\pi n\leq x\leq 2\pi -arcCos\frac{\sqrt{3} }{2} ,n\in Z$

$\frac{\pi }{6}+2\pi n\leq x\leq 2\pi-\frac{\pi }{6}+2\pi n,n\in Z \\\\\frac{\pi }{6}+2\pi n\leq x\leq \frac{11\pi }{6}+2\pi n,n\in Z \\\\Otvet:\boxed{[\frac{\pi }{6}+2\pi n ;\frac{11\pi }{6}+2\pi n],n\in Z}$

$3)tgx\geq-1\\\\-\frac{\pi }{2} +\pi n < x \leq arctg(-1)+\pi n,n\in Z\\\\-\frac{\pi }{2}+\pi n<x\leq-\frac{\pi }{4}+\pi n,n\in Z\\\\\Otvet:\boxed{x\in(-\frac{\pi }{2}+\pi n;-\frac{\pi }{4}+\pi n].n\in Z}\\\\\\4)Ctgx\geq\frac{\sqrt{3} }{3}\\\\\pi n< x \leq arcCtg\frac{\sqrt{3} }{3}+\pi n,n\in Z\\\\\pi n< x \leq \frac{\pi }{3}+\pi n,n\in Z \\\\Otvet:\boxed{x\in(\pi n;\frac{\pi }{3} +\pi n],n\in Z}$