Question

решите неравенство sin x >или равно минус 1/2

Answer 1

$sin xgeq -frac12;\ sin x=-frac12;\ x=-(-1)^nfracpi6+pi n;\ 1) xin(-fracpi6+2pi n; frac{7pi}{6}+2pi n):\ x=pi n, sinpi n=0>-frac12;\ 2)xin(frac{7pi}{6}+2pi n; frac{11pi}{6}+2pi n):\ x=frac{3pi}{2}+2pi n=sin(frac{3pi}{2}+2pi n)=-1<-frac12;\ \ \ \ \ xinleft[-fracpi6+2pi n; frac{7pi}{6}+2pi nright], nin Z.$