Question

Нужна П/6+sinXsinП/6<=1/2
2) система:
Х+у=П
SinX+SinY=1

Answer 1

$1) cosx*cos\frac{\pi }{6} +sinx*sin\frac{\pi }{6} \leq \frac{1}{2} \\cos(x-\frac{\pi }{6})\leq \frac{1}{2}\\\frac{\pi }{3}+2\pi k \leq x-\frac{\pi }{6}\leq \frac{5\pi }{3}+2\pi k\\\frac{\pi }{2}+2\pi k \leq x\leq \frac{13\pi }{6}+2\pi k\\\\2)\left \{ {{x+y=\pi } \atop {sinx+siny=1}} \right. \\\left \{ {{y=\pi-x } \atop {sinx+sin(\pi -x)=1}} \right.\\\left \{ {{y=\pi-x } \atop {sinx+sin\pi*cosx-cos\pi*sinx =1}} \right.\\\left \{ {{y=\pi-x } \atop {sinx+0*cosx+sinx =1}} \right. \\$

$\left \{ {{y=\pi-x } \atop {2sinx =1}} \right. \\\\\left \{ {{y=\pi-x } \atop {sinx =\frac{1}{2} }} \right. \\\left \{ {{y=\pi-x} \atop {x=(-1)^k \frac{\pi }{6}+\pi k }} \right. \\\left \{ {{x=(-1)^k\frac{\pi }{6}+\pi k } \atop {y=\pi +(-1)^{k+1}\frac{\pi }{6}+\pi k }} \right.$