Question

срончноооо дам по мах баллов

Answer 1

$1a)Sin2x=-1\\2x=-frac{pi }{2}+2pi n,nin Z\\x=-frac{pi }{4}+pi n,nin Z$

б) $Ctg3x=0\\3x=frac{pi }{2}+pi n,nin Z\\x=frac{pi }{6}+frac{pi n }{3}.nin Z$

$2)2Cos(2x-frac{pi }{3})-1=0\\2Cos(2x-frac{pi }{3})=1\\Cos(2x-frac{pi }{3})=frac{1}{2}\\2x-frac{pi }{3}=pm arcCosfrac{1}{2}+2pi n,nin Z\\2x-frac{pi }{3}=pm frac{pi }{3}+2pi n,nin Z\\1)2x=frac{pi}{3} +frac{pi }{3} +2pi n,nin Z\\2x=frac{2pi }{3}+2pi n,nin Z\\x_{1}=frac{pi }{3} +pi n,nin Z$

$2x=-frac{pi }{3}+frac{pi }{3}+2pi n,nin Z\\2x=2pi n,nin Z\\x_{2}=pi n,nin Z$

$3)Sinx=m,-1 leq m leq1\\2m^{2}-3m-2=0\\D=(-3)^{2}-4*2*(-2)=9+16=25=5^{2}\\m_{1} =frac{3-5}{2}=-1\\m_{2} =frac{3+5}{2}=4>1\\Sinx=-1\\x=-frac{pi }{2}+2pi n,nin Z$