Question

срончноооо дам по мах баллов

Answer 1

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

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

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

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

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