Question

Помогите пожалуйста!!! Очень нужно спасайте физматы.

Answer 1

$1)Sinx=\frac{1}{2}\\\\x=(-1)^{n}arcSin\frac{1}{2}+\pi n,nez\\\\x=(-1)^{n}\frac{\pi }{6}+\pi n,nez\\\\2)tg2x=0\\\\2x=\pi n,nez\\\\x=\frac{\pi n}{2},nez\\\\3)Sin3x=1\\\\3x=\frac{\pi }{2}+2\pi n,nez\\\\x=\frac{\pi }{6}+\frac{2\pi n }{3},nez$

$4)Sin(\frac{5x}{3}+\frac{\pi }{4})=\frac{\sqrt{3} }{2}\\\\\frac{5x}{3}+\frac{\pi }{4}=(-1)^{n} arcSin\frac{\sqrt{3} }{2}+\pi n,nez\\\\\frac{5x}{3}+\frac{\pi }{4}=(-1)^{n}\frac{\pi }{3}+\pi n,nez\\\\\frac{5x}{3} =(-1)^{n}\frac{\pi }{3}-\frac{\pi }{4}+\pi n,nez\\\\x=(-1)^{n}\frac{\pi }{5} -\frac{3\pi }{20}+\frac{3\pi n }{5} ,nez$

$5)6Cos^{2}x-5Cosx-1=0\\\\Cosx=;-1\leq m\leq 1\\\\6m^{2} -5m-1=0\\\\D=(-5)^{2} -4*6*(-1)=25+24=49=7^{2}\\\\m_{1}=\frac{5+7}{12}=1\\\\m_{2}=\frac{5-7}{12}=-\frac{1}{6} \\\\Cosx=1\\\\x=2\pi n,nez\\\\Cosx=-\frac{1}{6}\\\\x=+-arcCos(-\frac{1}{6})+2\pi n,nez$