Question

Решить уравнение, срочно!!!
3sin^2x -5sinx -2=0

Answer 1

$\displaystyle\bf\\3Sin^{2} x-5Sinx-2=0\\\\Sinx=m \ \ ; \ \ -1\leq m\leq 1\\\\3m^{2} -5m-2=0\\\\D=(-5)^{2} -4\cdot 3\cdot (-2)=25+24=49=7^{2} \\\\\\m_{1} =\frac{5-7}{6} =-\frac{1}{3} \\\\\\m_{2} =\frac{5+7}{6} =2 \ > 1- \ ne \ podxodit\\\\\\Sinx=-\frac{1}{3} \\\\\\x=(-1)^{n} arc Sin\Big(-\frac{1}{3} \Big)+\pi n,n\in Z\\\\\\\boxed{x=(-1)^{n+1} arc Sin\frac{1}{3} +\pi n,n\in Z}$