Question

6sin2 x + 11sin x + 4 = 0

Answer 1

$6sin^2x+11sinx+4=0;sinx=t, t in [-1;1]; 6t^2+11t+4=0;$ $D=121-96=25;$ 
$t=- frac{1}{2};sinx= - frac{1}{2};x=(-1)^n(- frac{ pi }{6})+ pi n, n in Z;$ 
$x=(-1)^{n+1}* frac{ pi }{6}+ pi n, n in Z;$
$t=- frac{16}{12}=-1frac{1}{3}$ -посторонний корень.
Ответ: $x=(-1)^{n+1}* frac{ pi }{6}+ pi n, n in Z;$