10sin^2x+11sinx-8=0

10sin²x+11sinx-8=0 sinx=a, |a|≤1 10a²+11a-8=0 D=11²-4*10*(-8)=121+320=441=[latex](\pm21)^2[/latex] [latex]a_1= \frac{-11-21}{2*10}= \frac{-32}{20}=-1,6\\a_2= \frac{-11+21}{2*10}= \frac{10}{20}=0,5\\a_1\neq sinx [/latex] sinx=0,5 [latex]x=(-1)^n\,\, \frac{\pi}{6}\,+\,\pi*n,n\in \mathbb{Z} [/latex]