# Solve the Equation 4sin^(2)+11sin x-3=0

Solve the Equation
$4{\mathrm{sin}}^{2}+11\mathrm{sin}x-3=0$
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Yasmin Lam
$4{\mathrm{sin}}^{2}x+11\mathrm{sin}x-3=0$
$\mathrm{sin}x=t;-1\le t\le 1$
$4{t}^{2}+11t-3=0$
D=121+48=169
${t}_{1}=\frac{-11-13}{8}=-3$
${t}_{2}=\frac{-11+13}{8}=\frac{1}{4}$
$\mathrm{sin}x=\frac{1}{4}$
$x=\left(-1{\right)}^{n}\ast \mathrm{arcsin}\frac{1}{4}+\pi \ast n$
$n\in Z$.
(${t}_{1}=-3$ is excluded because the condition is unsatisfactory)