Answer
$x=\{5.9756,3.4492\}$
Work Step by Step
$sin^2(x)-3sin(x)-1=0$
$sin(x)=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-3) \pm \sqrt{(-3)^2 - 4 (1)(-1)}}{2(1)}=\frac{3+\sqrt{13}}{2},\frac{3-\sqrt{13}}{2}$
$sin(x)=\frac{3-\sqrt{13}}{2}=-0.302$
$x=sin^{-1}(\frac{3-\sqrt{13}}{2})$
We know $sin(x)$ is negative in quadrant $III$ and $IV$
$x=5.9756\;\;\;\;\;\;\;\;or\;\;\;\;\;\;\;\;x=3.4492$
$sin(x)=\frac{3-\sqrt{13}}{2}\;\;\;\;$
$x=\{5.9756,3.4492\}$
