[tex]Formula \ fundamentala \ a \ trigonometriei:\\ \\ \boxed{\sin^2 x + \cos^2x=1}\\ \\ \sin^2 x + \cos^2 x=1 \Rightarrow \sin^2x+(\frac{\sqrt{3}}{2})^2=1\\ \\ \sin^2 x=1-\frac{3}{4}\\ \\ \sin^2 x=\frac{4}{4}-\frac{3}{4}\\ \\ \Rightarrow \sin^2x=\frac{1}{4} \Rightarrow \sin x=\sqrt{\frac{1}{4}}=\sqrt{(\frac{1}{2})^2}=\pm \frac{1}{2}\\ \\ OBS: \ x \in (0, \ \frac{\pi}{2}) \Rightarrow \sin x>0\\ \\ Deci \ \sin x=\frac{1}{2}[/tex]
