[tex] \displaystyle\\
\sin x = \frac{1}{2}\\\\
\text{Sinusul este pozitiv doar in cadranul 1 si in cadranul 2.}\\\\
\text{Cazul 1: } \\
x \in C1 ~\Rightarrow~x = 30^o \\
\Rightarrow~ \text{tg }x= \text{tg }30^o = \boxed{\frac{\sqrt{3}}{3}}\\\\
\text{Cazul 2: } \\
x \in C2 ~\Rightarrow~x = 150^o \\
\Rightarrow~ \text{tg }x= \text{tg }150^o =\text{tg }(180^o-30) =-\text{tg }30^o= \boxed{-\frac{\sqrt{3}}{3}} [/tex]