[tex]\displaystyle\bf\\\textbf{Propun sa transformam din radiani in grade.}\\\\\frac{4\pi}{3}=\frac{4\times180}{3}=4\times60=240^o\\\\\textbf{Unghiul de }~240^o~\textbf{ este in cadranul 3 deoarece:}\\\\180^o<240^o<270^o\\\\\textbf{In cadranul 3 sinusul este negativ.}\\\\\textbf{Aducem unghiul in cadranul 1.}\\\\sin\,240^o=sin(180^o+60^o)=-sin\,60^o=-\frac{\sqrt{3}}{2}\\\\\implies~\boxed{\bf~sin\,240^o=-\frac{\sqrt{3}}{2}}[/tex]