Answer
The exact value of the provided expression is $-\frac{\sqrt{3}}{2}$.
Work Step by Step
The reference angle for $\theta =240{}^\circ $ is:
$\begin{align}
& \theta '=240{}^\circ -180{}^\circ \\
& =60{}^\circ
\end{align}$
Now, the function value for the reference angle is:
$\sin 60{}^\circ =\frac{\sqrt{3}}{2}$
So, we see that the angle $240{}^\circ $ lies in quadrant III, so the sine function is negative:
$\begin{align}
& \sin 240{}^\circ =-\sin 60{}^\circ \\
& =-\frac{\sqrt{3}}{2}
\end{align}$
