To find the exact value of \(\sin\left(\frac{\pi}{3}\right)\) using the unit circle, we can first identify the angle \(\frac{\pi}{3}\) radians. This angle corresponds to \(60^\circ\).
On the unit circle, the coordinates of the point at \(60^\circ\) (or \(\frac{\pi}{3}\)) are given by \(\left(\cos\left(\frac{\pi}{3}\right), \sin\left(\frac{\pi}{3}\right)\right)\).
The coordinates for \(60^\circ\) are:
- \(\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}\)
- \(\sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2}\)
Thus, the exact value of \(\sin\left(\frac{\pi}{3}\right)\) is:
\[ \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \]
Therefore, the correct response is:
\(\text{Start Fraction Start Root 3 End Root over 2 End Fraction}\) (or just \(\frac{\sqrt{3}}{2}\)).
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