To find the value of \(\cos\left(\frac{2\pi}{3}\right)\), we can use the unit circle.
The angle \(\frac{2\pi}{3}\) radians is in the second quadrant. We can find it by recognizing that \(\frac{2\pi}{3}\) is equivalent to \(120^\circ\), which is calculated by converting radians to degrees using the formula:
\[ \frac{2\pi}{3} \cdot \frac{180^\circ}{\pi} = 120^\circ \]
On the unit circle, the coordinates for the angle \(120^\circ\) or \(\frac{2\pi}{3}\) are:
\[ \left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \]
The cosine value corresponds to the x-coordinate of the point on the unit circle. Therefore,
\[ \cos\left(\frac{2\pi}{3}\right) = -\frac{1}{2} \]
Thus, the value of \(\cos\left(\frac{2\pi}{3}\right)\) is \(-\frac{1}{2}\).