1. **Problem:** Calculate $\cos\left(\frac{\pi}{3}\right)$. 2. **Formula and rules:** The cosine of an angle in radians can be found using the unit circle or known special angles. Important to remember: $\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}$. 3. **Work:** From the unit circle, the angle $\frac{\pi}{3}$ radians (or 60 degrees) corresponds to the point $(\frac{1}{2}, \frac{\sqrt{3}}{2})$. The cosine value is the x-coordinate. 4. **Answer:** Therefore, $$\cos\left(\frac{\pi}{3}\right) = \frac{1}{2}.$$