1. The problem is to find the value of $\cos \frac{1}{2}$. 2. The cosine function, $\cos x$, gives the horizontal coordinate of a point on the unit circle at an angle $x$ radians from the positive x-axis. 3. Here, $x = \frac{1}{2}$ radians, which is approximately 0.5 radians. 4. To find $\cos \frac{1}{2}$, we can use a calculator or known cosine values. 5. Using a calculator, $\cos \frac{1}{2} \approx 0.8775825619$. 6. Therefore, the value of $\cos \frac{1}{2}$ is approximately $0.8776$ when rounded to four decimal places.