1. The problem asks for the value of $\cos 60^\circ$.\n\n2. Recall that cosine of an angle in a right triangle is the ratio of the adjacent side to the hypotenuse.\n\n3. The cosine values for special angles are well-known: $\cos 0^\circ = 1$, $\cos 30^\circ = \frac{\sqrt{3}}{2}$, $\cos 45^\circ = \frac{\sqrt{2}}{2}$, $\cos 60^\circ = \frac{1}{2}$, and $\cos 90^\circ = 0$.\n\n4. Therefore, $\cos 60^\circ = \frac{1}{2}$.\n\n5. Among the options given, option b. $\frac{1}{2}$ is the correct answer.