1. **State the problem:** Find an angle in the fourth quadrant that has the same cosine value as $\cos 74^\circ$. 2. **Recall the cosine function properties:** Cosine is positive in the first and fourth quadrants. 3. **Use the cosine symmetry rule:** For an angle $\theta$ in the first quadrant, the corresponding angle in the fourth quadrant with the same cosine value is given by: $$\theta_{4th} = 360^\circ - \theta$$ 4. **Apply the formula:** $$\theta_{4th} = 360^\circ - 74^\circ = 286^\circ$$ 5. **Conclusion:** The angle in the fourth quadrant with the same cosine value as $\cos 74^\circ$ is $286^\circ$. **Final answer:** $286^\circ$