1. The problem is to find the value of $\cos 10^\circ$. 2. The cosine function is a trigonometric function that gives the ratio of the adjacent side to the hypotenuse in a right triangle. 3. Since $10^\circ$ is not one of the standard angles with simple exact values, we typically use a calculator or trigonometric tables to find $\cos 10^\circ$. 4. Using a calculator, $\cos 10^\circ \approx 0.9848$. 5. Therefore, the value of $\cos 10^\circ$ is approximately $0.9848$.