1. The problem is to evaluate $\cos 0$ and understand its value in quadrant I. 2. Recall the definition: $\cos \theta$ is the x-coordinate of the point on the unit circle at angle $\theta$. 3. At $0$ radians (or $0^\circ$), the point on the unit circle is $(1,0)$. 4. Therefore, $\cos 0 = 1$. 5. Since $\cos 0 = 1$, it is not equal to $0$. 6. Also, $0$ radians lies on the positive x-axis, which is the boundary of quadrant I, but $\cos 0$ is definitely $1$, not $0$. 7. So the statement "$\cos 0 = 0$ in quadrant I" is incorrect; the correct value is $\cos 0 = 1$.