Arrange the numbers $\cos 2, \cos 4, \cos 6$ and $\cos 8$ from the biggest to the smallest where $2,4,6,8$ are given as radians.
To arrange the numbers $\cos 2, \cos 4, \cos 6,$ and $\cos 8$ from the biggest to the smallest, we need to consider the properties of the cosine function and the given angles in radians.

1. **Understanding the Cosine Function:**
   The cosine function, $\cos x$, is periodic with a period of $2\pi$ and is decreasing in the interval $(0, \pi)$. This means that for $0 < a < b < \pi$, we have $\cos a > \cos b$.

2. **Convert Angles to the Interval $(0, 2\pi)$:**
   The given angles are $2, 4, 6,$ and $8$ radians. Since $2\pi \approx 6.28$, we can see that $2$ and $4$ radians are within the interval $(0, 2\pi)$, but $6$ and $8$ radians are not. We need to convert $6$ and $8$ radians to their equivalent angles within $(0, 2\pi)$:
   \[
   6 \text{ radians} = 6 - 2\pi \approx 6 - 6.28 = -0.28 \text{ radians}
   \]
   \[
   8 \text{ radians} = 8 - 2\pi \approx 8 - 6.28 = 1.72 \text{ radians}
   \]
   Since cosine is an even function, $\cos(-x) = \cos(x)$, we can use the positive equivalent angles:
   \[
   \cos 6 = \cos(2\pi - 6) \approx \cos(0.28)
   \]
   \[
   \cos 8 = \cos(2\pi - 8) \approx \cos(1.72)
   \]

3. **Compare the Cosine Values:**
   Now we need to compare the values of $\cos 2, \cos 4, \cos 0.28,$ and $\cos 1.72$:
   \[
   0 < 0.28 < 1.72 < 2 < 4 < \pi
   \]
   Since $\cos x$ is decreasing in $(0, \pi)$, we have:
   \[
   \cos 0.28 > \cos 1.72 > \cos 2 > \cos 4
   \]

4. **Substitute Back the Original Angles:**
   \[
   \cos 6 > \cos 8 > \cos 2 > \cos 4
   \]

The final answer is $\boxed{\cos 6 > \cos 8 > \cos 2 > \cos 4}$