I've noticed some relationships with cosine and square root. 
Yesterday I've noticed some relationships with cosine and square root. Anything interesting about it?

I was trying to find the smallest width on an hexagon with radius $1.0$ and I noticed that I could get it both by $\sqrt 3$ and the or two times the cosine of $30^\circ$.

I wondered if there would be more matches and so I notice these even though might look silly...
$2 \times \cos 90^\circ = \sqrt 0$
$2 \times \cos 60^\circ = \sqrt 1$
$2 \times \cos 45^\circ = \sqrt 2$
$2 \times \cos 30^\circ = \sqrt 3$
$2 \times \cos 0^\circ = \sqrt 4$
Is there anything interesting to know about these?
Thanks
 A: This rules we used in high school with fingers do apply for both sine and cosine see the pictures

See also the following 

A: Your list is sometimes given in trig books as a mnemonic device.  Looking a little deeper the pattern that the angles in a regular $n$-gon give algebraic values for the $\cos$ function is showing itself, though the pattern of simple surds does not continue, e.g. $\cos (\frac{2\pi}{5})=\frac{1}{4}(\sqrt{5}-1)$
A: The last figure was also teached to me mnemotecnically to memorize the value of trigonometric functions on certain angles, notice that you can also calculate the tangent by ignoring dividing 2 this way:
Take the 0 and the 4 of the fist column (0 radians), divide and take the root, you have: $tan (0)= \sqrt(\dfrac{0}{4})=0$
For the second column we have $\dfrac{\pi}{6}$, take the 1 and the 3, divide and take the root again: $tan (\dfrac{\pi}{6})=\sqrt(\dfrac{1}{3})=\dfrac{\sqrt(1)}{\sqrt(3)}=\dfrac{1}{\sqrt 3}$
Similarily, $tan(\dfrac{\pi}{4})=\sqrt(\dfrac{2}{2})=\sqrt(1)=1$
$tan(\dfrac{\pi}{3})=\sqrt(\dfrac{3}{1})=\sqrt 3$
Finally, take for the 4th column ($\dfrac{\pi}{2}$) 4 and $0$.  $tan(\dfrac{\pi}{2})=\sqrt(\dfrac{4}{0})!$ wich is in agreement of the fact that $tan$ is not defined on $\dfrac{\pi}{2}$ and thus cannot be.
