Memorizing the identities $\cos {\pi \over 3}=\sin {\pi \over 6} = {1 \over 2}$ I memorized $\sin {\pi \over 4} = \cos {\pi \over 4}= {1\over \sqrt{2}}$ easily by using the diagonal inside the unit square.
I am having great trouble memorizing the identities $\cos {\pi \over 3}=\sin {\pi \over 6} = {1 \over 2}$ because I keep confusing whether it is $\cos {\pi \over 3}$ or $\cos {\pi \over 6}$ that equals ${1\over 2}$. 

Is there a picture similar to the unit square picture or something
  like it to memorize this identity?


There is an old trick, just memorize that 
$$
\sin 0            =\frac{\sqrt{0}}{2}\qquad 
\sin \frac{\pi}{6}=\frac{\sqrt{1}}{2} \qquad
\sin \frac{\pi}{4}=\frac{\sqrt{2}}{2} \qquad 
\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2} \qquad
\sin \frac{\pi}{2}=\frac{\sqrt{4}}{2} \qquad
$$
and $\cos x$ goes the other way.
