TITLE: Memorizing the identities $\cos {\pi \over 3}=\sin {\pi \over 6} = {1 \over 2}$
QUESTION [5 upvotes]: 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?

REPLY [2 votes]: \begin{array}{|c|c|c|c|c|c|} \hline 
{}&{0^\circ}&{30^\circ}&{45^\circ}&{60^\circ}&{90^\circ} \\ \hline
{\rm sin (\alpha)} &\sqrt 0 \over 2&{\sqrt 1 \over 2}&{\sqrt 2 \over 2}&{\sqrt 3 \over 2}&{\sqrt 4 \over  2}\\ \hline
{\rm cos (\alpha)} &{\sqrt 4 \over 2}&{\sqrt 3 \over 2}&{\sqrt 2 \over 2}&{\sqrt 1 \over 2}&{\sqrt 0 \over 2}\\ \hline
{\rm tan (\alpha)} &0&{{1} \over \sqrt{3}}&{1}&{\sqrt 3}&\infty\\ \hline
{\rm ctan (\alpha)} &\infty&{\sqrt{3}}&1&{1 \over \sqrt 3}&0 \\ \hline
\end{array}