A Trig Mnemonic Revisited with Texify!

Some time ago, I posted a piece about math mnemonics. Buried near the bottom was my feeble attempt to make a table showing a well-known (?) fascinating pattern for sin and cos values for the common angles in Quadrant I. Over the years, some students have found this to be as useful as memorizing ordered pairs on the unit circle or deriving everything from 30-60-90 and 45-45-90 (which I still prefer personally). I've seen students make this table at the top of their trig unit exam - they figured it was worth the effort! I'm reprinting this today using an image created in LaTeX and the absolutely wonderful and easy to use Texify website. This has been a real boon for those using Blogger since LaTeX has not yet been supported. Many math bloggers have been using it for a while now and I'm sure they appreciate its power and simplicity as much as I do. Its author is Andrey Burkov and Ars Mathematica gives him proper credit here. Certainly if an old dog like me can learn new tricks like this, anyone can! By the way at the Texify site, there is an extremely well-written tutorial with many examples to follow. I suspect I will be using this a lot for my new posts and perhaps cleaning up my old. Let me know if the table below is as readable as it appears to me. and, of course, if you like the pattern, you can tell me that too!

The original post used the klutziest of notations and was barely readable. This should be a lot better! I omitted the row for the tan function which is just the quotient of rows 2 and 3: