I work in a walk-in tutor lab at my university, and one of the other tutors showed me this a couple of years back and **changed my life.**

First, you make a table that looks like this.

Then, go ahead and add in some nice denominators of 2 in every entry in the table.

Then give yourself some nice square roots on the numerators.

Alright – now we’re going to fill it in. The only value you have to remember is that sin(0)=0. So we put 0 in the numerator for 0 in the sine column. Then we count up as we move down.

Then we do the opposite in the cosine column.

Then we simplify!

And voila – a beautiful unit circle table.