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.
![How to Easily Remember the Unit Circle? 1 How To Easily Remember the Unit Circle](https://abakcus.com/wp-content/uploads/2020/09/How-To-Easily-Remember-the-Unit-Circle-1024x1024.jpg.webp)
Then, go ahead and add in some nice denominators of 2 in every entry in the table.
![How to Easily Remember the Unit Circle? 2 How To Easily Remember the Unit Circle 2](https://abakcus.com/wp-content/uploads/2020/09/How-To-Easily-Remember-the-Unit-Circle-2-1024x1024.jpg.webp)
Then give yourself some nice square roots on the numerators.
![How to Easily Remember the Unit Circle? 3 How To Easily Remember the Unit Circle 3](https://abakcus.com/wp-content/uploads/2020/09/How-To-Easily-Remember-the-Unit-Circle-3-1024x1024.jpg.webp)
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.
![How to Easily Remember the Unit Circle? 4 How To Easily Remember the Unit Circle 4](https://abakcus.com/wp-content/uploads/2020/09/How-To-Easily-Remember-the-Unit-Circle-4-1024x1024.jpg.webp)
Then we do the opposite in the cosine column.
![How to Easily Remember the Unit Circle? 5 How To Easily Remember the Unit Circle 5](https://abakcus.com/wp-content/uploads/2020/09/How-To-Easily-Remember-the-Unit-Circle-5-1024x1024.jpg.webp)
Then we simplify!
![How to Easily Remember the Unit Circle? 6 How To Easily Remember the Unit Circle 6](https://abakcus.com/wp-content/uploads/2020/09/How-To-Easily-Remember-the-Unit-Circle-6-1024x1024.jpg.webp)
And voila – a beautiful unit circle table.