In preparation for my first Trigonometry test, I decided to create my own unit circle using Affinity Designer (Well, penpot at first until I ran into performance issues)

I did this in order to discover any patterns, and to better understand it before I try to create a shorthand version.
unit circle.svg
After creating this, I recognized a pattern that I think can be best described with this reference I created

shorthand 2.svg
Which I will reduce down to this when I write this when using the Unit circle (There’s a mistake, k+1 and k-1 should be swapped)
Quick SHorthand.svg