How does a calculator find sinx?

Online Python IDE: https://www.online-python.com/
My code: https://www.online-python.com/diwYZl2Luj

Credit to @HowToBasic for the clips I used in the video. I figured he wouldn't mind me stealing just a few seconds... hopefully.

Knowledge of the following topics are essential to understand this video:
Basic trigonometry (obviously)
Radians & Degrees
Matrices

Chapters:
0:00 Explaination
5:26 Programming