Derive Most Math Trigonometry Formulas via Euler Identity

When I was in high school, I remember that I had to memorize all trigonometry formulas. I didn’t have a single way to resort to when I was locked. Fortunately, As I will show here, most trigonometry formulas can be derived via simple algebraic modifications of Euler's Formula. This way, any time we are locked and can’t remember what the formula was, we can simply derive it. Euler’s Formula $$e^{ix} = \cos(x) + i\sin(x)$$ ...

September 3, 2025 · 8 min · 1695 words · Amir

Bayesian Linear Regression Full Derivation

Introduction Many articles like this in the towardsdatascience tell us how to use Bayesian Linear Regression and why. I am not going to repeat that. I want to derive the formulas from scratch entirely. I also understand that comprehending this stuff is slightly challenging if you don’t have a strong mathematics background. Note: All of my notation is from Bishop’s book. The main difference between Bayesian and Non-Bayesian regression is that Bayesian regression assumes that weights are Random variables. ...

March 20, 2021 · 5 min · 957 words · Amir