For those of you who know how to solve absolute value inequalities, here is how they also mean something like “numbers between 8 and 14.”
Category: Pre-Calculus
In The Feynman Lectures on Physics, Volume 3 Chapter 5, Feynman poses a challenge to the reader: show that a particular combination of plus, minus and zero states of a spin one particle transforms under a rotation just like a vector does. In this previous video I reviewed the details of proving it for rotations around the z-axis. Here I go over the more complicated proof for rotations around the y-axis.
In The Feynman Lectures on Physics, Volume 3 Chapter 5, Feynman poses a challenge to the reader: show that a particular combination of plus, minus and zero states of a spin one particle transforms under a rotation just like a vector does. Here I go over how to work that problem using only what was covered in the book up to that point.
A moderately difficult trig identity: prove 
Here’s one of the things about complex numbers which is easier if you know it so well you don’t have to think about it: the formula for sin x. Nice and easy. Assumes you already know Euler’s formula, eix = cos x + i sin x.
Assuming you know the basics (tan=sin/cos, etc), here are strategies and examples for proving simple trig identities.
Gauss was just ten years old when he discovered how to quickly add up a long series of numbers. Here I tell the story of how he outwitted his teacher and I also walk you through a mathematical proof.