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Math Physics Pre-Calculus Proofs Proving Identities Science Trigonometry

Spin One Particle Rotates Like a Vector, y-axis

InĀ 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.

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Complex Numbers Math Physics Pre-Calculus Proofs Proving Identities Science Trigonometry

Spin One Particle Rotates Like a Vector, z-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.

Categories
Math Math Analysis Pre-Calculus Proofs Proving Identities Trigonometry

Another Trig Identity

A moderately difficult trig identity: prove \frac{ \frac{1}{tan(x)}+cot(x) }{ \frac{1}{tan(x)}+tan(x) }= \frac{2}{sec^2(x)} using u-substitution.

Categories
Math Analysis Pre-Calculus Proofs Proving Identities Trigonometry

Proving Trig Identities: Some Strategies

Assuming you know the basics (tan=sin/cos, etc), here are strategies and examples for proving simple trig identities.