We explore the method of finding a corresponding single trigonometric function r sin(θ+α) or r cos(θ-β) for a sum of trigonometric functions in the form of f(θ) = a cos θ + b sin θ.

Explore formulas for transforming products of trigonometric functions into sums or differences, derive these formulas from trigonometric addition theorems, and then derive formulas for transforming sums or differences of trigonometric functions into products.

We examine the double-angle and triple-angle formulas and derive them from the Trigonometric Addition Formulas. We also derive the half-angle formulas from the double-angle formulas.

Examine the definitions of trigonometric functions and the relationships between them, and derive the addition formulas for trigonometric functions and their derivative formulas.

Learn how to design effective prompts for multilingual translation of Markdown files and automate the workflow using Python with the Anthropic/Gemini API. This first part of the series details the prompt design process.

Why writing good code matters, and core principles for clean, readable, maintainable software—plus PS/CP trade‑offs and practical examples.

Learn what technical debt is, why it arises in software projects, and how to minimize it with conventions, clean code, automation, and refactoring.

Calculate the intensity of a neutron beam as it penetrates a target material, derive the mean free path of neutrons, and determine macroscopic cross-sections for homogeneous mixtures and molecules containing multiple nuclides.

Explore the concepts of microscopic and macroscopic cross-sections and types of neutron interactions with nuclei, examining actual cross-section data from the Korea Atomic Energy Research Institute to understand neutron scattering and absorption behavior across energy regions.

We explore the Bernoulli equation and its solution method, as well as the logistic equation, which is a special form of the Bernoulli equation.