What is trigonometry and how do sine and cosine work?
Trigonometry has a scary name, but it's really just the study of triangles — especially the cozy right triangle, the one with a perfect square corner. Long ago, people who wanted to measure things they couldn't reach — the height of a mountain, the distance to a ship, the width of a river — discovered that triangles held a secret. If you knew an angle and one side, you could figure out all the rest. Trigonometry is the toolkit that unlocks that secret.
Here's the magical part. Take a right triangle, and pick one of the slanted angles to focus on — let's call it your "angle of interest." No matter how big or small you draw the triangle, as long as that angle stays the same, the shape of the triangle stays the same too. Stretch it, shrink it — the sides always keep the same proportions to each other. That steadiness is the whole reason trigonometry works.
