Where Do Sine Waves Come From? Trigonometry Visually Explained

Where do sine and cosine come from, and why do they make waves? This video starts from a simple right triangle and builds up, step by step and fully animated, to the waves behind sound, light and radio. It's high-school level and you don't need any prior knowledge. What you'll learn: What opposite, adjacent and hypotenuse mean, and the SOH-CAH-TOA trick Why sin θ depends only on the angle and not on the size of the triangle How the unit circle turns every angle into a point (cos θ, sin θ) Why sin²θ + cos²θ = 1 is just Pythagoras What radians are and why a full turn is 2π How a spinning point draws the sine wave, and why cosine is the same wave shifted How amplitude and frequency shape a wave, and how they sound (turn your volume up!) Chapters: 0:00 Where do sine waves come from? 0:21 Right triangles & SOH-CAH-TOA 1:20 The unit circle 2:14 Radians: why 2π? 2:59 From a circle to a wave 3:43 Amplitude & frequency (listen!) 4:25 Recap Perfect for students who want to understand trigonometry, not just memorize it. Great for revising before exams, too. Animated with Python (Manim)