The Origin of Trigonometric Ratios
This animation traces how sine, cosine, and tangent emerged from similar right triangles, showing that angle-side ratios stay constant regardless of triangle size. It builds from a simple right triangle to the unit circle, linking side ratios to coordinates and revealing why trigonometric values depend only on angle. Useful for HSC first-year students building intuition before memorizing formulas or tables.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Show how the trigonometric ratios developed. Audience: Hsc 1st year student
Make the next one in this series
- Show how the unit circle extends trigonometric ratios beyond 90 degrees.
- Animate the derivation of the sine and cosine rules from triangle geometry.
- Show how ancient astronomers used chords before sine and cosine were defined.
