The Trig Ruler Interactive Trigonometry Model
A hands-on, mechanical STEM calculating instrument engineered by Maths Industrial Design, transforming abstract trigonometric ratios into tangible geometric measurements directly on the unit circle.
The Instrument
Unit Circle in Your Hands
Features three interconnected precision acrylic arms representing the fundamental edges of a right-angle triangle, indexed from 0 to 1.0 (100 decimal units).
Dual Pivot Interlock
Engineered with smooth brass pivots and tracking guides that preserve a rigid 90° angle between Base and Perpendicular scales as the Hypotenuse rotates.
Trig Scale Anatomy
Acts as the unit radius (r = 1.0). Rotating the arm across the circular protractor sets any acute angle θ between 0° and 90° (full 0–360° dial attached).
Horizontal reference arm graduated in hundredths (0.01 to 1.0). The intersection coordinate provides the direct decimal value of cos(θ).
Vertical leg sliding along the Base. The height measured at the intersection provides the direct decimal value of sin(θ).
Demonstrates the identity sin²(θ) + cos²(θ) = 1 visually and physically across every angular adjustment without electronic calculators.
Reading & Benchmarks
Standard Benchmark Values
| Angle (θ) | Base / cos(θ) | Perp / sin(θ) |
|---|---|---|
| 0° | 1.00 | 0.00 |
| 30° | 0.866 (~0.87) | 0.50 |
| 45° | 0.707 (~0.71) | 0.707 (~0.71) |
| 60° | 0.50 | 0.866 (~0.87) |
| 90° | 0.00 | 1.00 |
1. Pivot the Hypotenuse arm to the target angle on the 0–360° circular dial.
2. Align the Perpendicular arm perpendicular to the Base to form a true right triangle.
3. Read the intersection mark directly on the Base for Cosine and on the Perpendicular arm for Sine.