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.

Apparatus & Anatomy

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).

Trig Ruler with Hypotenuse, Base, Perpendicular arms and 360-degree protractor disc

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.

Trigonometric Mapping

Trig Scale Anatomy

1. Hypotenuse Scale & 360° Disc

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).

2. Base Scale (Cosine Axis)

Horizontal reference arm graduated in hundredths (0.01 to 1.0). The intersection coordinate provides the direct decimal value of cos(θ).

3. Perpendicular Scale (Sine Axis)

Vertical leg sliding along the Base. The height measured at the intersection provides the direct decimal value of sin(θ).

Pythagorean Mechanical Proof

Demonstrates the identity sin²(θ) + cos²(θ) = 1 visually and physically across every angular adjustment without electronic calculators.

Operation & Verification

Reading & Benchmarks

Standard Benchmark Values

Angle (θ) Base / cos(θ) Perp / sin(θ)
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
Step-by-Step Ratio Reading

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.

cos(θ) = Base / 1.0 | sin(θ) = Perp / 1.0 | tan(θ) = Perp / Base