Trigonometry Basics for Developers and Designers

Why Developers Need Trigonometry

Trigonometry is the math of angles and distances. It underlies circular motion, wave animations, audio waveforms, radar charts, analog clocks, and collision detection. Understanding sine and cosine unlocks an enormous range of visual and interactive effects.

The Big Three Functions

For a right triangle with angle θ:

• sin(θ) = opposite / hypotenuse
• cos(θ) = adjacent / hypotenuse
• tan(θ) = opposite / adjacent = sin / cos

Radians vs Degrees

Most programming languages use radians. Convert with:

• Degrees to radians: rad = deg * (π / 180)
• Radians to degrees: deg = rad * (180 / π)

Full circle = 360° = 2π radians.

Practical Applications

Circular Motion

Place points on a circle of radius r centered at (cx, cy):

x = cx + r * cos(angle) y = cy + r * sin(angle)

Distribute 12 items evenly: increment angle by 2π/12 = 30° between each.

Wave Animation

A sine wave oscillates between -1 and 1. Control amplitude (height), frequency (speed), and phase (offset):

y = amplitude * sin(frequency * x + phase)

Rotation

Rotate point (x, y) by angle θ around the origin:

x' = x * cos(θ) - y * sin(θ) y' = x * sin(θ) + y * cos(θ)

Distance and Angle Between Points

Distance: d = sqrt((x2-x1)² + (y2-y1)²) Angle: θ = atan2(y2-y1, x2-x1)

Use atan2 instead of atan because it handles all four quadrants correctly.

Quick Reference