# Archimedes's Spiral and Its Tangents

Archimedes's Spiral and Its Tangents

This Demonstration uses parametric equations and radius vectors to plot Archimedes's spiral (blue) and the curve of its tangents (orange), which represent the derivative. The function is in polar coordinates or in this implementation, in rectangular coordinates.

ϕ(t)=at

ϕ(t)=ax/(4π)(sinx,-cosx)