Preface

This section is devoted to inetgrating factors as functions of dependent variable. coordinates.

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Glossary

Integrating factors as functions of dependent variable

Cycloid

The Parametrization

cycloid[a_, b_][t_] := {a*t - b*Sin[t], a - b*Cos[t]}
Manipulate[
ParametricPlot[
cycloid[a, b][t] // Evaluate, {t, -\[Pi]/2, 5*\[Pi]/2}], {a, 1, 5}, {b, 1, 5}]

 

Cycloid[\[Rho]_, \[Tau]_] := {\[Rho]*\[Tau] - \[Rho]^2* Sin[\[Tau]/\[Rho]], \[Rho]^2*(1 - Cos[\[Tau]/\[Rho]])};
PolarPlot[Cycloid[1.5,theta],{theta, 0, 4*Pi}]

 

Example:
PolarPlot[{Exp[Cos[x]] - 2*Cos[4*x], x}, {x, 0, 2*Pi}]
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