M408M Learning Module Pages
Main page ## Chapter 10: Parametric Equations and Polar Coordinates## Learning module LM 10.1: Parametrized Curves:3 kinds of functions, 3 kinds of curvesThe cycloid Visualizing parametrized curves Tracing curves and ellipses Lissajous figures ## Learning module LM 10.2: Calculus with Parametrized Curves:## Learning module LM 10.3: Polar Coordinates:## Learning module LM 10.4: Areas and Lengths of Polar Curves:## Learning module LM 10.5: Conic Sections:## Learning module LM 10.6: Conic Sections in Polar Coordinates:## Chapter 12: Vectors and the Geometry of Space## Chapter 13: Vector Functions## Chapter 14: Partial Derivatives## Chapter 15: Multiple Integrals |
## The cycloidOne of the most important examples
of a parametrized curve is a The following video derives the formula for a cycloid:$$x=r(t-\sin(t));\qquad y=r(1-\cos(t)).$$Please watch carefully, since this example will show up repeatedly in later learning modules. Note: There is a small error
towards the end of the video. The top of
the curve is at $(\pi r, 2r)$, not at $(\pi r, r)$.
Also, you can't |