Parametric Curves: Example 10: The Cycloid: Proof Part 4 (Notes)

in #mathematics • 9 years ago (edited)

In this video I look further into the cycloid and this time show how we can remove the angle in the parametric equations to obtain a Cartesian equation involving x and y only. The resulting equation is much more complicated than the original parametric equations, and in fact is only applicable along a specific interval, due to the inverse trig function involved in the derivation. This is a great exercise in showing how to go from parametric equation form to Cartesian form so make sure to watch this video!


Watch on DTube:

Watch on BitChute: https://www.bitchute.com/video/1ap7Y0KpFBoa/

Download PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIhuA3WxyVJJuZeWMJ1A


View Video Notes Below!


Download These Notes: Link is in Video Description.
View These Notes as an Article: https://steemit.com/@mes
Subscribe via Email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donate

Reuse of My Videos:

  • Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.

Fight Back Against Censorship:

  • Bookmark sites/channels/accounts and check periodically
  • Remember to always archive website pages in case they get deleted/changed.

Join my private Discord Chat Room: https://mes.fm/chatroom

Check out my Reddit and Voat Math Forums:

Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
Watch my #AntiGravity Video Series: https://mes.fm/antigravity-playlist
Follow My #FreeEnergy Video Series: https://mes.fm/freeenergy-playlist


NOTE: If you don't have time to watch this whole video:

  • Skip to the end for Summary and Conclusions
  • Play this video at a faster speed.
    --TOP SECRET LIFE HACK: Your brain gets used to faster speed. (#Try2xSpeed)
    --Try 4X+ Speed by Browser Extensions, HookTube.com, Modifying Source Code.
    --Browser Extension Recommendation: https://mes.fm/videospeed-extension
  • Download and Read Notes.
  • Read notes on Steemit #GetOnSteem
  • Watch the video in parts.

Example: Eliminate θ in the parametric equations for a cycloid to show it has the Cartesian equation:

Reveal spoiler

https://www.desmos.com/calculator/czpfk3jexp

Reveal spoiler

Reveal spoiler

Note: It is not possible to write y = f(x) in a closed-form expression.

  • I will explain closed-form expressions in more detail in a later video so stay tuned!