Polar Coordinates: Example 10: Graphing r = sin(8ϴ/5)


In this video I further into Polar Coordinates and this time look at Example 10 which involves graphing the function r = sin(8ϴ/5) using the amazing Desmos graphing calculator. Similar to my last video on graphing polar curves, I show how we can use the Desmos calculator to graph polar curves directly or by converting them to Parametric curves. Also in this video I show to determine the domain of the angle ϴ in which the polar curve repeats itself. I do this both visually using the graphing calculator, as well as analytically by using the periodic rotations of a typical sine wave. Note that this is just a quick and simple illustration of determining the domain for the simple case that the function does in fact have an exact whole number of rotations before it starts repeating itself. The curve graphed in this video is an amazing circular spiral flower shape and shows just how amazing the types of curves that can be plotted in polar coordinates (or as parametric equations)! Try it out yourself and let me know of any crazy shapes you can create!!

You can use my graph as a starting point: https://www.desmos.com/calculator/raiwkuult1

Watch video on:

Download PDF Notes: https://1drv.ms/b/s!As32ynv0LoaIhvRDgaCbbcSUjWAFlA

View Video Notes Below!

Download these notes: Link is in video description.
View these notes as an article: https://peakd.com/@mes
Subscribe via email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donate
Buy MES merchandise! https://mes.fm/store
More links: https://linktr.ee/matheasy

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.

Recommended Books:

Subscribe to MES Truth: https://mes.fm/truth
MES Links Telegram channel: https://t.me/meslinks

Join my forums!

Follow along my epic video series:

NOTE #1: If you don't have time to watch this whole video:

Browser extension recommendations:

Polar Coordinates: Example 10: Graphing r = sin(8ϴ/5)

Polar Coordinates Example 10.jpeg


Graph the curve r = sin (8θ/5).




Note, we can graph the same curve by also converting the polar curve to Parametric Equations:

To determine, analytically, the domain of θ, we can ask the question: How many complete rotations are required until the curve starts to repeat itself?

Recall that one rotation is just 2π radians, or 360 degrees.

If the answer is n rotations, then we must have: