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

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhvRDgaCbbcSUjWAFlA

View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-example-10-graphing-r-sin-8-5

Related Videos:

Polar Coordinates: Graphing With Polar Curves with Desmos Calculator: https://youtu.be/xY9Be9HHRsk Polar Coordinates: Example 9: Cardioid: Part 4: https://youtu.be/R6UtQD8tUF0 Polar Coordinates: Example 9: Cardioid: Part 3: Question B: https://youtu.be/-TZHaTjHfb8 Polar Coordinates: Example 9: Cardioid: Part 2: Question A: https://youtu.be/gUYmzZ8Cfhg Polar Coordinates: Example 9: Cardioid: Part 1: Slope Formula & Trigonometric Algebra: https://youtu.be/MlIhueP36EE Polar Coordinates: Tangents to Polar Curves: https://youtu.be/DJso0gmxCBY Polar Coordinates: Symmetry: https://youtu.be/TWxforTOvxM Polar Coordinates: Example 8: Four-Leaved Rose: https://youtu.be/mTk5j0jD3dE Polar Coordinates: Example 7: Cardioid: https://youtu.be/rPErcaqNUIY Polar Coordinates: Example 6: Part 2: Polar Circle to Cartesian: https://youtu.be/biUHN-BphkE Polar Coordinates: Example 5: Straight Lines: https://youtu.be/AGSz3EVi05A Polar Coordinates: Example 4: Circle: https://youtu.be/ebsaIlXaZxs Polar Coordinates: Example 3: Cartesian to Polar Polar Coordinates: Example 2: Polar to Cartesian: https://youtu.be/mvpb9QshNNU Polar Coordinates: Cartesian Connection: https://youtu.be/HcaTYrpmGaU Polar Coordinates: Example 1: https://youtu.be/q_kpqPpoLqE Polar Coordinates: https://youtu.be/-KAdZL-N4ok Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw .

... https://www.youtube.com/watch?v=m-A35NDX7b0