In this video I go over further into Polar Coordinates and this time elaborate on one of the interesting properties they have, namely that they can be written in an infinite number of ways. This is because the of the circular nature of the polar coordinate system. For example, for any point written in polar coordinates, we can obtain an equivalent representation by simply rotating the angle by an additional 360 degrees or 2pi radians. Likewise, we can use a negative angle, or even a negative distance, all of which represents the same exact point. This is different from the basic Cartesian coordinate system which has only one way to represent each point. In this video, I illustrate how we can write general formulas for the angle of a point in polar coordinates, which show that we can indeed have an infinite number of ways to describe the same point. This is a great video in illustrating the main difference between polar and Cartesian coordinates so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhud8JYSio2Gv_Wc1CQ
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-infinite-representations
Related Videos:
Polar Coordinates: Example 1:
Polar Coordinates:
Parametric Equations and Polar Coordinates: .
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I don’t always represent polar coordinates but when I do I usually represent them in an infinite number of ways ;)
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/video-notes-polar-coordinates-infinite-representations