In this video I go over several new ways of describing curves, which allows for graphing some pretty amazing shapes and drawings, these are: Parametric Curves and the Polar Coordinate system. I go over a brief introduction on these concepts but in l…
In this video I go over several new ways of describing curves, which allows for graphing some pretty amazing shapes and drawings, these are: Parametric Curves and the Polar Coordinate system. I go over a brief introduction on these concepts but in later videos I will go into great detail on both topics. Parametric equations involves an additional perimeter, t, to the typical x and y variables, so that they both are functions of t, i.e. x = f(t) and y = g(t)). The resulting curves that can be graphed from these parametric equations are the very same letters and symbols that a laser printer would use. A specific example of the curve that can be graphed from parametric equations is the cycloid, which is a shape formed by tracing a point on the perimeter of a circle as it rotates about a line. This is a pretty cool shape and I briefly go over it in this video.
Polar Coordinates are a special type of coordinate system that is very well suited for circular curves. An example of the type of curve that can be sketched is the Cardioid which is similar to a cycloid except that the circle, which has the point on the perimeter being traced, also rotates about a circle of the same radius. The resulting shape looks like a heart. In fact, polar coordinates can be used to sketch some truly amazing graphs.
I will go into these types of curves in great detail in later video so stay tuned for more!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIht4_4ErI7-ij_VhsHQ
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-equations-and-polar-coordinates
Related Videos:
Polar Coordinates Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0HUFiPLsYw5_Ljd5riOUzjP
Parametric Curves Playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0H0AMIZV8HU3LVxSSf_Y9pi
Guidelines to Curve Sketching: http://youtu.be/tOn7ZSAntKs .
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