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Parametric Curves: Example 5: Lissajous Figure

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First published at 00:20 UTC on February 14th, 2018.

Math Easy Solutions

MES

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In this video I go over another example on Parametric Curves and this time look at the manually sketching the shape formed by the parametric equations: x = cos(t) and y = sin(2t). The shape formed is known as the Lissajous figure and has a unique and iconic shape. I sketch the figure by first graphing x = cost(t) and y = sin(2t) separately but by aligning them horizontally and vertically so that the x and y axes align to the axes of the Lissajous figure. From this alignment we can then begin to plot x and y points at each value of t. Although the shape that I manually draw isn't the neatest, I show how to generate this curve using an online parametric equation graphing calculator. While it is good to use online tools to plot the points it is still important to know how to generate these curves by hand because it requires the underlying understanding of the nature of these parametric curves. This is a great video on manually graphing parametric equations so make sure to watch this video!

Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIht9M4Jk82lFfHjyYDg

View Video Notes on Steemit: https://steemit.com/steemstem/@mes/parametric-curves-example-5-lissajous-figure

Related Videos:

Parametric Curves: Example 4: https://youtu.be/WZYIS1My-g4
Parametric Curves: Example 3: https://youtu.be/VpiJdEviBbk
Parametric Curves: Example 2: https://youtu.be/SBkzZDlqTTE
Parametric Curves: Example 1: https://youtu.be/0k7QyWa9-HA
Parametric Equations and Curves: https://youtu.be/Kd3XF4LZoFE
Parametric Equations and Polar Coordinates: https://youtu.be/usSors49Gdw
Trigonometry: Sine, Cosine and Tan Functions: http://youtu.be/WKTIlF2oWw8 .

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