Question
The curves with equations $ x = \alpha \sin nt $, $ y = b \cos t $ are called Lissajous figures. Investigate how these curves vary when $ a $, $ b $, and $ n $ vary. (Take $ n $ to be a positive integer.)
Step 1
These are parametric curves described by the equations $x = a \sin nt$ and $y = b \cos t$. Here, $a$ and $b$ are the amplitudes of the oscillations in the $x$ and $y$ directions, respectively, and $n$ is the frequency ratio. Show more…
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$$ \begin{array}{l}{\text { The curves with equations } x=a \sin n t, y=b \cos t \text { are }} \\ {\text { called Lissajous figures. Investigate how these curves vary }} \\ {\text { when } a, b, \text { and } n \text { vary. (Take } n \text { to be a positive integer.) }}\end{array} $$
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