In this video I look further into the cycloid and this time show how we can remove the angle in the parametric equations to obtain a Cartesian equation involving x and y only. The resulting equation is much more complicated than the original parametric equations, and in fact is only applicable along a specific interval, due to the inverse trig function involved in the derivation. This is a great exercise in showing how to go from parametric equation form to Cartesian form so make sure to watch this video!
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Example: Eliminate θ in the parametric equations for a cycloid to show it has the Cartesian equation:
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https://www.desmos.com/calculator/czpfk3jexp
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Note: It is not possible to write y = f(x) in a closed-form expression.
- I will explain closed-form expressions in more detail in a later video so stay tuned!
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