Parametric Curves: Example 9: The Cycloid: Proof Part 3

In this video I go over further into proving the parametric equations for the Cycloid curve and this time show that these equations do in fact work for all angles that the circle rotates to. In my earlier videos I derived the proof for the cases where θ is between 0 and π/2, as well as between π/2 and π. In this video I first show that the equations still work for the values θ = 0, π/2, and pi. From there I show that it still works for all other values of θ because of the cyclical nature of the trigonometric functions in the cycloid equations. Thus as the values of θ change, the derivation for the parametric equations will mirror all our previous derivations and thus give the exact same result. This is a great example to see how we can spot patterns in the derivation of parametric equations that involve trig functions, so make sure to watch this video!

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Related Videos:

Parametric Curves: Example 8: The Cycloid: Proof Part 2: https://youtu.be/_LAmOMbXXts Parametric Curves: Example 7: The Cycloid: Proof Part 1: https://youtu.be/XmHpIZqeRKk Parametric Curves: Example 6: Graphing Devices: https://youtu.be/cwpEasc9mhQ Parametric Curves: Example 5: Lissajous Figure: https://youtu.be/0OT1OnnAQ9I 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 Angles - Degrees vs Radians: What are Radians??: http://youtu.be/bOdrVvQWRdE Trigonometry Identities: cos(x +/- y) = cos(x)cos(y) -/+ sin(x)sin(y) : http://youtu.be/VuQczhk7HOs Trigonometry Identities: sin(x +/- y) = sin(x)cos(y) +/- cos(x)sin(y): http://youtu.be/edtk9thfwbM .

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