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Parametric Curves: Example 8: The Cycloid: Proof Part 2
In this video I go further into the derivation of the cycloid curve's parametric equations and this time go over the case where the angle which the circle rotates is between π/2 and π. The only difference in the derivation for this case, as compared with my earlier derivation for the case where the angle is between 0 and π/2 is that we are instead having to subtract the angle from π radians. But we use trig identities or the definition of trigonometric functions to show that we can write sine and cosine in exactly the same way as in my last video. This is an interesting video on showing how trig functions can be written and manipulated in different ways while still getting the same result, so make sure to watch this video!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuAF20ak6-dEuQy61w
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-curves-example-8-the-cycloid-proof-part-2
Related Videos:
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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