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!
Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhuA3WxyVJJuZeWMJ1A
View Video Notes on Steemit: https://steemit.com/mathematics/@mes/parametric-curves-example-10-the-cycloid-proof-part-4-notes
Related Videos:
Parametric Curves: Example 9: The Cycloid: Proof Part 3:
Parametric Curves: Example 8: The Cycloid: Proof Part 2:
Parametric Curves: Example 7: The Cycloid: Proof Part 1:
Parametric Curves: Example 6: Graphing Devices:
Parametric Curves: Example 5: Lissajous Figure:
Parametric Curves: Example 4:
Parametric Curves: Example 3:
Parametric Curves: Example 2:
Parametric Curves: Example 1:
Parametric Equations and Curves:
Parametric Equations and Polar Coordinates:
Inverse Trigonometric Functions: Inverse cosine, sine, and tan Functions:
Trigonometry Identities: Proof that sin^2(x) + cos^2(x) = 1: .
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I don't always derive the equation of the cycloid curve but when I do it's usually in Cartesian form ;)
View Video Notes: https://steemit.com/mathematics/@mes/parametric-curves-example-10-the-cycloid-proof-part-4-notes
I love this
Very interesting my friend @mes
I really wonder how you do it; seemingly never running out of MATH formulas to post, must be full of stuff in there my friend, YOUR BRAINS I mean.
These posts of yours may be hidden one day, so better write these now on STEEMIT.
Regards.
hahaha thx! I'm definitely filled with something haha. Yup glad I got Steemit to post all my math stuff on the blockchain!!