Parametric Curves: Example 7: The Cycloid: Proof Part 1

In this video I go over the cycloid curve and derive the parametric equations for the case in which the angle inside the circle is between 0 and π/2. The cycloid is formed by tracing a point on the circumference of a circle as it rotates along a straight line. The resulting parametric equations are shown below:

x = r(θ – sinθ)
y = r(1 – cosθ)

Although I derived these equations for the case where θ is between 0 and π/2, these equations do in fact work for all values of θ. I will go over the proof for other values of θ in a later video so stay tuned for that!

Also, these parametric equations can be rearranged to eliminate θ and to write x as a function of y, but the resulting Cartesian equation is much more complicated. I will nonetheless derive the Cartesian form of the cycloid in a later video, as well as the very interesting history of the cycloid, so stay tuned!

Download the notes in my video:!As32ynv0LoaIht9rJUo4SMEVW-eiJg

View Video Notes on Steemit:

Related Videos:

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:
Trigonometry: Sine, Cosine and Tan Functions:
Angles – Degrees vs Radians: What are Radians??: .


DONATE! ʕ •ᴥ•ʔ

Like, Subscribe, Favorite, and Comment Below!

Follow us on:

Official Website:
Email me:

Try our Free Calculators:

BMI Calculator:
Grade Calculator:
Mortgage Calculator:
Percentage Calculator:

Try our Free Online Tools:

iPhone and Android Apps:

%d bloggers like this: