Parametric Equations for a Cycloid Curve

This video shows how to find the Parametric Equations for a Cycloid curve in terms of polar parameters radius r and angle theta. This problem is most often seen in second semester calculus with analytic geometry.

[merci]

you earned a subscriber cuz of that cat and for helping me pass my math test, but mostly the cat

[sgardypena]

Such an amazing explanation. Thank you so much for this.

[MathswithKhan]

Thanks a lot for such a nice content with perfect method

[aneeshmatta]

Thank you so much, very clear explanation.

[password]

Brilliantly concise (plus, the cats are very soothing :3)

[PRASHANTKUMAR-rohv]

cats draws attention and they look so cute by their activities

[ptyptypty]

LOL, I love the CATS!!.. thank you for sharing that.... and YES.. I did follow the Lecture on the parameterizing of the Cycloid.. VERY GOOD!!... thank you...

[thomashughes]

Another interesting development I found was:


(R=1): The parametric for y is "1-cos(t)". That is the derivative of the x, viz, "t-sin(t)"; therefore, "1-cos(t) = tan(a)".


So, the tan(2pi/180) = 0.577. Set 0.577=1-cos(t). Solve for "t" = 1.134. Plug it into "1-cos(1.134)", and you get 0.577. So, the R(tan(a)), or R(1-cos(t)) will give you "y" on the cycloid. :D


This can be proved using Newton's Numerical Values formula! :D

[thomashughes]

If I may give something back to the channel, Aloixa, I "integrated myself into a corner", and I came up with an arc length formula for finding the x coordinate when you know the arc length, viz:


"t = 2[ARCCOS((s-4)/4)]".


"s" is the length of the arc (8r is the total length). "t" is "Theta". Use the result to find the "t" in the parametric equations for the x and y. Remember to use radians instead of degrees (this is for students, like me, who forget sometimes :D )

[notadvertiserfriendly]

thanks for uploading this helpful video. i like the cats 🐱

[ahmedelgak]

easy, brief and visualized explanation
this is what "perfect" means

[priyasvibe_vlogs]

What is the Cartesian equation of this cycloid and how it Will be calculated?

[steventoce]

very nice. what software do you use to create these videos?

[thomasvanhecke]

Can you make a video about the hypocycloid and the epicycloid?

[mryoutuser]

Can you please make a video on Cycloid equation when a circle rotates on/in another circle?

[SimchaWaldman]

There is something I don't understand: If θ is anti-clockwise, how come it's clockwise on the rotating circle?

[all_i_do_is_rap]

what is the cat for besides distracting

[ashur]

Thank you for the explanation but the cat video was pretty distracting ngl

[cicciograna]

Very good explaination, but to be honest the cats moving around are very distracting, not to mention that they eat away precious video space.

[alexanderr]

Whats the point of these Math lessons?