cykloida

r  (radius of the circle)

S

t

$x=rt-c\sin{t}$, $y=r-c\cos{t}$, $t\in R$

$\text{Angle }t$

$\text{Circle }k$

$\text{Cycloid [shadow]}$

$\text{Cycloid}$

$\text{Point }B$

$\text{Line }x$

c = 1 (slider from 0 to (5 * r), step 0.1)
r = 1 (slider from 0.1 to 5, step 0.1)
t = 14.9 (slider from 0 to (4.8 * π), step 0.1)
A: ((r * t), r)
k = Circle(A, r)
B: ((r * t) - (c * sin(t)), r - (c * cos(t)))
f = Segment(B, A)
C: (0, r - c)
b = CurveCartesian((r * tt) - (c * sin(tt)), r - (c * cos(tt)), tt, (-0.8 * π), (4.8 * π))
E: ((r * t), 0)
g = Segment(A, E)
h = Ray(A, B)
i = Line((0, 0), (1, 0))
D: ((r * t) - (r * sin(t)), r - (r * cos(t)))
α = Angle(D, A, E)
j = Segment(D, A)
a = CurveCartesian((r * tt) - (c * sin(tt)), r - (c * cos(tt)), tt, 0, t)
text2: "Cycloid " + (LaTeX[If[r ≟ c, "\text{ Ordinary }(c=r)", If[r > c, "\text{ Curtate }(c<r)", "\text{ Prolate }(c>r)"]]]) + ""
d = true
e = true
l = true
n = true
o = true
m = true
text1_1: "$x=" + (LaTeX[r]) + "t-" + (LaTeX[c]) + "\sin{t}$, $y=" + (LaTeX[r]) + "-" + (LaTeX[c]) + "\cos{t}$, $t=" + (LaTeX[t]) + "$"