m(t)

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 9.4.6.1  S. 279 Afg. 9.6
www.kurven-erkunden-und-verstehen.de

Ha 2017

a = 3
T = Point(xAxis)
fy(x) = (a / 3 * ((2 * sin(x)) - sin((2 * x))))
K_y: (x(T), fy(x(T)))
fx(x) = (a / 3 * ((2 * cos(x)) - cos((2 * x)))) + a
K_x: (x(T), fx(x(T)))
b = 4
kardi: (((4 * a) - (3 * x))^(3) * x) = ((9 * y^(2)) * ((4 * a^(2)) - ((12 * a) * x) + (6 * x^(2)) + (3 * y^(2))))
P_1 = Point(kardi)
f = Tangent(P_1, kardi)
A: (b, 0)
g = Segment(A, P_1)
Q' = Rotate(P_1, 120°, A)
α = Angle(P_1, A, Q')
h = Ray(A, Q')
Q'' = Rotate(Q', 120°, A)
β = Angle(Q', A, Q'')
K: (y(K_x), y(K_y))
i = Ray(A, Q'')
D, E, P_3, L = Intersect(kardi, i)
s = Line(P_3, f)
F = Point(xAxis)
t = Angle(F, A, P_1)
m(x) = (cos(x) - cos((2 * x))) / ((-sin(x)) + sin((2 * x)))
j: x = (2 * π / 6)
k: x = (2 * π / 2)
l: x = (5 * π / 3)
B, C, P_2 = Intersect(kardi, h)
n = Line(P_2, f)
p = OrthogonalLine(T, xAxis)
c = Slope(f)
q: y = c
st = Intersect(q, yAxis)
d = false