r(x)

K=(θ, r(θ))

θ

r(θ)

P=(r(θ); θ)

r(θ)

θ

P_n=(|r(θ)|;θ)

θ

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 8.2.3.2: S. 242
www.kurven-erkunden-und-verstehen.de

Ha 2016

θ = 2.85 (slider from -5 to (2 * π) + 2, step 0.05)
a = 5 (slider from -5 to 10, step 0.01)
c = 1.3 (slider from -5 to 5, step 0.01)
r(x) = ((c * log(x)) * sin((a * x)))
rt(x) = (c * sin((a * x)))
K: (θ, r(θ))
T: (x(K), 0)
O: (0, 0)
b = Segment(K, T)
P: (rt(θ); θ)
d = Segment(P, O)
A = Point(xAxis)
α = Angle(A, O, P)
P_n = Mirror(P, O)
β = Angle(A, O, P_n)
e = Segment(O, P_n)
anf = 0
end = 10.7
f = CurveCartesian((rt(t) * cos(t)), (rt(t) * sin(t)), t, anf, end)
Text1: "a=" + a + ""
Text2: "rt(x)=" + (LaTeX[rt]) + ""
g = CurveCartesian((r(t) * cos(t)), (r(t) * sin(t)), t, 0, end)
Text3: "r(x)=" + (LaTeX[r]) + ""
h(x) = (1.3 * log(x))
i: sin(a)
p(x) = sin((a * x))
q(x) = (-h(x))
j = false