Sinus- und Kosinus hyperbolicus
Author: Prof. Dr. Dörte Haftendorn

cosh x

sinh x

1

Pfeilfläche=x

x^2-y^2=1

O

\cosh(x)

\sinh(x)

tanh x

https://www.geogebra.org/haftendorn
Haftendorn, Buch (Springer):
Kurven erkunden und verstehen
Kap 9.6.4.1: S.300
www.kurven-erkunden-und-verstehen.de

Ha 2016

f(x) = x
g(x) = (-x)
Q = Point(hyp)
O = Point(yAxis)
a = Line(O, Q)
a' = Mirror(a, xAxis)
Q' = Mirror(Q, xAxis)
C: (x(Q), 0)
E = (1, 0)
h(x) = sqrt(x^(2) - 1)
b = Integral(h, x(E), x(C))
hh(x) = (-h(x))
d = Integral(hh, x(E), x(C))
Vieleck1, p, m, p' = Polygon(O, Q', Q)
ch(x) = (exp(x) + exp((-x))) / 2
pf: Vieleck1 - (2 * b)
Text2: "cosh(Pfeilfläche) = " + (cosh(pf))
Text3: "x(P)=strecke(MT) = " + (x(C))
t = Segment(O, C)
y_t = Segment(Q, C)
Text4: "sinh(Pfeilfläche) = " + (sinh(pf))
Text5: "y(P)=y_t=Strecke(TP)= " + y_t
Text1: "Pfeilfläche = " + pf + ""
X: (pf, 0)
P_c: (pf, t)
Ortslinie1 = Locus(P_c, Q)
q(x) = sinh(x)
r(x) = cosh(x)
P_s: (pf, y_t)
i = Segment(P_c, X)
j = Segment(P_s, X)
k = Line(Q, xAxis)
l = Line(P_s, xAxis)
A = Intersect(q, xAxis, (0, 0))
n = Segment(A, X)
s = OrthogonalLine(E, xAxis)
B = Intersect(a, p')
D = Intersect(a, s)
e = Segment(D, E)
c = false