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

cosh t

sinh t

1

Pfeilfläche=t

t

x(t)

y(t)

t

Ziehe Q

auf der Hyperbel

f(x) = x
g(x) = (-x)
Q = Point(c)
O = Point(yAxis)
a = Line(O, Q)
a' = Mirror(a, xAxis)
P' = 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, P', Q)
ch(x) = (exp(x) + exp((-x))) / 2
pf: Vieleck1 - (2 * b)
t = Segment(O, C)
y_t = Segment(Q, C)
T: (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, T)
j = Segment(P_s, T)
u = Vector((0, cosh(pf)), P_c)
v = Vector((0, sinh(pf)), P_s)
Text3: "areacosh(" + (x(C)) + ") = " + pf + ""
Text5: "areasinh(" + y_t + ") = " + pf + ""
s: y = 1
Text2: "cosh(t) = " + (cosh(pf)) + ""
Text1: "Pfeilfläche = t = " + pf + ""
Text4: "sinh(t) = " + (sinh(pf)) + ""
k = OrthogonalLine(Q, f)
l = OrthogonalLine(P', g)
A = Intersect(g, l)
B = Intersect(f, k)
n = Segment(B, Q)
e = Segment(P', A)
D = (0.0873333333333333, -0.9986666666666667)
F = (0.5006666666666666, -0.9986666666666667)