Author: Alfred Nussbaumer

\sinh (\alpha)

\cosh  (\alpha)

Flächeninhalt

sinh

cosh

c' = Mirror(c, xAxis)
a = CurveCartesian(sin(t), cos(t), t, 0.0, 6.28)
b = CurveCartesian(cosh(t), sinh(t), t, -1.5, 1.5)
A = Intersect(c, c')
B = Point(b)
d = Ray(A, B)
α = Angle(xAxis, d)
e = OrthogonalLine(B, xAxis)
f = OrthogonalLine(B, yAxis)
C = Intersect(f, yAxis)
D = Intersect(e, xAxis)
g = Segment(D, B)
h = Segment(B, C)
i = CurveCartesian(-cosh(t), sinh(t), t, -3.0, 3.0)
k = Integral(1.04 / 144.0 * x, 0.0, x(B))
j: y = y(B) / x(B) * x
m(x) = y(B) / x(B) * x
l = Integral(m(x), 0.0, x(B))
n(x) = sqrt(x^(2.0) - 1.0)
p(x) = n(x)
o = Integral(m(x), 0.0, 1.0)
q = Integral(m(x) - p(x), 1.0, x(B))
r = Integral(m(x), p(x), 1.0, x(B))
Text4: "Fläche:" + (o + r)
Text5: "cosh:" + (x(B))
Text6: "sinh:" + (y(B))
Text3: "\alpha =" + ((o + r) * 2.0)
s = Integral(-m(x), 0.0, 1.0)
t = Integral(-m(x), -sqrt(x^(2.0) - 1.0), 1.0, x(B))
B1: 2.0 * (o + r)
B2: sinh(B1)
B3: cosh(B1)
E = Midpoint(C, B)
F = Midpoint(B, D)