y

1

1

-1

-1

y

0

\alpha

90°

270°

180°

360°

540°

450°

990°

630°

720°

810°

900°

1080°

\alpha

0°

1

-1

\alpha

x=1

\textrm{Tangente}

0

gl1: x^(2) + y^(2) = 1
α = 0 rad (slider from 0° to 720°, step 3°)
A: (1, 0)
B: (0, 0)
A' = Rotate(A, α, B)
β = Angle(A, B, A')
f = Ray(B, A')
C: (0, y(Corner[3]))
c = Circle(B, C)
a: sqrt((y(C))^(2) + 1)
d = Circle((0, 0), a)
D = Intersect(d, f, 1)
pihalbe: pi / 2
E = Point(xAxis)
G: (x(E), y(Corner[1]))
H: (x(E), y(C))
u = Vector(G, H)
W = Corner(3)
I: (x(W), 0)
v = Vector(E, I)
J: (x(E) + (α / (180°) * pi), tan((α / (180°) * pi)))
K: (x(E) + (α / (180°) * pi), 0)
w = Vector(K, J)
i = OrthogonalLine(A', xAxis)
j = OrthogonalLine(A', yAxis)
P, Q = Intersect(c, xAxis)
O: (0, y(Corner[1]))
m = Vector(O, C)
R: (0, 1)
S: (-1, 0)
T: (0, -1)
U: (x(E), 1)
V: (x(E), -1)
q = Segment(Q, E)
Text12: "\alpha = " + (LaTeX[α]) + ""
sinus: sin(α)
cosinus: cos(α)
D_1 = Corner(1)
E_1: (0, y(D_1))
H_1: (x(E) + pihalbe, 0)
I_1: (x(E) + (2 * pihalbe), 0)
J_1: (x(E) + (3 * pihalbe), 0)
K_1: (x(E) + (4 * pihalbe), 0)
L_1: (x(E) + (5 * pihalbe), 0)
M_1: (x(E) + (6 * pihalbe), 0)
N_1: (x(E) + (7 * pihalbe), 0)
O_1: (x(E) + (8 * pihalbe), 0)
P_1: (x(E) + (9 * pihalbe), 0)
Q_1: (x(E) + (10 * pihalbe), 0)
R_1: (x(E) + (11 * pihalbe), 0)
S_1: (x(E) + (12 * pihalbe), 0)
D_2: H + (pihalbe / 2, 0)
F = Point(xAxis)
F' = Mirror(F, yAxis)
l = Vector(F, F')
B' = Mirror(B, B)
D' = Mirror(D, B)
gl2: x = 1
gl3: x = x(F')
g = Line(A', B')
gl4: x = x(F)
Z = Intersect(gl4, g)
N = Intersect(gl3, g)
n = Segment(Z, N)
A_1 = Intersect(n, gl2)
k = Segment(A_1, J)
p(x) = If[x(E) ≤ x ≤ x(E) + α, tan(x - x(E))]
l2 = Sequence(If[α > (((2 * step) + 1) * 90°), x = x(E) + (((2 * step) + 1) * pihalbe)], step, 0, 30)
tangens: tan(α)
Text13: "\tan\alpha = " + (LaTeX[tangens]) + ""
b = Vector(A, A_1)
L = Point(gl2)
M: (-1.1, 1.3)