x

y

1

1

-1

-1

y

0

\alpha

90°

270°

180°

360°

540°

450°

990°

630°

720°

810°

900°

1080°

\alpha

0°

0°

x

1

-1

1

-1

90°

180°

270°

360°

450°

540°

630°

720°

\alpha

Sinuskonstruktion

Cosinuskonstruktion

\alpha

gl1: x^(2) + y^(2) = 1
α = 6.754424205218055 rad (slider from 0° to 1080°, step 3°)
A: (1, 0)
B: (0, 0)
A' = Rotate(A, α, B)
β = Angle(A, B, A')
f = Ray(B, A')
C = Point(yAxis)
c = Circle(B, C)
D = Intersect(c, f, 1)
g = Segment(B, D)
pihalbe: pi / 2
E = Point(xAxis)
F: (y(E), (-x(E)))
G: (x(E), (-y(C)))
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), sin((α / (180°) * pi)))
h(x) = If[x(E) ≤ x ≤ 100, sin(x - x(E))]
K: (x(E) + (α / (180°) * pi), 0)
w = Vector(K, J)
i = OrthogonalLine(A', xAxis)
j = OrthogonalLine(A', yAxis)
L = Intersect(i, xAxis)
M = Intersect(j, yAxis)
a = Vector(M, A')
b = Vector(L, A')
k = Segment(A', J)
e = CurveCartesian(x(E) + w, sin(w), w, 0, (α / (180°) * pi))
N, O = Intersect(c, yAxis)
P, Q = Intersect(c, xAxis)
l = Vector(P, Q)
m = Vector(O, C)
R: (0, 1)
S: (-1, 0)
T: (0, -1)
U: (x(E), 1)
n = Ray(R, U)
V: (x(E), -1)
p = Ray(T, V)
q = Segment(Q, E)
l3 = Sequence(If[α > (((2 * step) + 1) * 90°), Segment[(x(E) + (((2 * step) + 1) * pihalbe), 0), (x(E) + (((2 * step) + 1) * pihalbe), (-1)^(step))]], step, 0, 30)
Text12: "\alpha = " + (LaTeX[α]) + ""
sinus: sin(α)
cosinus: cos(α)
Text13: "\sin\alpha = " + (LaTeX[sinus]) + ""
Text14: "\cos\alpha=" + (LaTeX[cosinus]) + ""
Z: (x(P), y(F))
A_1: (x(Q), y(F))
d = Vector(Z, A_1)
B_1: (-1, y(F))
C_1: (1, y(F))
r = Ray(A, C_1)
s = Ray(S, B_1)
D_1 = Corner(1)
E_1: (0, y(D_1))
t = Vector(F, E_1)
f_1 = Segment(O, F)
F_1: (cos((α / (180°) * pi)), y(F) - (α / (180°) * pi))
g_1 = Segment(A', F_1)
G_1: (0, y(F) - (α / (180°) * pi))
u_1 = Vector(G_1, F_1)
o = CurveCartesian(cos(w), y(F) - w, w, 0, (α / (180°) * pi))
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)
T_1: (0, y(F) - (1 * pihalbe))
U_1: (0, y(F) - (2 * pihalbe))
V_1: (0, y(F) - (3 * pihalbe))
W_1: (0, y(F) - (4 * pihalbe))
Z_1: (0, y(F) - (5 * pihalbe))
A_2: (0, y(F) - (6 * pihalbe))
B_2: (0, y(F) - (7 * pihalbe))
C_2: (0, y(F) - (8 * pihalbe))
D_2: H + (pihalbe / 2, 0)
E_2: A_1 - (0, pihalbe / 2)
l1 = Sequence(If[α > ((2 * step) * 90°), Segment[(0, y(F) - ((2 * step) * pihalbe)), ((-1)^(step), y(F) - ((2 * step) * pihalbe))]], step, 1, 30)
a_1 = true
b_1 = true