Author: Daniel Mentrard
Date: Janvier  2008

 \frac{  \sqrt{ 3 }  }{2 } 

 \frac{  \sqrt{ 2 }  }{2 } 

 -\frac{1}{2 } 

 -\frac{  \sqrt{ 2 }  }{2 } 

 -\frac{  \sqrt{ 3 }  }{2 } 

 \frac{  \sqrt{ 3 }  }{2 } 

 \frac{1}{2 } 

 \frac{  \sqrt{ 2 }  }{2 } 

 \frac{  \sqrt{ 3 }  }{2 } 

 \frac{  \sqrt{ 2 }  }{2 } 

 \frac{1}{2 } 

 -\frac{1}{2 } 

 \frac{ - \sqrt{ 2 } }{2 }  

 \frac{ - \sqrt{ 3 } }{2 }  

y = sin (x)

y = cos (x)

α

Source : Daniel Mentrard
http://dmentrard.free.fr/GEOGEBRA/
Adaptation: JM Delley
http://math.bibop.ch

j = 11.257373675363421 (slider from -18.84955592153876 to 18.84955592153876, step 0.1308996938995747)
O = Intersect(xAxis, yAxis)
c = Circle(O, 1)
C_1, D = Intersect(c, xAxis)
r = Segment(C_1, D)
I_1 = Point(r)
M = Rotate(D, j, O)
M1 = If(j < 0, M)
K, L = Intersect(c, yAxis)
s = Line(K, L)
n: floor(j / (2 * 3.141592653589793))
n18: j - 2 * n * 3.141592653589793
n16: n * 2
n15: n * 4 + 3
n9: n * 6 + 5
n8: n * 8 + 7
n7: n * 12 + 11
n6: n * 6 + 4
n5: n * 8 + 5
n4: n * 12 + 7
n10: n * 12 + 5
n12: n * 8 + 3
n11: n * 6 + 2
n14: n * 4 + 1
n2: n * 2 * 3 + 1
n1: n * 2 * 6 + 1
n3: n * 2 * 4 + 1
a = OrthogonalLine(M, yAxis)
S = Intersect(a, yAxis)
β = Angle(D, O, M)
b = OrthogonalLine(M, xAxis)
C = Intersect(b, xAxis)
d = Segment(O, S)
e = Segment(O, C)
g = Segment(M, S)
h = Segment(M, C)
G = Midpoint(M, S)
H = Midpoint(M, C)
u = Vector(M, G)
v = Vector(M, H)
I = Rotate(D, 0.52, O)
γ = Angle(I, O, D)
J = Rotate(D, 1.0471975511965976, O)
δ = Angle(D, O, J)
M_1 = Mirror(J, yAxis)
N = Mirror(I, yAxis)
O_2 = Mirror(M_1, xAxis)
P = Mirror(J, xAxis)
Q = Mirror(I, xAxis)
R = Mirror(Q, yAxis)
T = Rotate(D, 0.7853981633974483, O)
ε = Angle(D, O, T)
U = Mirror(T, yAxis)
V = Mirror(T, xAxis)
W = Mirror(U, xAxis)
F = (-0.36666666666666664, 10.533333333333333)
s_4 = If(Distance[M, K] < 0.1, F)
i = Segment(R, I)
k = Segment(T, W)
l = Segment(J, O_2)
m = Segment(Q, N)
p = Segment(P, M_1)
q = Segment(L, K)
t = Line(C_1, D)
T36: "α\; =\; " + j + "\; rad"
n13: n * 2 + 1
n17: n * 2 + 2
T3: "\frac{" + n3 + "π} {4}"
T2: "\frac{" + n1 + "π} {6}"
T5: "\frac{" + n2 + "π} {3}"
T4: "\frac{" + n14 + "π} {2}"
T11: "\frac{" + n11 + "π} {3}"
T12: "\frac{" + n12 + "π} {4}"
T13: "\frac{" + n10 + "π} {6}"
T16: "\frac{" + n4 + "π} {6}"
T17: "\frac{" + n5 + "π} {4}"
T18: "\frac{" + n6 + "π} {3}"
T6: "\frac{" + n7 + "π} {6}"
T7: "\frac{" + n8 + "π} {4}"
T8: "\frac{" + n9 + "π} {3}"
T10: "\frac{" + n15 + "π} {2}"
T14: "" + n13 + "π"
T9: "" + n16 + "π"
T45: "" + n17 + "π"
T50: " " + n + "\; tour(s)"
b_1 = Segment(O, M)
Z = Point(t)
E_1 = Point(t)
C_2 = Point(s)
D_2 = Point(s)
E_2 = Point(s)
F_2 = Point(s)
c_1 = Segment(U, V)
B = Point(c)
k_1 = CircleArc(O, M1, D)
M2 = If(j > 0, M)
k_2 = CircleArc(O, D, M2)
α = Angle(I_1, O, M2)
ζ = Angle(M1, O, I_1)
degre: j * 3 * 360 * ° / (6 * 3.141592653589793)
T15: "α = " + degre
f = Segment(J, O)
a1 = Segment(T, O)
b1 = Segment(I, O)