Apprendre les angles remarquables sur le cercle trigo
Author: ffred

Cet applet permet de parcourir le cercle trigonométrique à l'aide point point M et d'afficher les valeurs des angles, (sinus et cosinus) à connaître et à savoir retrouver.

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

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

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

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

+\frac{\Pi}{2}

+\frac{2\Pi}{3}

+\frac{3\Pi}{4}

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

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

+\frac{5\Pi}{6}

+\Pi

-\frac{5\Pi}{6}

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

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

-\frac{3\Pi}{4}

-\frac{2\Pi}{3}

-\frac{\Pi}{2}

-\frac{\Pi}{3}

-\frac{\Pi}{4}

-\frac{\Pi}{6}

0

+\frac{\Pi}{6}

+\frac{\Pi}{4}

+\frac{\Pi}{3}

Parcourir le cercle trigonométrique 
à la recherche des angles remarquables

Le point M est mobile

+

O = Intersect(xAxis, yAxis)
c = Circle(O, 1)
M = Point(c)
B = (0.7071067811865476, 0.7071067811865476)
E = If(Distance[B, M] < 0.05, B)
a = OrthogonalLine(E, xAxis)
b = OrthogonalLine(E, yAxis)
E_1 = Intersect(a, xAxis)
E_2 = Intersect(b, yAxis)
C = (0.5, 0.8660254037844386)
F = If(Distance[M, C] < 0.05, C)
d = OrthogonalLine(F, xAxis)
e = OrthogonalLine(F, yAxis)
F_1 = Intersect(d, xAxis)
F_2 = Intersect(e, yAxis)
I = Intersect(c, xAxis, 2)
α = Angle(I, O, E)
f = Segment(E, O)
g = Segment(F, O)
β = Angle(I, O, F)
A = (0.8660254037844386, 0.5)
D = If(Distance[A, M] < 0.05, A)
h = OrthogonalLine(D, xAxis)
i = OrthogonalLine(D, yAxis)
D_1 = Intersect(h, xAxis)
D_2 = Intersect(i, yAxis)
j = Segment(O, D)
γ = Angle(I, O, D)
J = (0, 1)
G = If(Distance[J, M] < 0.05, J)
k = Line(G, O)
δ = Angle(I, O, G)
l = Segment(G, O)
H = (-0.5, 0.8660254037844386)
H_1 = If(Distance[M, H] < 0.05, H)
m = OrthogonalLine(H_1, xAxis)
n = OrthogonalLine(H_1, yAxis)
p = Segment(O, H_1)
ε = Angle(I, O, H_1)
K = (-0.7071067811865476, 0.7071067811865476)
K_1 = If(Distance[M, K] < 0.05, K)
q = Segment(O, K_1)
ζ = Angle(I, O, K_1)
r = OrthogonalLine(K_1, yAxis)
s = OrthogonalLine(K_1, xAxis)
L = (-0.8660254037844386, 0.5)
L_1 = If(Distance[L, M] < 0.05, L)
t = OrthogonalLine(L_1, yAxis)
a_1 = OrthogonalLine(L_1, xAxis)
b_1 = Segment(O, L_1)
η = Angle(I, O, L_1)
N = (-1, 0)
N_1 = If(Distance[M, N] < 0.05, N)
θ = Angle(I, O, N_1)
P = (-0.8660254037844386, -0.5)
P_1 = If(Distance[M, P] < 0.05, P)
c_1 = OrthogonalLine(P_1, yAxis)
d_1 = OrthogonalLine(P_1, xAxis)
e_1 = Segment(O, P_1)
ι = Angle(P_1, O, I)
Q = (-0.7071067811865476, -0.7071067811865476)
Q_1 = If(Distance[M, Q] < 0.05, Q)
f_1 = OrthogonalLine(Q_1, xAxis)
g_1 = OrthogonalLine(Q_1, yAxis)
h_1 = Segment(O, Q_1)
κ = Angle(Q_1, O, I)
R = (-0.5, -0.8660254037844386)
R_1 = If(Distance[M, R] < 0.05, R)
i_1 = OrthogonalLine(R_1, xAxis)
j_1 = OrthogonalLine(R_1, yAxis)
k_1 = Segment(O, R_1)
λ = Angle(R_1, O, I)
S = (0, -1)
S_1 = If(Distance[M, S] < 0.05, S)
l_1 = Segment(O, S_1)
μ = Angle(S_1, O, I)
T = (0.5, -0.8660254037844386)
T_1 = If(Distance[M, T] < 0.05, T)
m_1 = Segment(O, T_1)
ν = Angle(T_1, O, I)
n_1 = OrthogonalLine(T_1, yAxis)
p_1 = OrthogonalLine(T_1, xAxis)
U = (0.7071067811865476, -0.7071067811865476)
U_1 = If(Distance[M, U] < 0.05, U)
q_1 = OrthogonalLine(U_1, xAxis)
r_1 = OrthogonalLine(U_1, yAxis)
V = (0.8660254037844386, -0.5)
V_1 = If(Distance[M, V] < 0.05, V)
s_1 = OrthogonalLine(V_1, xAxis)
t_1 = OrthogonalLine(V_1, yAxis)
a_2 = Segment(V_1, O)
ξ = Angle(V_1, O, I)
I_1 = If(Distance[M, I] < 0.05, I)
W = Intersect(n, yAxis)
Y = Intersect(m, xAxis)
Z = Intersect(s, xAxis)
A_1 = Intersect(r, yAxis)
B_1 = Intersect(yAxis, t)
C_1 = Intersect(xAxis, a_1)
G_1 = Intersect(d_1, xAxis)
J_1 = Intersect(c_1, yAxis)
M_1 = Intersect(xAxis, f_1)
O_1 = Intersect(g_1, yAxis)
W_1 = Intersect(i_1, xAxis)
Y_1 = Intersect(j_1, yAxis)
Z_1 = Intersect(n_1, yAxis)
A_2 = Intersect(xAxis, p_1)
B_2 = Intersect(q_1, xAxis)
C_2 = Intersect(r_1, yAxis)
G_2 = Intersect(s_1, xAxis)
H_2 = Intersect(t_1, yAxis)
ο = Angle(I, O, M)
b_2 = Segment(O, M)
I_2 = (1.0030799670709454, 0.9807550622989477)
J_2 = (1.3, 1)
K_2 = (1.1412935318314217, 1.2997094425154316)
c_2 = CircleArc(I_2, J_2, K_2)
L_2 = (1.1678730635161287, 1.2199708474613107)
M_2 = (1.1147140001467148, 1.2465503791460177)
u = Vector(L_2, M_2)