Correspondance entre réels et points du cercle trigonométrique
Author: Joël Gauvain  Lycée René Josué Valin  La Rochelle

x

Voir le point de coordonnées (x ; sin x)

Voir le point de coordonnées (x ; cos x)

Voir la courbe décrite par ce point

Voir la courbe décrite par ce point

Voir la trace de ce point

Voir la trace de ce point

\frac{\pi}{6}

\frac{1}{2}

\frac{\pi}{4}

\frac{\pi}{3}

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

\frac{2\pi}{3}

\frac{\pi}{2}

\frac{3\pi}{4}

\frac{5\pi}{6}

\pi

\frac{7\pi}{6}

-\frac{1}{2}

\frac{5\pi}{4}

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

\frac{4\pi}{3}

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

\frac{3\pi}{2}

\frac{5\pi}{3}

\frac{7\pi}{4}

\frac{11\pi}{6}

2\pi

-\frac{\pi}{6}

-\frac{\pi}{4}

-\frac{\pi}{3}

-\frac{\pi}{2}

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

-\frac{2\pi}{3}

-\frac{3\pi}{4}

-\frac{5\pi}{6}

-\pi

x

Exercice 1

Exercice 2

Exercice 3

Exercice 4

Exercice 5

Exercice 6

+

-

Mathématiques à Valin

Vous pouvez déplacer le cercle trigonométrique en
déplaçant son centre O.
Placez les 4 points situés aux sommets des triangles 
sur l'axe des réels en tenant compte des valeurs
associées inscrites dans ces triangles roses.
Pour vous aider, déplacez  le triangle vert sur l'axe
des réels, et observez  l'égalité des longueurs du
segment vert et de l'arc vert du cercle trigonométrique.

Valider les 4 réponses

Exercice 1

Exercice 2

Exercice 3

Exercice 4

Exercice 5

Exercice 6

\text{Erreur}

\text{Erreur}

\text{Erreur}

\text{Erreur}

\text{Erreur}

\text{Erreur}

Juste

Juste

Juste

Juste

Juste

Juste

\ovalbox{\text{ Exercice 1 }}

\ovalbox{\text{ Exercice 2}}

\ovalbox{\text{ Exercice 3}}

\ovalbox{\text{ Exercice 4}}

\ovalbox{\text{ Exercice 5}}

\ovalbox{\text{ Exercice 6}}

exo2 = 5 (slider from 0 to 5, step 1)
p_1: y = 0.12
ci = (0.008888888888888946, 1)
W1 = (2.20074074074074, -2.2555555555555555)
Rm2 = (0, -0.5)
X = Point(p_1)
O = (-0.00370370370370387, 0.0022222222222222196)
i = (0, 1)
M: exp((x(X) * i)) + O
E: O + i
F: O - i
Rmr2 = (0, -0.7071067811865476)
c = Circle(O, 1)
A: O + 1
o = Intersect(xAxis, yAxis)
B = Midpoint(o, X)
A': O + exp((x(B) * i))
d = CircumcircleArc(A, A', M)
D: O - 1
b = Segment(D, A)
e = Segment(E, F)
f = OrthogonalLine(M, e)
C = Intersect(f, e)
P: C - O
g = OrthogonalLine(M, b)
G = Intersect(g, b)
h = Segment(M, C)
j = Segment(M, G)
k = Segment(C, O)
l = Segment(G, O)
m = Segment(M, O)
n = Segment(P, o)
T: X + P
p = Segment(T, X)
q = Segment(P, T)
Q: ((G - O) * i)
r = Segment(o, Q)
R: X + Q
s = Segment(X, R)
t = Segment(Q, R)
u = false
v = false
lieu1 = Locus(T, X)
lieu2 = Locus(R, X)
w = false
z = false
Fc(x) = If[(x > 0) ∧ (x  <  x(X)), cos(x)]
a_1 = false
b_1 = false
Fsi(x) = If[(x > 0) ∧ (x  <  x(X)), sin(x)]
P6 = (0.5235987755982988, 0)
c_1 = Segment(P6, X)
O_2 = (0, 0.5)
d_1 = Segment(P, O_2)
P4 = (0.7853981633974483, 0)
l4 = Segment(P4, X)
R2 = (0, 0.7071067811865476)
LR2 = Segment(Rm2, P)
P3 = (1.0471975511965976, 0)
R3 = (0, 0.8660254037844386)
LR3 = Segment(R3, P)
P23 = (2.0943951023931953, 0)
P2 = (6.283185307179586, 0)
P34 = (2.356194490192345, 0)
P56 = (2.6179938779914944, 0)
Pii = (3.141592653589793, 0)
P76 = (3.665191429188092, 0)
LRm2 = Segment(Rmr2, P)
P54 = (3.9269908169872414, 0)
Lm2 = Segment(Rm2, P)
P43 = (4.1887902047863905, 0)
Rm32 = (0, -0.8660254037844386)
LRm32 = Segment(Rm32, P)
P32 = (4.71238898038469, 0)
P53 = (5.235987755982989, 0)
P74 = (5.497787143782138, 0)
P116 = (5.759586531581287, 0)
Pi2 = (1.5707963267948966, 0)
Pim6 = (-0.5235987755982988, 0)
LRv2 = Segment(R2, P)
Pim3 = (-1.0471975511965976, 0)
Pim4 = (-0.7853981633974483, 0)
Pim2 = (-1.5707963267948966, 0)
Pm23 = (-2.0943951023931953, 0)
Pm34 = (-2.356194490192345, 0)
Pm56 = (-2.6179938779914944, 0)
Pmpi = (-3.141592653589793, 0)
QR3 = Segment(R3, Q)
QRv2 = Segment(R2, Q)
Qd1 = Segment(Q, O_2)
Qm2 = Segment(Rm2, Q)
QRm2 = Segment(Rmr2, Q)
QRm32 = Segment(Rm32, Q)
I = (0.84074074074074, -1.3577777777777778)
J = (0.84074074074074, -4.584444444444444)
K = (-1.1859259259259265, -4.575555555555556)
L1: O + exp((i * 3.141592653589793 / 6))
L2: O + exp(((5 * i) * 3.141592653589793 / 6))
L3: O + exp(((7 * i) * 3.141592653589793 / 6))
L4: O + exp(((11 * i) * 3.141592653589793 / 6))
L5: O + exp((i * 3.141592653589793 / 4))
L6: O + exp(((3 * i) * 3.141592653589793 / 4))
L7: O + exp(((5 * i) * 3.141592653589793 / 4))
L8: O + exp(((-i) * 3.141592653589793 / 4))
e_1 = Segment(L1, L2)
f_1 = Segment(L4, L3)
g_1 = Segment(L5, L7)
l_1 = Segment(L6, L8)
L9: O + exp((i * 3.141592653589793 / 3))
L10: O + exp(((2 * i) * 3.141592653589793 / 3))
L11: O + exp(((-i) * 3.141592653589793 / 3))
L12: O + exp(((-2 * i) * 3.141592653589793 / 3))
m_1 = Segment(L9, L11)
n_1 = Segment(L10, L12)
gc2(x) = If[(x > x(X)) ∧ (x  <  0), sin(x)]
fs2(x) = If[(x > x(X)) ∧ (x  <  0), cos(x)]
z_1: W1 + (0.45 * exp(((-2 * ci) * 3.141592653589793 / 3)))
S2: W1 + (0.45 * exp(((-ci) * 3.141592653589793 / 3)))
poly2, z_2, s_1, s2 = Polygon(W1, S2, z_1)
W2 = (2.2718518518518507, -1.3133333333333312)
poly3 = triponse(ci, W2)
N = (3.622962962962961, -1.3133333333333312)
U = (2.6540740740740736, -1.8111111111111111)
V = (3.089629629629629, -2.042222222222222)
W = (3.5340740740740735, -1.5444444444444445)
Z = (3.08074074074074, -2.5044444444444443)
A_1 = (2.6451851851851846, -2.2555555555555555)
poly4 = triponse(ci, N)
poly5 = triponse(ci, U)
poly6 = triponse(ci, V)
poly7 = triponse(ci, W)
poly8 = triponse(ci, Z)
poly9 = triponse(ci, A_1)
L = (3.098518518518518, -1.8111111111111111)
S = (3.5518518518518514, -1.8111111111111111)
B_1 = (2.6451851851851846, -2.5044444444444443)
C_1 = (3.089629629629629, -1.5444444444444445)
D_1 = (3.5429629629629624, -2.2555555555555555)
E_1 = (3.5251851851851845, -2.042222222222222)
F_1 = (2.6451851851851846, -2.033333333333333)
G_1 = (2.209629629629629, -1.5355555555555556)
H_1 = (3.160740740740739, -1.3133333333333312)
I_1 = (2.20074074074074, -2.0244444444444443)
poly10 = triponse(ci, L)
poly11 = triponse(ci, S)
poly12 = triponse(ci, B_1)
poly13 = triponse(ci, C_1)
poly14 = triponse(ci, D_1)
poly15 = triponse(ci, E_1)
poly16 = triponse(ci, F_1)
poly17 = triponse(ci, G_1)
poly18 = triponse(ci, H_1)
XV2: (x(X), 0)
a = Segment(o, XV2)
k1 = Segment(W1, P6)
k2 = Segment(W2, P4)
k3 = Segment(N, P3)
k4 = Segment(U, Pi2)
k5 = Segment(A_1, P23)
k6 = Segment(Z, P34)
k7 = Segment(W, P56)
k8 = Segment(Pii, V)
k9 = Segment(P76, L)
k10 = Segment(P54, S)
k11 = Segment(P43, B_1)
k12 = Segment(P32, C_1)
k13 = Segment(P53, D_1)
k14 = Segment(P74, E_1)
k15 = Segment(P116, F_1)
k16 = Segment(P2, H_1)
q1 = Segment(Pim6, G_1)
J_1 = (2.20074074074074, -2.5044444444444443)
K_1 = (2.716296296296295, -1.3133333333333312)
L_1 = (2.6451851851851846, -1.5444444444444445)
M_1 = (3.098518518518518, -2.2555555555555555)
N_1 = (3.5251851851851845, -2.5044444444444443)
O_1 = (2.20074074074074, -1.8111111111111111)
poly19 = triponse(ci, I_1)
poly20 = triponse(ci, J_1)
poly21 = triponse(ci, K_1)
poly22 = triponse(ci, L_1)
poly23 = triponse(ci, M_1)
poly24 = triponse(ci, N_1)
poly25 = triponse(ci, O_1)
q2 = Segment(I_1, Pim4)
q3 = Segment(Pim3, J_1)
q4 = Segment(Pim2, K_1)
q5 = Segment(Pm23, L_1)
q6 = Segment(Pm34, M_1)
exo = 1
q7 = Segment(Pm56, N_1)
q8 = Segment(Pmpi, O_1)
juste1: (q4  <  0.03) ∧ (k2  <  0.03) ∧ (k3  <  0.03) ∧ (k16  <  0.03)
juste2: (q5  <  0.03) ∧ (k7  <  0.03) ∧ (k12  <  0.03) ∧ (q1  <  0.03)
juste3: (q8  <  0.03) ∧ (k10  <  0.03) ∧ (k4  <  0.03) ∧ (k9  <  0.03)
juste4: (q2  <  0.03) ∧ (k8  <  0.03) ∧ (k14  <  0.03) ∧ (k15  <  0.03)
juste5: (q6  <  0.03) ∧ (k1  <  0.03) ∧ (k5  <  0.03) ∧ (k13  <  0.03)
juste6: (q7  <  0.03) ∧ (q3  <  0.03) ∧ (k6  <  0.03) ∧ (k11  <  0.03)
FP: O + (1.2 * exp((i * 3.141592653589793 / 2)))
FP2: O + (1.2 * exp(i))
h_1 = CircleArc(O, FP2, FP)
A_2 = Point(h_1)
LM: O + (1.2 * exp((-3.141592653589793 * i / 2)))
LM2: O + (1.2 * exp((-i)))
k_1 = CircleArc(O, LM, LM2)
B_2 = Point(k_1)
cur: 0.63 + (i * (-2.5 + (exo2 * 0.232)))
i_1 = Segment(X, XV2)
j_1 = Segment(O, o)
grade: 0
n1: If[q4  <  0.03, 5 / 12, 0] + If[k2  <  0.03, 5 / 12, 0] + If[k3  <  0.03, 5 / 12, 0] + If[k16  <  0.03, 5 / 12, 0]
α1: 1
texte42: "Score " + grade + " / 10"
n3: If[q8  <  0.03, 5 / 12, 0] + If[k10  <  0.03, 5 / 12, 0] + If[k4  <  0.03, 5 / 12, 0] + If[k9  <  0.03, 5 / 12, 0]
n4: If[q2  <  0.03, 5 / 12, 0] + If[k8  <  0.03, 5 / 12, 0] + If[k14  <  0.03, 5 / 12, 0] + If[k15  <  0.03, 5 / 12, 0]
n5: If[q6  <  0.03, 5 / 12, 0] + If[k1  <  0.03, 5 / 12, 0] + If[k5  <  0.03, 5 / 12, 0] + If[k13  <  0.03, 5 / 12, 0]
n6: If[q7  <  0.03, 5 / 12, 0] + If[q3  <  0.03, 5 / 12, 0] + If[k6  <  0.03, 5 / 12, 0] + If[k11  <  0.03, 5 / 12, 0]
α2: 1
α3: 1
α4: 1
α5: 1
α6: 1
n2: If[q5  <  0.03, 5 / 12, 0] + If[k7  <  0.03, 5 / 12, 0] + If[k12  <  0.03, 5 / 12, 0] + If[q1  <  0.03, 5 / 12, 0]
voirexo1: true
voirexo2: true
voirexo3: true
voirexo4: true
voirexo5: true
voirexo6: true

Tool: triponse
Input: ci, S
Output: poly2

z_1: S + (0.45 * exp(((-2 * ci) * 3.141592653589793 / 3)))
S2: S + (0.45 * exp(((-ci) * 3.141592653589793 / 3)))
poly2, z_2, s_1, s2 = Polygon(S, S2, z_1)