Inéquations trigonométriques
Author: Joël Gauvain
Date: 1 Décembre 2012

Dans la première partie vous devez colorier en vert les points du cercle trigonométrique associés aux solutions de l'inéquation proposée.
Les extrémités des arcs sont représentables de deux manières ...  ou  .... suivant qu'ils appartiennent ou n'appartiennent pas à l'arc.
Cliquez sur l'une des huit images situées à droite de la figure pour choisir le type d'arc de cercle voulu, puis déplacez le point rouge pour modifier l'arc.

$ \cos\,x $

$ \sin
\,x $

$ \leqslant $

$ \geqslant $

$ < $

$ > $

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

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

$ \frac{1}{2} $

$ 0 $

$ -\frac{1}{2} $

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

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

Nouvel énoncé

Valider la figure

$ [\,0\,;\,2\pi]\, $

[\,-\pi\,;\,\pi\,]

[\,-2\pi\,;\,0]

\text{Donner les deux réels } a \text{ et } b \text{ (avec }a<b\text{) de}

\text{qui sont associés aux extrémités de l'arc représenté en vert.}

a =

2

b =

Valider a et b

$a  \text{  doit être inférieur à } b$

$ a\text{ n'appartient pas à l'intervalle donné} $

$ b\text{ n'appartient pas à l'intervalle donné} $

\text{Saisissez }a \text{ et }b

\ovalbox{\;[\;}

[

\ovalbox{ \; ;\;}

$ \ovalbox{\;]\;} $

\ovalbox{↩}

$ \ovalbox{∪} $

\text{Clavier virtuel}

\text{L'ensemble des solutions est : }

$ [ $

$ ] $

$ ; $

$ [ $

$ ] $

$ ∪ $

$ [ $

$] $

$ ; $

$ [ $

$ ] $

$ \ovalbox{\begin{array}{} ↩ \ ↩ \end{array} } $

Valider l'ensemble des solutions

Faux

Choix de la courbe

$ \cos\left(\frac{5\pi}{6}\right) $

$ \sin\left(-\frac{\pi}{3}\right) $

$ \cos\left(\frac{3\pi}{4}\right) $

$ \sin\left(-\frac{\pi}{4}\right) $

$ \cos\left(\frac{2\pi}{3}\right) $

$ \sin\left(-\frac{\pi}{6}\right)$

$ \cos\left(\frac{\pi}{2}\right) $

$ \sin \pi $

$ \cos\left(\frac{\pi}{3}\right) $

$ \sin\left(\frac{\pi}{6}\right) $

$ \cos\left(\frac{\pi}{4}\right) $

$ \sin\left(\frac{\pi}{4}\right) $

$ \cos\left(\frac{\pi}{6}\right) $

$ \sin\left(\frac{\pi}{3}\right) $

\text{Vous avez tracé la courbe de la fonction  sinus}

\text{Vous avez tracé la courbe de la fonction } x\longmapsto-\sin x

\text{Vous avez tracé la courbe de la fonction }  x\longmapsto-\cos x

\text{Vous avez tracé la courbe de la fonction cosinus}

\text{L'arc tracé est associé à une inéquation}

\text{du type }\cos x \geqslant k

\text{du type }\cos x\leqslant k

\text{du type }\cos x< k

\text{du type }\cos x > k

\text{du type }\sin x \leqslant k

\text{du type }\sin x<k

\text{du type }\sin x\geqslant k

\text{du type }\sin x> k

Réalisation Joël Gauvain
Lycée René Josué Valin
17000 La Rochelle

\text{Les nombres }a \text{ et } b \text{ sont solutions de l'inéquation}

\text{Les nombres }a\text{ et }b\text{ ne sont pas solutions de l'inéquation}

RAZ

\ovalbox{\text{Dernier exercice}}

O = (0, 0)
c2 = Circle(O, 1)
C, A = Intersect(c2, xAxis)
D, B = Intersect(c2, yAxis)
a = Segment(C, A)
b = Segment(B, D)
E = Point(a)
F = Point(b)
I, J = Intersect(c2, i)
j = Segment(I, J)
K, L = Intersect(c2, d)
M, N = Intersect(c2, e)
l = Segment(K, L)
m = Segment(M, N)
n: 0
q2: x = x(E)
T, U = Intersect(c2, q2)
r = Segment(A, E)
s = CircumcircleArc(U, A, T)
t = Segment(T, U)
c_1 = CircumcircleArc(T, C, U)
a_1 = Segment(E, C)
V = Point(a)
b_1: x = x(V)
W, Z = Intersect(c2, b_1)
d_1 = Segment(V, A)
e_1 = CircumcircleArc(Z, A, W)
f_1 = Segment(W, Z)
g_1 = CircumcircleArc(W, C, Z)
h_1 = Segment(V, C)
i_1: y = y(F)
A_1, B_1 = Intersect(c2, i_1)
j_1 = Segment(A_1, B_1)
k_1 = CircumcircleArc(A_1, B, B_1)
p_1 = CircumcircleArc(A_1, D, B_1)
X = Point(b)
l_1: y = y(X)
D_1, E_1 = Intersect(c2, l_1)
m_1 = Segment(D_1, E_1)
q_1 = CircumcircleArc(D_1, B, E_1)
r_1 = Segment(X, B)
s_1 = Segment(X, D)
t_1 = CircumcircleArc(D_1, D, E_1)
a_2 = Segment(F, B)
b_2 = Segment(F, D)
v10: (abs(x(E) + 0.866)  <  0.02) ∧ n ≟ 2
v20: (abs(x(E) + 0.866)  <  0.02) ∧ n ≟ 1
v40: (abs(x(V) + 0.866)  <  0.02) ∧ n ≟ 3
v30: (abs(x(V) + 0.866)  <  0.02) ∧ n ≟ 4
v50: (abs(y(F) + 0.866)  <  0.02) ∧ n ≟ 6
v60: (abs(y(X) + 0.866)  <  0.02) ∧ n ≟ 8
v70: (abs(y(F) + 0.866)  <  0.02) ∧ n ≟ 5
v80: (abs(y(X) + 0.866)  <  0.02) ∧ n ≟ 7
v11: (abs(x(E) + 0.707)  <  0.02) ∧ n ≟ 2
v12: (abs(x(E) + 0.5)  <  0.02) ∧ n ≟ 2
v13: (abs(x(E))  <  0.02) ∧ n ≟ 2
v14: (abs(x(E) - 0.5)  <  0.02) ∧ n ≟ 2
v15: (abs(x(E) - 0.707)  <  0.02) ∧ n ≟ 2
v16: (abs(x(E) - 0.866)  <  0.02) ∧ n ≟ 2
v21: (abs(x(E) + 0.707)  <  0.02) ∧ n ≟ 1
v22: (abs(x(E) + 0.5)  <  0.02) ∧ n ≟ 1
v23: (abs(x(E))  <  0.02) ∧ n ≟ 1
v24: (abs(x(E) - 0.5)  <  0.02) ∧ n ≟ 1
v25: (abs(x(E) - 0.707)  <  0.02) ∧ n ≟ 1
v26: (abs(x(E) - 0.866)  <  0.02) ∧ n ≟ 1
v31: (abs(x(V) + 0.707)  <  0.02) ∧ n ≟ 4
v32: (abs(x(V) + 0.5)  <  0.02) ∧ n ≟ 4
v33: (abs(x(V))  <  0.02) ∧ n ≟ 4
v34: (abs(x(V) - 0.5)  <  0.02) ∧ n ≟ 4
v35: (abs(x(V) - 0.707)  <  0.02) ∧ n ≟ 4
v36: (abs(x(V) - 0.866)  <  0.02) ∧ n ≟ 4
v41: (abs(x(V) + 0.707)  <  0.02) ∧ n ≟ 3
v42: (abs(x(V) + 0.5)  <  0.02) ∧ n ≟ 3
v43: (abs(x(V))  <  0.02) ∧ n ≟ 3
v44: (abs(x(V) - 0.5)  <  0.02) ∧ n ≟ 3
v45: (abs(x(V) - 0.707)  <  0.02) ∧ n ≟ 3
v46: (abs(x(V) - 0.866)  <  0.02) ∧ n ≟ 3
v51: (abs(y(F) + 0.707)  <  0.02) ∧ n ≟ 6
v52: (abs(y(F) + 0.5)  <  0.02) ∧ n ≟ 6
v53: (abs(y(F))  <  0.02) ∧ n ≟ 6
v54: (abs(y(F) - 0.5)  <  0.02) ∧ n ≟ 6
v55: (abs(y(F) - 0.707)  <  0.02) ∧ n ≟ 6
v56: (abs(y(F) - 0.866)  <  0.02) ∧ n ≟ 6
v61: (abs(y(X) + 0.707)  <  0.02) ∧ n ≟ 8
v62: (abs(y(X) + 0.5)  <  0.02) ∧ n ≟ 8
v63: (abs(y(X))  <  0.02) ∧ n ≟ 8
v64: (abs(y(X) - 0.5)  <  0.02) ∧ n ≟ 8
v65: (abs(y(X) - 0.707)  <  0.02) ∧ n ≟ 8
v66: (abs(y(X) - 0.866)  <  0.02) ∧ n ≟ 8
v71: (abs(y(F) + 0.707)  <  0.02) ∧ n ≟ 5
v72: (abs(y(F) + 0.5)  <  0.02) ∧ n ≟ 5
v73: (abs(y(F))  <  0.02) ∧ n ≟ 5
v74: (abs(y(F) - 0.5)  <  0.02) ∧ n ≟ 5
v75: (abs(y(F) - 0.707)  <  0.02) ∧ n ≟ 5
v76: (abs(y(F) - 0.866)  <  0.02) ∧ n ≟ 5
v81: (abs(y(X) + 0.707)  <  0.02) ∧ n ≟ 7
v82: (abs(y(X) + 0.5)  <  0.02) ∧ n ≟ 7
v83: (abs(y(X))  <  0.02) ∧ n ≟ 7
v84: (abs(y(X) - 0.5)  <  0.02) ∧ n ≟ 7
v85: (abs(y(X) - 0.707)  <  0.02) ∧ n ≟ 7
v86: (abs(y(X) - 0.866)  <  0.02) ∧ n ≟ 7
dix = 0 (slider from -2 to 8, step 1)
uni = -1 (slider from -1 to 6, step 1)
num = If((uni ≠ 3) ∨ (dix  <  5), (dix * 10) + uni, (dix * 10) + uni - 40)
vrai1: num ≟ 10 ∧ v10 ∨ num ≟ 11 ∧ v11 ∨ num ≟ 12 ∧ v12 ∨ num ≟ 13 ∧ v13 ∨ num ≟ 14 ∧ v14 ∨ num ≟ 15 ∧ v15 ∨ num ≟ 16 ∧ v16
vrai2: num ≟ 20 ∧ v20 ∨ num ≟ 21 ∧ v21 ∨ num ≟ 22 ∧ v22 ∨ num ≟ 23 ∧ v23 ∨ num ≟ 24 ∧ v24 ∨ num ≟ 25 ∧ v25 ∨ num ≟ 26 ∧ v26
vrai3: num ≟ 30 ∧ v30 ∨ num ≟ 31 ∧ v31 ∨ num ≟ 32 ∧ v32 ∨ num ≟ 33 ∧ v33 ∨ num ≟ 34 ∧ v34 ∨ num ≟ 35 ∧ v35 ∨ num ≟ 36 ∧ v36
vrai4: num ≟ 40 ∧ v40 ∨ num ≟ 41 ∧ v41 ∨ num ≟ 42 ∧ v42 ∨ num ≟ 43 ∧ v43 ∨ num ≟ 44 ∧ v44 ∨ num ≟ 45 ∧ v45 ∨ num ≟ 46 ∧ v46
vrai5: num ≟ 50 ∧ v50 ∨ num ≟ 51 ∧ v51 ∨ num ≟ 52 ∧ v52 ∨ num ≟ 53 ∧ v53 ∨ num ≟ 54 ∧ v54 ∨ num ≟ 55 ∧ v55 ∨ num ≟ 56 ∧ v56
vrai6: num ≟ 60 ∧ v60 ∨ num ≟ 61 ∧ v61 ∨ num ≟ 62 ∧ v62 ∨ num ≟ 63 ∧ v63 ∨ num ≟ 64 ∧ v64 ∨ num ≟ 65 ∧ v65 ∨ num ≟ 66 ∧ v66
vrai7: num ≟ 70 ∧ v70 ∨ num ≟ 71 ∧ v71 ∨ num ≟ 72 ∧ v72 ∨ num ≟ 73 ∧ v73 ∨ num ≟ 74 ∧ v74 ∨ num ≟ 75 ∧ v75 ∨ num ≟ 76 ∧ v76
vrai8: num ≟ 80 ∧ v80 ∨ num ≟ 81 ∧ v81 ∨ num ≟ 82 ∧ v82 ∨ num ≟ 83 ∧ v83 ∨ num ≟ 84 ∧ v84 ∨ num ≟ 85 ∧ v85 ∨ num ≟ 86 ∧ v86
vrai: vrai1 ∨ vrai2 ∨ vrai3 ∨ vrai4 ∨ vrai5 ∨ vrai6 ∨ vrai7 ∨ vrai8
montre = false
haut = If(n ≟ 2 ∨ n ≟ 1, x(E), If[n ≟ 4 ∨ n ≟ 3, x(V), If[n ≟ 6 ∨ n ≟ 5, y(F), If[n ≟ 7 ∨ n ≟ 8, y(X), 0]]])
pp = 0 (slider from -1 to 1, step 1)
texte22: "" + (LaTeX[texte17]) + ""
texte23: "" + (LaTeX[texte19]) + ""
texte24: "" + (LaTeX[texte20]) + ""
ChampTextea = Textfield(textea1)
va = NaN
va100 = 100
va' = If(Defined[va], va, va100)
vb = NaN
ChampTexteb = Textfield(texteb1)
vb100 = 100
vb' = If(Defined[vb], vb, vb100)
ja1: pp ≟ -1 ∧ uni ≟ 0 ∧ (dix > 4) ∧ va' ≟ (4 * π / 3)
jb1: pp ≟ -1 ∧ uni ≟ 0 ∧ (dix > 4) ∧ vb' ≟ (5 * π / 3)
ja2: pp ≟ 0 ∧ uni ≟ 0 ∧ (dix > 4) ∧ va' ≟ (-2 * π / 3)
jb2: pp ≟ 0 ∧ uni ≟ 0 ∧ (dix > 4) ∧ vb' ≟ ((-π)) / 3
ja3: pp ≟ 1 ∧ uni ≟ 0 ∧ (dix > 4) ∧ va' ≟ (-2 * π / 3)
jb3: pp ≟ 1 ∧ uni ≟ 0 ∧ (dix > 4) ∧ vb' ≟ ((-π)) / 3
ja4: pp ≟ -1 ∧ uni ≟ 1 ∧ (dix > 4) ∧ va' ≟ (5 * π / 4)
jb4: pp ≟ -1 ∧ uni ≟ 1 ∧ (dix > 4) ∧ vb' ≟ (7 * π / 4)
ja5: pp ≟ 0 ∧ uni ≟ 1 ∧ (dix > 4) ∧ va' ≟ (-3 * π / 4)
jb5: pp ≟ 0 ∧ uni ≟ 1 ∧ (dix > 4) ∧ vb' ≟ ((-π)) / 4
ja6: pp ≟ 1 ∧ uni ≟ 1 ∧ (dix > 4) ∧ va' ≟ (-3 * π / 4)
jb6: pp ≟ 1 ∧ uni ≟ 1 ∧ (dix > 4) ∧ vb' ≟ ((-π)) / 4
ja8: pp ≟ -1 ∧ uni ≟ 2 ∧ (dix > 4) ∧ va' ≟ (7 * π / 6)
jb8: pp ≟ -1 ∧ uni ≟ 2 ∧ (dix > 4) ∧ vb' ≟ (11 * π / 6)
ja9: pp ≟ 0 ∧ uni ≟ 2 ∧ (dix > 4) ∧ va' ≟ (-5 * π / 6)
jb9: pp ≟ 0 ∧ uni ≟ 2 ∧ (dix > 4) ∧ vb' ≟ ((-π)) / 6
ja10: pp ≟ 1 ∧ uni ≟ 2 ∧ (dix > 4) ∧ va' ≟ (-5 * π / 6)
jb10: pp ≟ 1 ∧ uni ≟ 2 ∧ (dix > 4) ∧ vb' ≟ ((-π)) / 6
ja11: pp ≟ -1 ∧ uni ≟ 4 ∧ (dix > 4) ∧ va' ≟ π / 6
jb11: pp ≟ -1 ∧ uni ≟ 4 ∧ (dix > 4) ∧ vb' ≟ (5 * π / 6)
ja12: pp ≟ 0 ∧ uni ≟ 4 ∧ (dix > 4) ∧ va' ≟ π / 6
jb12: pp ≟ 0 ∧ uni ≟ 4 ∧ (dix > 4) ∧ vb' ≟ (5 * π / 6)
ja13: pp ≟ 1 ∧ uni ≟ 4 ∧ (dix > 4) ∧ va' ≟ (-11 * π / 6)
jb13: pp ≟ 1 ∧ uni ≟ 4 ∧ (dix > 4) ∧ vb' ≟ (-7 * π / 6)
ja14: pp ≟ -1 ∧ uni ≟ 5 ∧ (dix > 4) ∧ va' ≟ π / 4
jb14: pp ≟ -1 ∧ uni ≟ 5 ∧ (dix > 4) ∧ vb' ≟ (3 * π / 4)
ja15: pp ≟ 0 ∧ uni ≟ 5 ∧ (dix > 4) ∧ va' ≟ π / 4
jb15: pp ≟ 0 ∧ uni ≟ 5 ∧ (dix > 4) ∧ vb' ≟ (3 * π / 4)
ja16: pp ≟ 1 ∧ uni ≟ 5 ∧ (dix > 4) ∧ va' ≟ (-7 * π / 4)
jb16: pp ≟ 1 ∧ uni ≟ 5 ∧ (dix > 4) ∧ vb' ≟ (-5 * π / 4)
ja17: pp ≟ -1 ∧ uni ≟ 6 ∧ (dix > 4) ∧ va' ≟ π / 3
jb17: pp ≟ -1 ∧ uni ≟ 6 ∧ (dix > 4) ∧ vb' ≟ (2 * π / 3)
ja18: pp ≟ 0 ∧ uni ≟ 6 ∧ (dix > 4) ∧ va' ≟ π / 3
jb18: pp ≟ 0 ∧ uni ≟ 6 ∧ (dix > 4) ∧ vb' ≟ (2 * π / 3)
ja19: pp ≟ 1 ∧ uni ≟ 6 ∧ (dix > 4) ∧ va' ≟ (-5 * π / 3)
jb19: pp ≟ 1 ∧ uni ≟ 6 ∧ (dix > 4) ∧ vb' ≟ (-4 * π / 3)
ajustesin: ja1 ∨ ja2 ∨ ja3 ∨ ja4 ∨ ja5 ∨ ja6 ∨ ja8 ∨ ja9 ∨ ja10 ∨ ja11 ∨ ja12 ∨ ja13 ∨ ja14 ∨ ja15 ∨ ja16 ∨ ja17 ∨ ja18 ∨ ja19
bjustesin: jb1 ∨ jb2 ∨ jb3 ∨ jb4 ∨ jb5 ∨ jb6 ∨ jb8 ∨ jb9 ∨ jb10 ∨ jb11 ∨ jb12 ∨ jb13 ∨ jb14 ∨ jb15 ∨ jb16 ∨ jb17 ∨ jb18 ∨ jb19
ga1: pp ≟ -1 ∧ uni ≟ 0 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (5 * π / 6)
gb1: pp ≟ -1 ∧ uni ≟ 0 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (7 * π / 6)
ga2: pp ≟ 0 ∧ uni ≟ 0 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-5 * π / 6)
gb2: pp ≟ 0 ∧ uni ≟ 0 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (5 * π / 6)
ga3: pp ≟ 1 ∧ uni ≟ 0 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-7 * π / 6)
gb3: pp ≟ 1 ∧ uni ≟ 0 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (-5 * π / 6)
ga4: pp ≟ -1 ∧ uni ≟ 1 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (3 * π / 4)
gb4: pp ≟ -1 ∧ uni ≟ 1 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (5 * π / 4)
ga5: pp ≟ 0 ∧ uni ≟ 1 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-3 * π / 4)
gb5: pp ≟ 0 ∧ uni ≟ 1 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (3 * π / 4)
ga6: pp ≟ 1 ∧ uni ≟ 1 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-5 * π / 4)
gb6: pp ≟ 1 ∧ uni ≟ 1 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (-3 * π / 4)
ga7: pp ≟ -1 ∧ uni ≟ 2 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (2 * π / 3)
gb7: pp ≟ -1 ∧ uni ≟ 2 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (4 * π / 3)
ga8: pp ≟ 0 ∧ uni ≟ 2 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-2 * π / 3)
gb8: pp ≟ 0 ∧ uni ≟ 2 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (2 * π / 3)
ga9: pp ≟ 1 ∧ uni ≟ 2 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-4 * π / 3)
gb9: pp ≟ 1 ∧ uni ≟ 2 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (-2 * π / 3)
ga10: pp ≟ -1 ∧ uni ≟ 3 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ π / 2
gb10: pp ≟ -1 ∧ uni ≟ 3 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (3 * π / 2)
ga11: pp ≟ 0 ∧ uni ≟ 3 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ ((-π)) / 2
gb11: pp ≟ 0 ∧ uni ≟ 3 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ π / 2
ga12: pp ≟ 1 ∧ uni ≟ 3 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-3 * π / 2)
gb12: pp ≟ 1 ∧ uni ≟ 3 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ ((-π)) / 2
ga13: pp ≟ -1 ∧ uni ≟ 4 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ π / 3
gb13: pp ≟ -1 ∧ uni ≟ 4 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (5 * π / 3)
ga14: pp ≟ 0 ∧ uni ≟ 4 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ ((-π)) / 3
gb14: pp ≟ 0 ∧ uni ≟ 4 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ π / 3
ga15: pp ≟ 1 ∧ uni ≟ 4 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-5 * π / 3)
gb15: pp ≟ 1 ∧ uni ≟ 4 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ ((-π)) / 3
ga16: pp ≟ -1 ∧ uni ≟ 5 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ π / 4
gb16: pp ≟ -1 ∧ uni ≟ 5 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (7 * π / 4)
ga17: pp ≟ 0 ∧ uni ≟ 5 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ ((-π)) / 4
gb17: pp ≟ 0 ∧ uni ≟ 5 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ π / 4
ga18: pp ≟ 1 ∧ uni ≟ 5 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-7 * π / 4)
gb18: pp ≟ 1 ∧ uni ≟ 5 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ ((-π)) / 4
ga19: pp ≟ -1 ∧ uni ≟ 6 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ π / 6
gb19: pp ≟ -1 ∧ uni ≟ 6 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ (11 * π / 6)
ga20: pp ≟ 0 ∧ uni ≟ 6 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ ((-π)) / 6
gb20: pp ≟ 0 ∧ uni ≟ 6 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ π / 6
ga21: pp ≟ 1 ∧ uni ≟ 6 ∧ (dix  <  5) ∧ (dix > 0) ∧ va' ≟ (-11 * π / 6)
gb21: pp ≟ 1 ∧ uni ≟ 6 ∧ (dix  <  5) ∧ (dix > 0) ∧ vb' ≟ ((-π)) / 6
ajustecos: ga1 ∨ ga2 ∨ ga3 ∨ ga4 ∨ ga5 ∨ ga6 ∨ ga7 ∨ ga8 ∨ ga9 ∨ ga10 ∨ ga11 ∨ ga12 ∨ ga13 ∨ ga14 ∨ ga15 ∨ ga16 ∨ ga17 ∨ ga18 ∨ ga19 ∨ ga20 ∨ ga21
bjustecos: gb1 ∨ gb2 ∨ gb3 ∨ gb4 ∨ gb5 ∨ gb6 ∨ gb7 ∨ gb8 ∨ gb9 ∨ gb10 ∨ gb11 ∨ gb12 ∨ gb13 ∨ gb14 ∨ gb15 ∨ gb16 ∨ gb17 ∨ gb18 ∨ gb19 ∨ gb20 ∨ gb21
ajuste: ajustecos ∨ ajustesin
bjuste: bjustecos ∨ bjustesin
valide: false
abinv: (va'  <  50) ∧ (vb'  <  50) ∧ (va' > vb') ∧ vrai ∧ montre ∧ valide
ahors: (pp ≟ -1 ∧ ((va'  <  0) ∨ (va' > (2 * π))) ∨ pp ≟ 0 ∧ ((va'  <  (-π)) ∨ (va' > π)) ∨ pp ≟ 1 ∧ ((va'  <  (-2 * π)) ∨ (va' > 0))) ∧ vrai ∧ montre ∧ valide
bhors: (pp ≟ -1 ∧ ((vb'  <  0) ∨ (vb' > (2 * π))) ∨ pp ≟ 0 ∧ ((vb'  <  (-π)) ∨ (vb' > π)) ∨ pp ≟ 1 ∧ ((vb'  <  (-2 * π)) ∨ (vb' > 0))) ∧ vrai ∧ montre ∧ valide
abjustes: ajuste ∧ bjuste
sina: sin(va')
texte28 = SurdText(sina)
cosa: cos(va')
texte30 = SurdText(cosa)
sinb: sin(vb')
texte32 = SurdText(sinb)
cosb: cos(vb')
texte34 = SurdText(cosb)
C_1 = (0.4774074074074123, -1.0477777777777797)
F_1 = (0.83, -1.05)
H_1 = (1.33074, -1.05)
I_1 = (3.1, -1.05)
J_1 = (3.1, -1.65)
calx = If(uni ≟ 0, -0.8660254037844386, If[uni ≟ 1, -0.7071067811865476, If[uni ≟ 2, -0.5, If[uni ≟ 3, 0, If[uni ≟ 4, 0.5, If[uni ≟ 5, 0.7071067811865476, 0.8660254037844386]]]]])
AS: (cos(va'), sin(va'))
AST: ((1.15 * cos(va')), (1.15 * sin(va')))
BS: (cos(vb'), sin(vb'))
BST: (1.15 * BS)
AC1: (cos(va'), sin(va'))
ACT: (1.15 * AC1)
BC: (cos(vb'), sin(vb'))
BCT: (1.15 * BC)
z = 1 (slider from 0 to 13, step 1)
texte42 = SurdText(vb', {3.141592653589793})
K_1 = (0.8774074074074133, -0.9944444444444465)
K1 = 0
Cl2: K_1 + (0.4, 0)
Cl3: K_1 + (0.7, 0)
Cl4: K_1 + (1.1, 0)
Cl5: K_1 + (0.4, -0.24)
Cl6: K_1 + (0.7, -0.24)
Cl7: K_1 + (0, -0.45)
Cl8: K_1 + (0.28, -0.45)
Cl9: K_1 + (0.52, -0.45)
Cl10: K_1 + (0.8, -0.45)
Cl11: K_1 + (1.1, -0.5)
L_1: (x(K_1) + 1.82, y(K_1))
L1 = 0
M_1: (x(L_1), y(L_1) - 0.7)
N_1: (x(K_1), y(M_1))
O_1: (x(K_1) + 0.85, y(K_1))
d_2 = PolyLine(K_1, N_1, M_1, L_1, O_1)
P_1 = (-2.5981481481481468, -1.6077777777777793)
LL1 = 0
LY1: LL1 ≟ 1
exL = 0
texte55 = SurdText(va', {3.141592653589793})
bsup = If(pp ≟ -1, 6.283185307179586, If[pp ≟ 0, 3.141592653589793, 0])
binf = If(pp ≟ -1, 0, If[pp ≟ 0, -3.141592653589793, -6.283185307179586])
texte56 = SurdText(binf, {3.141592653589793})
texte47: "$ \ovalbox{" + (LaTeX[texte56]) + " } $"
texte57 = SurdText(bsup, {3.141592653589793})
texte45: "$ \ovalbox{" + (LaTeX[texte57]) + "} $"
Q_1: (x(P_1) + 0.15, y(P_1))
Q1 = 0
Q_2: (x(Q_1), If[va' ≟ 0 ∨ va' ≟ (-2 * π) ∨ va' ≟ (2 * π) ∨ va' ≟ (-π) ∨ va' ≟ π, y(Q_1) - 0.08, y(Q_1)])
LL2 = 0
LL3 = 0
texte46: "$ " + (LaTeX[texte56]) + " $"
texte58: "" + (LaTeX[texte57]) + ""
exz = 0
R_1: (x(P_1) + 0.5, y(P_1))
LL4 = 0
S_1: (x(P_1) + 0.6, y(P_1))
texte60 = SurdText(va', {3.141592653589793})
S_2: (x(S_1), If[va' ≟ 0 ∨ va' ≟ (-2 * π) ∨ va' ≟ (2 * π) ∨ va' ≟ (-π) ∨ va' ≟ π, y(S_1) - 0.08, y(S_1)])
texte61: "$ " + (LaTeX[texte56]) + " $"
texte64: "$ " + (LaTeX[texte57]) + " $"
exL4 = 3
LL5 = 0
exL5 = 1
V_1: (x(P_1) + 1.15, y(P_1))
LL6 = 0
LL7 = 0
LL8 = 0
LL9 = 0
U_1: (x(P_1) + 1.35, y(P_1))
W_1: (x(P_1) + 1.45, y(P_1))
LL10 = 0
LL11 = 0
texte70: "$ " + (LaTeX[texte56]) + " $"
LL12 = 0
Z_1: (x(P_1) + 1.8, y(P_1))
texte73: "$ " + (LaTeX[texte57]) + " $"
texte75: "$ " + (LaTeX[texte56]) + " $"
texte78: "$ " + (LaTeX[texte57]) + " $"
A_2: (x(P_1) + 2.2, y(P_1))
T_1: (x(P_1) + 1, y(P_1))
somLL: LL1 + (10 * LL2) + (100 * LL3) + (1000 * LL4) + (10000 * LL5) + (100000 * LL6) + (1000000 * LL7) + (10000000 * LL8) + (100000000 * LL9) + (1000000000 * LL10) + (10000000000 * LL11)
vmoy: (va' + vb') / 2
cas3: somLL ≟ 24131122111 ∧ (dix ≟ 2 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 1 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 5 ∧ (sin(vmoy) > sin(va')) ∨ dix ≟ 7 ∧ (sin(vmoy)  <  sin(va')))
cas1: somLL ≟ 24132112111 ∧ (dix ≟ 4 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 3 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 6 ∧ (sin(vmoy) > sin(va')) ∨ dix ≟ 8 ∧ (sin(vmoy)  <  sin(va')))
cas2: somLL ≟ 23121 ∧ (dix ≟ 2 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 1 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 5 ∧ (sin(vmoy)  <  sin(va')) ∨ dix ≟ 7 ∧ (sin(vmoy) > sin(va')))
cas4: somLL ≟ 13122 ∧ (dix ≟ 4 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 3 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 6 ∧ (sin(vmoy)  <  sin(va')) ∨ dix ≟ 8 ∧ (sin(vmoy) > sin(va')))
cors = false
nbexo = 0 (slider from 0 to 200, step 1)
texte83: "\text{Inéquation n° }" + (LaTeX[nbexo]) + ""
score = 0 (slider from 0 to 200, step 0.25)
gain = 0 (slider from 0 to 1, step 0.25)
essai = 0 (slider from 0 to 1, step 1)
gain1 = 0.25 (slider from 0 to 0.25, step 0.25)
gaina = 0.25 (slider from 0 to 0.25, step 0.25)
gainb = 0.25 (slider from 0 to 0.25, step 0.25)
gaini = 0.25 (slider from 0 to 0.25, step 0.25)
toutjuste: (cas1 ∨ cas2 ∨ cas3 ∨ cas4) ∧ cors
voirlepoint = false
decal = 0
absZ = 1
ZZ: (cos(absZ - decal), sin(absZ - decal))
B_2 = (-4.358148148148149, -2.016666666666668)
c = 0 (slider from 0 to 4, step 1)
G, H = Intersect(c2, r_2)
P, Q = Intersect(c2, s_2)
k = Segment(G, H)
n_1 = Segment(P, Q)
L_2, M_2 = Intersect(c2, t_2)
a_3 = Segment(L_2, M_2)
O2 = 0
V2 = 0
voircliq: true
B_3 = (-2.4025925925925904, -2.07)
C_3: (x(B_3) + 5.3, y(B_3))
D_3: (x(B_3), y(B_3) - 0.4)
valc = 0
ju1: (dix  <  5) ∧ (dix > 0) ∧ abs(pp) ≟ 1 ∧ c ≟ 1
ju2: (dix > 4) ∧ abs(pp) ≟ 1 ∧ c ≟ 2
ju3: (dix > 4) ∧ pp ≟ 0 ∧ c ≟ 3
ju4: (dix > 0) ∧ (dix  <  5) ∧ c ≟ 4 ∧ pp ≟ 0
F3 = 0
texte94 = SurdText(vb', {3.141592653589793})
uni2 = 4 (slider from 0 to 5, step 1)
courbefausse: valc ≟ 1 ∧ (¬(ju1 ∨ ju2 ∨ ju3 ∨ ju4)) ∧ (c > 0) ∧ (¬voircliq)
arcnonvalable: (n ≠ 0) ∧ montre ∧ (¬vrai) ∧ ((n ≠ 1) ∧ dix ≟ 2 ∨ (n ≠ 7) ∧ dix ≟ 8 ∨ (n ≠ 2) ∧ dix ≟ 1 ∨ (n ≠ 4) ∧ dix ≟ 3 ∨ (n ≠ 3) ∧ dix ≟ 4 ∨ (n ≠ 6) ∧ dix ≟ 5 ∨ (n ≠ 8) ∧ dix ≟ 6 ∨ (n ≠ 5) ∧ dix ≟ 7)
cas21: somLL ≟ 13122 ∧ (dix ≟ 2 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 1 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 5 ∧ (sin(vmoy)  <  sin(va')) ∨ dix ≟ 7 ∧ (sin(vmoy) > sin(va')))
cas41: somLL ≟ 23121 ∧ (dix ≟ 4 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 3 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 6 ∧ (sin(vmoy)  <  sin(va')) ∨ dix ≟ 8 ∧ (sin(vmoy) > sin(va')))
cas11: somLL ≟ 24131122111 ∧ (dix ≟ 4 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 3 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 6 ∧ (sin(vmoy) > sin(va')) ∨ dix ≟ 8 ∧ (sin(vmoy)  <  sin(va')))
cas31: somLL ≟ 24132112111 ∧ (dix ≟ 2 ∧ (cos(vmoy)  <  cos(va')) ∨ dix ≟ 1 ∧ (cos(vmoy) > cos(va')) ∨ dix ≟ 5 ∧ (sin(vmoy) > sin(va')) ∨ dix ≟ 7 ∧ (sin(vmoy)  <  sin(va')))
Z_3 = (-4.278148148148148, -1.1988888888888907)
B_4: (x(Z_3) + 3.6, y(Z_3))
C_4: (x(B_4), y(B_4) + 0.35)
D_4: (x(Z_3) + 0.15, y(C_4))
l_4 = PolyLine(Z_3, B_4, C_4, D_4)
posfrac55 = IndexOf("\cdot \frac{", texte55)
texte550 = Take(texte55, 1, posfrac55 - 1)
posmoins550 = IndexOf("-", texte550)
texte551 = If(¬Defined[posfrac55], texte55, If[Defined[posmoins550], "-\frac{" + (Take[texte550, 2]) + (Take[texte55, posfrac55 + 12]), "\frac{" + (Take[texte550, 1]) + (Take[texte55, posfrac55 + 12])])
texte41: "$ \ovalbox{" + (LaTeX[texte551]) + "} $"
texte62: "$ " + (LaTeX[texte551]) + " $"
texte36_1: "" + (LaTeX[texte551]) + ""
texte37: "" + (LaTeX[texte551]) + ""
texte29: "\cos\left(" + (LaTeX[texte551]) + "\right)=" + (LaTeX[texte30]) + ""
texte71: "$ " + (LaTeX[texte551]) + " $"
texte76: "$ " + (LaTeX[texte551]) + " $"
texte93: texte551
posfrac94 = IndexOf("\cdot \frac{", texte94)
texte940 = Take(texte94, 1, posfrac94 - 1)
posmoins940 = IndexOf("-", texte940)
texte941 = If(¬Defined[posfrac94], texte94, If[Defined[posmoins940], "-\frac{" + (Take[texte940, 2]) + (Take[texte94, posfrac94 + 12]), "\frac{" + (Take[texte940, 1]) + (Take[texte94, posfrac94 + 12])])
texte77: "$ " + (LaTeX[texte941]) + " $"
texte72: "$ " + (LaTeX[texte941]) + " $"
texte63: "$ " + (LaTeX[texte941]) + " $"
texte48: "" + (LaTeX[texte941]) + ""
texte43_1: "$ \ovalbox{" + (LaTeX[texte941]) + "} $"
texte38: "" + (LaTeX[texte941]) + ""
texte36: "" + (LaTeX[texte941]) + ""
texte33: "\cos\left(" + (LaTeX[texte941]) + "\right)=" + (LaTeX[texte34]) + ""
texte43: "" + (LaTeX[texte941]) + ""
texte125: "" + (LaTeX[texte551]) + ""
textea2: "a=" + (LaTeX[texte551]) + "\phantom{\frac{3}{3}}"
texteb2: "b=" + (LaTeX[texte941]) + "\phantom{\frac{3}{3}}"
int1 = If(pp ≟ -1 ∧ (dix > 0) ∧ (uni > -1), "[0\;;\;2\pi]", "")
int2 = If(pp ≟ 0 ∧ (dix > 0) ∧ (uni > -1), "[-\pi\;;\;\pi]", "")
int3 = If(pp ≟ 1 ∧ (dix > 0) ∧ (uni > -1), "[-2\pi\;;\;0]", "")
int: int1 + int2 + int3
texte16: "\text{Résoudre dans }" + (LaTeX[int]) + "\text{ l'inéquation suivante:}"
texte27: "\sin\left(" + (LaTeX[texte551]) + "\right)=" + (LaTeX[texte28]) + "\phantom{\frac{sqrt{2}}{2}}"
texte31: "\sin\left(" + (LaTeX[texte941]) + "\right)=" + (LaTeX[texte32]) + "\phantom{\frac{sqrt{2}}{2}}"
grade: score
notemax: 10
texte84: "\text{Score : }" + (LaTeX[score]) + "\text{ / }" + (LaTeX[nbexo]) + ""