Cercle trigonométrique
Author: Yvan Monka - m@ths et tiques 2013

-1

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

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

-\frac{1}{2}

0

\frac{1}{2}

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

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

1

Déplacer M

1

1

0

l1: {"   0  ", "\frac{ π}{6}", "\frac{ π}{4}", "\frac{π}{3}", "\frac{π}{2}", "\frac{2π}{3}", "\frac{3π}{4}", "\frac{5π}{6}", "  π"}
B1 = 2
B2 = 2
B3 = 2
B4 = 2
B5 = 2
B6 = 2
B7 = 2
B8 = 2
B9 = 2
s1 = Join({Sequence[LaTeX[Object["A" + (i)]], i, 5, 9], Sequence[LaTeX[Object["A" + (i)]], i, 8, 5, -1]})
l = Join({Sequence["-" + (Element[l1, i]), i, 8, 2, -1], l1})
c1 = Sequence(LaTeX[Object["A" + (i)]], i, 9, 1, -1)
s = Join({Sequence["-" + (Element[s1, i]), i, 8, 2, -1], s1})
c = Join({Sequence[Element[c1, i], i, 8, 2, -1], c1})
l2 = Append("α", l)
c2 = Append("cos(α)", c)
s2 = Append("sin(α)", s)
A = Intersect(xAxis, yAxis)
d = Circle(A, 1)
v: {-2.6179938779914944, -2.356194490192345, -2.0943951023931953, -1.5707963267948966, -1.0471975511965976, -0.7853981633974483, -0.5235987755982988, 0, 0.5235987755982988, 0.7853981633974483, 1.0471975511965976, 1.5707963267948966, 2.0943951023931953, 2.356194490192345, 2.6179938779914944, 3.141592653589793}
a = 5 (slider from -7 to 8, step 1)
M: (cos(Element[v, a + 8]), sin(Element[v, a + 8]))
cos: (x(M), 0)
sin: (0, y(M))
b = Segment(cos, M)
e = Segment(M, sin)
i = Segment(M, A)
tableau = LaTeX("\bgcolor{50de99}" + (TableText[{l2, c2, s2}, "lc"]))
texte5: "  " + (LaTeX[Element[l, a + 8]]) + ""
texsin: "\fgcolor{ff0000} {sin\left(  " + (LaTeX[Element[l, a + 8]]) + "\right) = " + (LaTeX[Element[s, 8 + a]]) + "}}"
"\bgcolor{30ee00}{cos(" + (LaTeX[Elément[l, a + 8]]) + ") = " + (LaTeX[Elément[c, 8 + a]]) + "" + (LaTeX[Si[f ∧ (a < 8), "\fgcolor{ff0000}{=cos(" + (Elément[l, -a + 8]) + ")}", ""]]) + "" + (LaTeX[Si[g, "\fgcolor{ff00ff}{=-cos(" + (Si[a < 0, "-", ""]) + (Elément[l, -abs(a) + 16]) + ")} ", ""]]) + "" + (LaTeX[Si[h, "\fgcolor{0000ff}{=-cos(" + (Si[a ≤ 0, Elément[l, a + 16], Elément[l, a]]) + ")}", ""]]) + "" + (LaTeX[Si[n, "=sin(" + (Si[a < -1 (4), Elément[l, -4 - a], Elément[l, 12 - a]]) + ")", ""]]) + "}": "\fgcolor{0000ff} {cos \left(    " + (LaTeX[Element[l, a + 8]]) + "\right) = " + (LaTeX[Element[c, 8 + a]]) + "}}"
B = Point(d)
C = Point(d)
u = Vector(A, B)
D = Point(u)
w = Vector(D, C)
α = Angle(B, D, M)
E = Midpoint(B, D)
F = Midpoint(M, D)
G = Midpoint(E, F)