enroulement

Enroulement sur le cercle trigonométrique

$ O $

$ M $

$ 0 $

$ \frac{\pi}{2} $

$ \pi $

$ \frac{3 \pi}{2} $

$ 2 \pi $

$ -\frac{ \pi}{2} $

$ -\pi $

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

$ -2\pi $

0

\pi

2 \pi

- 2 \pi

-\pi

\text{Nombre associé au point }  \red  M \text{ du cercle :}

O = Intersect(xAxis, yAxis)
c = Circle(O, 1)
a = 0 (slider from -48 to 48, step 1)
m: (a * pi / 24)
M: (cos(m), sin(m))
f_1 = If(a ≤ 0, 1, If[x > m, ((-(x - m)) * sin(m)) + cos(m), cos(x)])
g_1 = If(a ≤ 0, x, If[x > m, ((x - m) * cos(m)) + sin(m), sin(x)])
M_{0}: (f_1((0 * pi / 12)), g_1((0 * pi / 12)))
M_{6}: (f_1((6 * pi / 12)), g_1((6 * pi / 12)))
M_{12}: (f_1((12 * pi / 12)), g_1((12 * pi / 12)))
M_{18}: (f_1((18 * pi / 12)), g_1((18 * pi / 12)))
M_{24}: (f_1((24 * pi / 12)), g_1((24 * pi / 12)))
f_2 = If(a ≥ (0 * 0), 1, If[x < m, ((-(x - m)) * sin(m)) + cos(m), cos(x)])
g_2 = If(a ≥ (0 * 0), x, If[x < m, ((x - m) * cos(m)) + sin(m), sin(x)])
N_{6}: (f_2(((-6 * pi)) / 12), g_2(((-6 * pi)) / 12))
N_{12}: (f_2(((-12 * pi)) / 12), g_2(((-12 * pi)) / 12))
N_{18}: (f_2(((-18 * pi)) / 12), g_2(((-18 * pi)) / 12))
N_{24}: (f_2(((-24 * pi)) / 12), g_2(((-24 * pi)) / 12))
d = CircleArc(O, M_{0}, M)
e = CircleArc(O, M, M_{0})
f = Circle(O, M_{0})
g = Segment(M, M_{24})
h = Segment(M_{0}, M_{24})
i = Segment(M_{0}, N_{24})
j = Segment(M, N_{24})
k = Segment(O, M)
a' = GCD(a, 24)
D: abs(Div[a, a'])
Q: abs(Div[24, a'])
casGeneralPositif: "\frac{" + (LaTeX[D]) + " \pi}{" + (LaTeX[Q]) + "}"
PI: "\frac{\pi}{" + (LaTeX[Q]) + "}"
moinsPisurQ: "- \frac{\pi}{" + (LaTeX[Q]) + "}"
casGeneralNegatif: "- \frac{" + (LaTeX[D]) + " \pi}{" + (LaTeX[Q]) + "}"
Curve(x) = ?