Cosinus:activité\ de\ découverte

α

A

B

C

α

E

F

G

α

MathsEnClair.com

α = 0.593411945678072 rad (slider from 5*° to 85*°, step 1*°)
AB = 1.9 (slider from 0 to 3, step 0.1)
EF = 4.1 (slider from 0 to 8, step 0.1)
A = (-3.02, 0.44)
B = Point(Circle[A, abs(AB)])
a = Segment(A, B)
b = OrthogonalLine(A, a)
E = (1.86, 0.44)
F = Point(Circle[E, abs(EF)])
c = Segment(E, F)
A' = Rotate(A, (-α), B)
β = Angle(A', B, A)
d = Ray(B, A')
C = Intersect(b, d)
e = Segment(A, B)
f = Segment(B, C)
g = Segment(C, A)
γ = Angle(B, A, C)
h = OrthogonalLine(E, c)
E' = Rotate(E, (-α), F)
δ = Angle(E', F, E)
i = Ray(F, E')
G = Intersect(h, i)
ε = Angle(F, E, G)
D = Midpoint(A, B)
BC = Distance(B, C)
FG = Distance(F, G)
texte8: "adj\approx" + (LaTeX[AB]) + ""
H = Midpoint(B, C)
texte9: "hyp \approx" + (LaTeX[BC]) + ""
j = Segment(E, G)
k = Segment(F, G)
I = Midpoint(E, F)
texte10: "adj\approx" + (LaTeX[EF]) + ""
J = Midpoint(G, F)
texte11: "hyp\approx" + (LaTeX[FG]) + ""
A'': A - (0, 2)
q_1: AB / BC
q_2: EF / FG
E'': E - (0, 2)
texte12: "\begin{tabular}{c c}
\frac{adj}{hyp}\\ \ \\
\frac{BA}{BC}=\frac{" + (LaTeX[AB]) + "}{" + (LaTeX[BC]) + "}\\ \ \\
\frac {BA}{BC}\approx" + (LaTeX[q_1]) + "\\
\end {tabular}"
texte13: "\begin{tabular}{c c}\\
\frac {adj}{hyp}\\ \ \\
\frac{EF}{FG}=\frac{" + (LaTeX[EF]) + "}{" + (LaTeX[FG]) + "}\\ \ \\
\frac {EF}{FG}\approx" + (LaTeX[q_2]) + "\\
\end {tabular}"