A la découverte des propriétés des fonctions cosinus et sinus

Placer sur le cercle trigonométrique le point N tel que (AON)=-α

Placer sur le cercle trigonométrique le point P tel que (AOP)= π+α

Placer sur le cercle trigonométrique le point Q tel que (AOQ)=π-α

Cliquer pour 

Symétrie M N par rapport à OA

Symétrie M P

Symétrie M Q par rapport à OB

Placer sur le cercle trigonomètrique le point R tel que (AOR) = π/2-α 

Placer les points images des réels π/2-α et π/2+α 

Placer sur le cercle trigonométrique le point S tel que (AOS) = π/2 + α 

Symétrie N P par rapport à OB

Symétrie Q P par rapport à OA

Etude 1

Etude 1

Etude 2

Etude 2

sin(α)=0.6092

O = Intersect(xAxis, yAxis)
c = Circle(O, 1.0)
α = 0.786 (slider from 0 to 1.5707963267948966, step 0.131)
A = Point(c)
B = Point(c)
M: (cos(α), sin(α))
b = Segment(O, M)
d = OrthogonalLine(M, xAxis)
N: (cos(α), sin(-(α)))
e = Segment(O, N)
P: (cos(α + 3.141592653589793), sin(α + 3.141592653589793))
f_2 = Segment(O, P)
Q: (cos(3.141592653589793 - α), sin(3.141592653589793 - α))
g = Segment(Q, O)
A' = Point(c)
δ = Angle(A, O, Q)
γ = Angle(P, O, A)
h = OrthogonalLine(Q, yAxis)
i_1 = OrthogonalLine(P, yAxis)
j = OrthogonalLine(M, xAxis)
k = OrthogonalLine(Q, xAxis)
l = Segment(Q, M)
m_1 = Segment(M, N)
n_1 = Segment(N, P)
p_1 = Segment(P, Q)
J = Intersect(l, yAxis)
K = Intersect(p_1, xAxis)
L = Intersect(n_1, yAxis)
I = Intersect(m_1, xAxis)
q = false
p = false
β = Angle(N, O, A)
α_1 = Angle(A, O, M)
m = false
i = false
R: (cos(3.141592653589793 / 2.0 - α), sin(3.141592653589793 / 2.0 - α))
a = Segment(O, R)
ε = Angle(A, O, R)
S: (cos(3.141592653589793 / 2.0 + α), sin(3.141592653589793 / 2.0 + α))
s_1 = Segment(S, O)
t = OrthogonalLine(R, xAxis)
a_1 = OrthogonalLine(M, xAxis)
b_1 = OrthogonalLine(R, yAxis)
c_1 = OrthogonalLine(M, yAxis)
d_1 = OrthogonalLine(R, xAxis)
e_1 = OrthogonalLine(M, xAxis)
C = Intersect(b_1, yAxis)
D = Intersect(c_1, yAxis)
E = Intersect(xAxis, d_1)
F = Intersect(xAxis, e_1)
f_1 = OrthogonalLine(S, xAxis)
G: (cos(3.141592653589793 / 2.0 + α), 0.0)
g_1 = Segment(S, G)
h_1 = Segment(R, E)
j_1 = Segment(M, F)
k_1 = Segment(R, C)
l_1 = Segment(M, D)
q_1 = Segment(S, C)
r = false
H = Intersect(h_1, xAxis)
T = Intersect(j_1, xAxis)
distanceOH = Distance(O, H)
distanceOT = Distance(O, T)
TexteOT: Name[O] + (Name[T]) + " \, = \, " + distanceOT
distanceOD = Distance(O, D)
TexteOD: Name[O] + (Name[D]) + " \, = \, " + distanceOD
distanceOC = Distance(O, C)
s = false
V = Intersect(q_1, yAxis)
texte13: "sin(π/2 -α)=" + (Distance[O, C])
texte15: "cos(π/2-α)=" + (Distance[O, H])
texte14: "sin(α)=" + (Distance[O, D])
texte18: "cos(α)=" + (Distance[O, T])
TexteOH: Name[O] + (Name[H]) + " \, = \, " + distanceOH
TexteOC: Name[O] + (Name[C]) + " \, = \, " + distanceOC
texte12: "OT=" + (Distance[O, T])
texte19: "OD=" + (Distance[O, D])
r_1 = Segment(P, N)
t_1 = Segment(Q, P)
n = false
a_2 = Segment(D, Q)
v = false
w = false
z = false
u = true
f = true
ζ = Angle(A, O, S)
o = -0.60916
texte27: "OG=-" + (Distance[O, G])
texte30: "sin(π/2 +α)= " + (Distance[O, V])
texte28: "cos(π/2+α)= -" + (Distance[O, G])
texte17: "cos(α)=" + (Distance[O, T])
texte31: "sin(α)=" + (Distance[O, D])
texte29: "OV=" + (Distance[O, V])