Sinus i cosinus d'angles de diferents quadrants
Author: Pep Bujosa
Date: 16 Octubre 2013

Exploreu les realcions entre el sinus i el cosinus d'angles de diferents quadrants. Fixeu-vos amb els valors exactes d'alguns angles (Valors especials)

Valors especials

α = 0.9599310885968813 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
A = Intersect(xAxis, yAxis)
c = Circle(A, 1)
B, C = Intersect(c, xAxis)
C' = Rotate(C, α, A)
a = OrthogonalLine(C', xAxis)
E = Intersect(a, xAxis)
Polígon1, e, a_1, c' = Polygon(A, C', E)
h = OrthogonalLine(C', a_1)
F = Intersect(c, h, 2)
i = OrthogonalLine(F, xAxis)
G = Intersect(i, xAxis)
γ = Angle(G, A, F)
γ1 = If(Defined[γ], γ, 0*°)
E' = Mirror(E, xAxis)
m = Ray(C', A)
H, I = Intersect(c, m)
n = OrthogonalLine(I, xAxis)
J = Intersect(n, xAxis)
δ = Angle(J, A, I)
δ1 = If(Defined[δ], δ, 0*°)
C'' = Mirror(C', xAxis)
ε = Angle(E', A, C'')
ε1 = If(Defined[ε], ε, 0*°)
β = Angle(C, A, C')
b = OrthogonalLine(C', yAxis)
D = Intersect(b, yAxis)
d = Segment(A, E)
f = Segment(C', E)
g = Segment(C', D)
Polígon2, g_1, f_1, a_2 = Polygon(F, A, G)
j = Segment(A, F)
k = Segment(F, G)
l = Segment(A, G)
Polígon3, j_1, i_1, a_3 = Polygon(I, A, J)
p = Segment(A, J)
q = Segment(I, J)
r = Segment(I, A)
A' = Mirror(A, xAxis)
Polígon1', e', a', c'' = Polygon(A', C'', E')
s = Segment(C'', E')
t = Segment(E', A)
b_1 = Segment(C'', A)
text1: "sin " + α + " = " + (sin(α)) + ""
text2: "cos " + α + " = " + (cos(α)) + ""
sγ: s * γ
c_1 = Segment(C', F)
aa = If(α ≤ 90°, α, If[α ≤ 180°, γ1, If[α ≤ 270°, δ1, ε1]])
text3: "sin " + aa + " = " + (sin(aa)) + ""
text4: "cos " + aa + " = " + (cos(aa)) + ""
d_1 = OrthogonalLine(C, xAxis)
e_1 = Ray(A, F)
h_1 = Ray(C', A)
sα: s * α
textsin = SurdText(sin(α))
textcos = SurdText(cos(α))
text5: "sin(" + (LaTeX[α]) + ") = " + (LaTeX[textsin]) + ""
text6: "cos(" + (LaTeX[α]) + ") = " + (LaTeX[textcos]) + ""
o = false