α

β

α

1

cos(β)

sen(β)

sen(α+β)=

=\overline{EC}+\overline{CF}

senα=\overline{EC}/cosβ⇒\overline{EC}=senαcosβ

cosα=\overline{CF}/senβ⇒\overline{CF}=cosαsenβ

sen(\alpha+\beta)=senαcosβ+cosαsenβ

\overline{DA}

FÓRMULAS TRIGONOMÉTRICAS PARA LA SUMA DE ÁNGULOS

sen[90°+(α+β)]=sen[(90°+α)+β]=sen(90°+α)cosβ+cos(90°+α)senβ

cos(α+β)=

cos(α+β)=cosαcosβ-senαsenβ

=\overline{EF}

tag(α+β)=\frac{sen(α+β)}{cos(α+β)}=\frac{senαcosβ+cosαsenβ}{cosαcosβ-senαsenβ}=

\frac{\frac{senαcosβ+cosαsenβ}{cos\alpha cos\beta}}{\frac{cosαcosβ-senαsenβ}{cos\alpha cos\beta}}

tag(α+β)=\frac{tagα+tagβ}{1-tagαtagβ}

=\frac{\frac{senα}{cosα}+\frac{sen\beta}{cos\beta}}{1-\frac{sen\alpha}{cos\alpha}\frac{sen\beta}{cos\beta}}

α = 0.4363323129985824 rad (slider from 0 to 45*°, step 0.017453292519943295)
β = 0.5061454830783556 rad (slider from 0 to 45*°, step 0.017453292519943295)
A_1 = (2, 0)
B = (0, 0)
A' = Rotate(A_1, α, B)
γ = Angle(A_1, B, A')
A = Rotate(A', β, B)
δ = Angle(A', B, A)
a = Ray(B, A')
b = Segment(B, A)
c = OrthogonalLine(A, a)
C = Intersect(a, c)
d = Segment(C, A)
ε = Angle(A, C, B)
e = OrthogonalLine(C, xAxis)
f = OrthogonalLine(A, xAxis)
D = Intersect(f, xAxis)
E = Intersect(e, xAxis)
g = OrthogonalLine(A, f)
F = Intersect(g, e)
h = Segment(A, D)
i = Segment(F, E)
j = Segment(A, F)
ζ = Angle(F, C, A)
G = Point(b)
H = Point(a)
I = Point(d)
k = Segment(B, C)
J = Intersect(b, k)
polígono1, a_1, j_1, d_1 = Polygon(J, D, A)
polígono2, e_1, j_2, c_1 = Polygon(J, C, E)
polígono3, c_2, a_2, f_1 = Polygon(A, F, C)
PASO = 15 (slider from 1 to 15, step 1)