α

Reducció 4rt  >> 2n quadrant (β=180° + α)

2008 CGE

α = 0.7853981633974483 rad (slider from 0 to 1.5707963267948966, step 0.017453292519943295)
H' = Rotate((5.0, 0.0), α + 90.0 * °, (0.0, 0.0))
ε = Angle((5.0, 0.0), (0.0, 0.0), H')
A = (0, 0)
a = Segment((-5.0, 0.0), (5.0, 0.0))
c = Circle((0.0, 0.0), (5.0, 0.0))
k = Tangent((5.0, 0.0), c)
m = Segment(A, Intersect[Line[A, H'], k])
B = (5, 0)
F = (-5, 0)
G = (0, -5)
C = Point(c)
d = CircleArc(A, B, C)
E = Rotate((-5.0, 0.0), ε, A)
e = CircleSector((0.0, 0.0), (5.0, 0.0), H')
β = Angle(B, A, E)
f = CircleSector(A, B, E)
h = Segment(H', Intersect[OrthogonalLine[H', a], a])
g = Segment(E, Intersect[OrthogonalLine[E, a], a])
i = Segment(A, Intersect[OrthogonalLine[H', a], a])
j = Segment(A, Intersect[OrthogonalLine[E, a], a])
n = Segment(A, Intersect[Line[A, E], k])
p = Segment(B, Intersect[m, k])
b = Segment(C, G)
q = Segment(B, Intersect[n, k])
T3: "β = 180° + " + ε + " = " + (180.0 * ° + ε)
T4: "sin α = " + (h / 5.0)
T5: "cos α = " + (-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * i / 5.0)
T6: "tan α = " + (-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * p / 5.0)
T7: "sin β = - sin α = " + (-1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * 1.0 * g / 5.0)
T8: "cos β = - cos α = " + (j / 5.0)
T9: "tan β =  tan α = " + (-1.0 * 1.0 * 1.0 * p / 5.0)
texto1: ε + ""