α

Reducció 4rt  >> 1r quadrant (β=360°- α)

2008 CGE

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)
α = 0.7853981633974483 rad (slider from 0 to 1.5707963267948966, step 0.017453292519943295)
H' = Rotate((-5.0, 0.0), 180.0 * ° - α, (0.0, 0.0))
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 = CircleSector((0.0, 0.0), (5.0, 0.0), H')
E = Rotate((5.0, 0.0), α, (0.0, 0.0))
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])
ε = Angle(a, m)
T3: "β=360° - " + α + " = " + (360.0 * ° - α)
T4: "sin α = " + (h / 5.0)
T5: "cos α = " + (i / 5.0)
T6: "tan α = " + (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 * 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 * q / 5.0)