α

cos(α)

sin(α)

cos(180°-α)

r  [180°-α]

sin(180°-α)

r [90°-α]

cos(90°-α)

sin(90°-α)

F => α
F_1 => 180 - α
F_2 => 90 - α

O = Intersect(xAxis, yAxis)
c = Circle(O, 5)
B = Intersect(c, xAxis, 2)
α = 65 (slider from 0 to 360, step 1)
F = Rotate(B, α°, O)
α_1 = Angle(B, O, F)
C = Intersect(c, xAxis, 1)
f = Line(C, B)
D = Intersect(c, yAxis, 2)
E = Intersect(c, yAxis, 1)
g = Line(D, E)
h = OrthogonalLine(F, f)
X = Intersect(f, h)
i = OrthogonalLine(F, g)
Y = Intersect(g, i)
b = Segment(F, Y)
a = Segment(F, X)
r = Segment(O, F)
K = Intersect(c, f, 1)
m = Segment(F, K)
F_1 = Rotate(K, (180 - α)°, O)
β = Angle(K, O, F_1)
j = Segment(Y, F_1)
k = Segment(F_1, O)
n = OrthogonalLine(F_1, f)
X' = Intersect(f, n)
p = Segment(F_1, X')
F_2 = Rotate(K, (90 - α)°, O)
γ = Angle(K, O, F_2)
l = Segment(O, F_2)
q = OrthogonalLine(F_2, g)
Y' = Intersect(g, q)
s = Segment(F_2, Y')
t = OrthogonalLine(F_2, f)
X'' = Intersect(f, t)
a_1 = Segment(X'', F_2)