α/2

\cos \, \frac{\alpha}{2}=

\sin \, \frac{\alpha}{2}= 

\tan \, \frac{\alpha}{2}= 

-

\sqrt{\frac{1+\cos \alpha}{2}}=

-

-

\sqrt{\frac{1-\cos \alpha}{1+\cos \alpha}}=

-

-

A = Intersect(xAxis, yAxis)
B = Point(xAxis)
c = Circle(A, B)
C = Point(c)
α = Angle(B, A, C)
a = Segment(A, C)
B' = Rotate(B, α / 2, A)
β = Angle(B, A, B')
b = Segment(A, B')
sa: y(C)
ca: x(C)
s2a: y(B')
c2a: x(B')
d = Tangent(B, c)
e = Line(A, C)
D = Intersect(e, d)
f = Line(A, B')
F = Intersect(d, f)
g = Segment(B, D)
texto4: "" + (LaTeX[c2a]) + ""
texto5: "" + (LaTeX[c2a]) + ""
texto6: "" + (LaTeX[s2a]) + ""
texto7: "" + (LaTeX[s2a]) + ""
ta: y(D)
t2a: y(F)
texto8: "" + (LaTeX[t2a]) + ""
texto9: "" + (LaTeX[t2a]) + ""
texto10: "α=" + (LaTeX[α]) + ""
texto11: "\frac{\alpha}{2}=" + (LaTeX[β]) + ""
texto1: "\sqrt{\frac{1-\cos \alpha}{2}}=\sqrt{\frac{1-(" + (LaTeX[ca]) + ")}{2}}="
texto13: "\sqrt{\frac{1+(" + (LaTeX[ca]) + ")}{2}}="
texto16: "\sqrt{\frac{1-(" + (LaTeX[ca]) + ")}{1+(" + (LaTeX[ca]) + ")}}="
h = Segment(B, F)
i = OrthogonalLine(B', xAxis)
j = OrthogonalLine(B', yAxis)
k = OrthogonalLine(C, xAxis)
l = OrthogonalLine(C, yAxis)
m = OrthogonalLine(A, xAxis)
E = Intersect(l, m)
n = Line(A, B)
G = Intersect(k, n)
H = Intersect(i, n)
p = Segment(E, C)
q = Segment(C, G)
r = Segment(B', H)
I = Intersect(j, m)
s = Segment(I, B')