Use this slider

UNIT CIRCLE
for exploring

α

A = Intersect(xAxis, yAxis)
c = Circle(A, 1)
B, C = Intersect(c, xAxis)
a = OrthogonalLine(C, xAxis)
b = OrthogonalLine(B, xAxis)
α = 0.5235987755982988 rad (slider from -720° to 720°, step °)
P: (cos(α), sin(α))
d = Ray(A, P)
e = OrthogonalLine(P, xAxis)
D = Intersect(e, xAxis)
E = Intersect(d, a)
r: (π * α / (180°))
f = Segment(A, D)
g = Segment(D, P)
h = Segment(C, E)
l = 0.8660254037844386
m = 0.5
n = 0.5773502691896258
F = Intersect(d, b)
p = Segment(B, F)
text1: "Point P = " + P + "
     x = " + l + "
     y = " + m + "
     y/x = " + n + ""
text3: "Important segment lengths:
     AD = " + f + " 
     PD = " + g + "
     CE = " + h + "
     BF = " + p + "
     "
k = CircleArc(A, C, P)
text2: "to create central angle α (∠PAD in standard position).
Currently, α = " + α + "
Length of arc CP = " + k + ""
β = Angle(D, A, P)