特別角的三角函數(5)
Author: 藍邦偉  老師

1

1

x

36°

72°

72°

x

1-x

36°

 \frac{ x }{2 } 

特別角的正餘弦三角函數值:36°與54°

作一個單位圓

考慮單位圓的內接正十邊形

h

y

H

x

54°

O: 0.5 * Corner[1.0] + 0.5 * Corner[3.0]
r: 0.4 * (y(Corner[4.0]) - y(Corner[1.0]))
c = Circle(O, r)
n = 6 (slider from 0 to 8, step 1)
A_1 = (-2.459999999999999, -1.6199999999999994)
b: y = y(A_1)
A: O + (r * cos(252.0°), r * sin(252.0°))
l = Segment(O, A)
B: O + (r * cos(288.0°), r * sin(288.0°))
C: O + (r * cos((-(36.0))°), r * sin((-(36.0))°))
D: O + (r, 0.0)
E: O + (r * cos(36.0°), r * sin(36.0°))
F: O + (r * cos(72.0°), r * sin(72.0°))
G: O + (r * cos(108.0°), r * sin(108.0°))
H: O + (r * cos(144.0°), r * sin(144.0°))
I: O + (-(r), 0.0)
J: O + (r * cos(216.0°), r * sin(216.0°))
a = Segment(A, B)
d = Segment(B, C)
e = Segment(C, D)
f = Segment(D, E)
g = Segment(E, F)
h = Segment(F, G)
i = Segment(G, H)
j = Segment(H, I)
k = Segment(I, J)
m = Segment(J, A)
p = Segment(O, B)
q = AngularBisector(B, A, O)
K = Intersect(p, q)
s = Segment(A, K)
M = Midpoint(A, B)
t = Segment(O, M)
a_1 = OrthogonalLine(A, p)
L = Intersect(a_1, p)
b_1 = Segment(A, L)
α = Angle(A, M, O)
β = Angle(O, L, A)