廣義三角函數的定義
Author: 藍邦偉　老師

α

三角函數的定義

sinx

cosx

tanx

cotx

secx

cscx

A = Intersect(xAxis, yAxis)
c = Circle(A, 1.0)
α = 3.944444109507185 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
B_1 = Intersect(c, xAxis, 2.0)
B = Rotate(B_1, α, A)
β = Angle(B_1, A, B)
a_3 = Ray(A, B)
C: (x(B), 0.0)
poly1, c_1, a_1, b' = Polygon(A, B, C)
D = (1, 0)
b: x = x(D)
E = Intersect(a_3, b)
poly2, d, a_2, e = Polygon(A, E, D)
文字22: "tan " + α + " = \frac{" + a_2 + " }{" + e + " }=" + (tan(α))
F = Intersect(a_3, j)
G = (0, 1)
k = Segment(G, F)
文字23: "cos " + α + "= \frac{" + b' + " }{" + c_1 + " }=" + (cos(α))
文字21: "sin " + α + "= \frac{" + a_1 + "  }{" + c_1 + " } =" + (sin(α))
a = Segment(A, C)
u = Vector((x(Corner[1.0]), 0.0), (x(Corner[3.0]), 0.0))
v = Vector((0.0, y(Corner[1.0])), (0.0, y(Corner[3.0])))
D_1 = (-1, 0)
l = OrthogonalLine(D_1, u)
H = Intersect(l, a_3)
l_1 = Segment(A, F)
文字3: "sec" + α + "=  \frac{" + l_1 + " }{1 } =" + l_1
l_2 = Segment(A, E)
文字4: "csc" + α + "= \frac{ " + l_2 + " }{1 }=" + l_2
p = Segment(H, D_1)
文字7: "tan" + α + "= \frac{ -" + p + " }{1 }=-" + p
q = Segment(A, F)
文字8: "cot" + α + "=- \frac{" + q + " }{1 }=-" + q
文字9: "sec" + α + "=- \frac{ " + k + " }{ 1} =-" + k
l_3 = Segment(A, H)
文字10: "csc" + α + "= \frac{" + l_3 + "}{1 }=" + l_3
文字11: "sin" + α + "=- \frac{ " + a_1 + " }{1 }=-" + a_1
文字2: "cot" + α + "= \frac{ " + k + " }{1 }= " + k
文字13: "tan" + α + "= \frac{ " + p + " }{1 }=" + p
G_1 = (0, -1)
f = Line(G_1, u)
I = Intersect(f, a_3)
g = Segment(I, G_1)
文字14: "cot" + α + "= \frac{ " + g + " }{1 }=" + g
文字15: "sec" + α + "=- \frac{ " + p + " }{1 }=-" + p
k_2 = Segment(A, I)
文字16: "csc" + α + "=- \frac{ " + k_2 + " }{1 }=-" + k_2
文字17: "sin" + α + "=- \frac{ " + a_1 + " }{1 }=-" + a_1
i = true
文字18: "cos" + α + "= \frac{ " + a + " }{1 }=" + a
m = true
n = true
文字6: "tan" + α + "=- \frac{" + a_2 + " }{1 }=-" + a_2
o = true
文字12: "cot" + α + "= - \frac{" + g + "  }{1 }=-" + g
r = true
文字19: "sec" + α + "= \frac{ " + d + " }{1 }=" + d
s = true
文字20: "csc" + α + "= -\frac{ " + a_2 + " }{1 }=-" + a_2
T_1 = Corner(1.0)
T_4 = Corner(4.0)
T_2: (7.0 * Corner[1.0] + 3.0 * Corner[2.0]) / 10.0
T_3: (7.0 * Corner[4.0] + 3.0 * Corner[3.0]) / 10.0
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)