廣義三角函數的幾何意義(2)
Author: 藍邦偉 老師
Date: 1 1 月 2013

y=cotx,y=secx,y=cscx圖形的幾何意義

cotθ

secθ

cscθ

$ 廣義三角函數的幾何意義(2) $

$θ$

$θ$

1

2

3

$ cotθ $

$ secθ $

$ cscθ $

$ cotθ $

$ cotθ $

$ secθ $

$ secθ $

$ cscθ $

A = Intersect(xAxis, yAxis)
c = Circle(A, 1)
B = Point(c)
θ = 0.06283185307179587 rad (slider from 0*° to 6.283185307179586, step 0.1*°)
B' = Rotate(B, θ, A)
a = Ray(A, B')
d = OrthogonalLine(B, xAxis)
D = Intersect(a, d)
E = Intersect(e, a)
F = Intersect(xAxis, e)
α = Angle(B, A, B')
G, H = Intersect(c, yAxis)
f = Line(G, xAxis)
I = Intersect(a, f)
cotθ_1 = Segment(G, I)
J = Intersect(g, a)
cotθ = Segment(J, H)
secθ_1 = Segment(D, A)
cscθ_1 = Segment(A, I)
secθ = Segment(A, E)
cscθ = Segment(A, J)
b = Segment(D, B)
h = Segment(E, F)
β = Angle((1, 0), (0, 0), B')
γ = Angle(G, I, A)
i = true
j = false
k = false
C = Intersect(cotθ_1, cscθ_1)
K = Point(cotθ_1)
L = Point(secθ_1)
poly1, l, s, t = Polygon(A, B, D)
poly2, a_1, k_2, c_2 = Polygon(K, C, A)
poly3, h_1, a_2, j_1 = Polygon(A, J, H)
M = Point(b)
poly4, d_1, l_1, m = Polygon(L, M, D)
N = Point(secθ)
O = Point(h)
P = Point(secθ)
poly5, n, p, b_1 = Polygon(O, A, F)
poly6, f_1, p_1, o_1 = Polygon(P, O, F)
q = Segment(K, C)
r = Segment(J, H)