正切函數的圖形與單位圓投影
Author: 藍邦偉 老師

正切函數

y=tanx

A = Point(xAxis)
c = Circle(A, 1)
B = Point(c)
θ = 0 rad (slider from 0 to 6.283185307179586, step 1.0E-4)
B' = Rotate(B, θ, A)
f(x) = tan(x)
a = Segment(B', A)
b = Ray(A, B')
C = Intersect(d, b)
e = Line(C, xAxis)
D = Intersect(f, e, (26973.7145237223, 0))
g = OrthogonalLine(D, xAxis)
E = Intersect(f, e, (28509.95333132771, 0))
h = OrthogonalLine(E, xAxis)
P: (θ, tan(θ))
i = OrthogonalLine(P, xAxis)
j = Segment(C, A)
k = Line(P, xAxis)
l = Segment(C, B)
F = Intersect(i, xAxis)
m = Segment(P, F)
G = Point(xAxis)
n = Segment(G, F)
p = Segment(A, B')
q = Segment(A, B)
u = Vector((x(Corner[1]), 0), (x(Corner[2]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
r = Segment(G, F)
H = Intersect(c, a)
s = CircleArc(A, B, H)