銳角三角函數的幾何意義
Author: 藍邦偉  老師

$ 銳角三角函數的幾何意義 $

$ P $

$ A $

$ O $

$ B $

$ C $

$ D $

E

θ = 0.926769832808989 rad (slider from 0*° to 90*°, step 0.1*°)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.67 * Corner[1] + 0.33 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
c = Circle(O, 1)
list_1: {15*°, 30*°, 45*°, 60*°, 75*°, 105*°, 120*°, 135*°, 150*°, 165*°, 195*°, 210*°, 225*°, 240*°, 255*°, 285*°, 300*°, 315*°, 330*°, 345*°}
n_1 = 3 (slider from 0 to 5, step 1)
P: (cos(θ), sin(θ))
A: (x(P), 0)
a = Segment(P, A)
b = Segment(P, O)
d = Segment(O, A)
B = (1, 0)
α = Angle(B, O, P)
β = Angle(P, A, O)
e: x = x(B)
f = Ray(O, P)
C = Intersect(f, e)
text1: "$ sin" + (LaTeX[θ]) + "=\frac{\overline{AP}}{\overline{OP}}= \frac{" + (LaTeX[a]) + "}{1}$"
text2: "$ cos" + (LaTeX[θ]) + "=\frac{\overline{OA}}{\overline{OP}}=\frac{" + (LaTeX[d]) + "}{1} $"
g = Segment(C, B)
D = (0, 1)
h: y = y(D)
E = Intersect(h, f)
i = Segment(D, E)
γ = Angle(D, E, O)
text4: "$ cot" + (LaTeX[θ]) + "=\frac{\overline{DE}}{\overline{OD}}=\frac{" + (LaTeX[i]) + "}{1} $"
text5: "$ sec" + (LaTeX[θ]) + "=\frac{\overline{OC}}{\overline{OB}}=\frac{" + (LaTeX[Segment[O, C]]) + "}{1} $"
j = Segment(O, C)
text6: "$ csc" + (LaTeX[θ]) + " =\frac{\overline{OE}}{\overline{OD}}=\frac{" + (LaTeX[Segment[O, E]]) + "}{1}$"
n = 0 (slider from 0 to 6, step 1)
δ = Angle(C, B, O)
k = Segment(O, E)
ε = Angle(O, D, E)
F = (-1.4294557311812908, 1.4516372644996176)
text3: "$ tan" + (LaTeX[θ]) + " =\frac{\overline{BC}}{\overline{OB}}=\frac{" + (LaTeX[g]) + "}{1}$"