2D 座標架
Author: 藍邦偉  老師

$ O $

$θ=%v$

$n=%v$

$ 180°±θ與360°±θ的三角函數值 $

$ A $

$ P $

$P $

$ P $

$ P $

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: 0.6 * Corner[1] + 0.4 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1_1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
c_1 = Circle((0, 0), 1)
θ = 0 rad (slider from 0*° to 90*°, step 0.017453292519943295)
A = Rotate((1, 0), θ)
r = Segment(O, A)
A_1: (x(A), 0)
b = Segment(A, A_1)
C = Rotate((1, 0), 180° + θ)
B = Rotate((1, 0), 180° - θ)
D = Rotate((1, 0), -θ)
E = Rotate((1, 0), θ)
r_1 = Segment(O, B)
r_2 = Segment(O, C)
r_3 = Segment(O, D)
r_4 = Segment(O, E)
B_1: (x(B), 0)
C_1: (x(D), 0)
a = Segment(B_1, B)
d = Segment(D, C_1)
n = 1 (slider from 1 to 4, step 1)
f = Segment(O + (0, 0.01), A_1 + (0, 0.01))
α = Angle(B, B_1, O)
β = Angle(A, A_1, O)
δ = Angle(O, C_1, D)
f_1 = Segment(O, A_1)
text2: "$ A\;" + (LaTeX[A]) + "$
$P\;" + (LaTeX[If[n ≟ 1, B, If[n ≟ 2, C, If[n ≟ 3, D, E]]]]) + " $"
poly, a_1, o, a_2 = Polygon(O, A, A_1)
poly2, j, k, l = Polygon(O, C, B_1)
poly1, b_1, b_2, o_2 = Polygon(B, O, B_1)
poly3, d_1, o_3, c_4 = Polygon(O, C_1, D)
text3: "$ \left\lbrace \begin{array}{ll} sinθ=sin" + (LaTeX[θ]) + "=\frac{" + (LaTeX[y(A)]) + "}{1} \\ cosθ=cos" + (LaTeX[θ]) + "=\frac{" + (LaTeX[x(A)]) + "}{1} \\ tanθ=tan" + (LaTeX[θ]) + "=\frac{" + (LaTeX[y(A)]) + "}{" + (LaTeX[x(A)]) + "} \end{array}  \right.\  $"
poly4, m, p, q = Polygon(A_1, O, E)
text1: "$ " + (LaTeX[If[n ≟ 1, "180°-θ", If[n ≟ 2, "180°+θ", If[n ≟ 3, "-θ=360°-θ", "360°+θ"]]]]) + " $"
text4: "$ \left\lbrace \begin{array}{ll} sin(180°-θ)=sin" + (LaTeX[180° - θ]) + "=\frac{" + (LaTeX[y(B)]) + "}{1} \\ cos(180°-θ)=cos" + (LaTeX[180° - θ]) + "=\frac{" + (LaTeX[x(B)]) + "}{1} \\ tan(180°-θ)=tan" + (LaTeX[180° - θ]) + "=\frac{" + (LaTeX[x(B)]) + "}{" + (LaTeX[y(B)]) + "} \end{array}  \right.\  $"
h = Segment(O, B_1)
c = Segment(B_1, C)
g = Segment(O, B_1)
γ = Angle(C, B_1, O)
i = Segment(O - (0, 0.01), A_1 - (0, 0.01))
e = Segment(A_1, E)
ε = Angle(E, A_1, O)
text5: "$ \left\lbrace  \begin{array}{ll} sin(180°+θ)=sin" + (LaTeX[180° + θ]) + "=\frac{" + (LaTeX[y(C)]) + "}{1} \\ cos(180°+θ)=cos" + (LaTeX[θ + 180°]) + "=\frac{" + (LaTeX[x(C)]) + "}{1} \\ tan(180°+θ)=tan" + (LaTeX[θ + 180°]) + "=\frac{" + (LaTeX[y(C)]) + "}{" + (LaTeX[x(C)]) + "} \end{array} \right.\  $"
text6: "$ \left\lbrace\begin{array}{ll} sin(-θ)=sin" + (LaTeX[-θ]) + "=\frac{" + (LaTeX[y(D)]) + "}{1} \\ cos(-θ)=cos" + (LaTeX[-θ]) + "=\frac{" + (LaTeX[x(D)]) + "}{1} \\ tan(-θ)=tan" + (LaTeX[-θ]) + "=\frac{" + (LaTeX[y(D)]) + "}{" + (LaTeX[x(D)]) + "} \end{array}   \right.\  $"
text7: "$ \left\lbrace\begin{array}{ll} sin(360°+θ)=sin" + (LaTeX[360° + θ]) + "=\frac{" + (LaTeX[y(E)]) + "}{1} \\ cos(360°+θ)=cos" + (LaTeX[360° + θ]) + "=\frac{" + (LaTeX[x(E)]) + "}{1} \\ tan(360°+θ)=tan" + (LaTeX[θ + 360°]) + "=\frac{" + (LaTeX[y(E)]) + "}{" + (LaTeX[x(E)]) + "} \end{array}   \right.\ $"