2D 座標架
Author: 藍邦偉  老師
Date: 21 10 月 2013

內插法求正弦函數的近似值

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x

Q_2: 0.6 * Corner[1] + 0.4 * 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])
s = 0 (slider from 0 to 3, step 1)
α = 0.8726646259971648 rad (slider from 0 to 89*°, step 0.017453292519943295)
n = 36 (slider from 1 to 59, step 1)
A = (4.272154058973239, -1.600678275592357)
B: A + (3, 0)
D: A + (0, 6)
C: B + D - A
a = PolyLine(A, B, C, D, A)
P: A + (0, 0.6 * Mod[n, 10])
q: floor(n / 10)
textb: "" + (LaTeX[round(10000 * sin(α + (q / 6)°)) / 10000]) + ""
texta: "" + (LaTeX[α]) + "" + (LaTeX[If[q ≟ 0, "", "" + (10 * q) + "'"]]) + ""
textd: "" + (LaTeX[If[n ≥ 50, α + °, α]]) + "" + (LaTeX[If[n ≥ 50, "", "" + (10 * q + 10) + "'"]]) + ""
R: (x(B), y(P))
c = Segment(P, R)
textp: "" + (LaTeX[α]) + "" + (LaTeX[If[n ≟ 0, "", "" + n + "'"]]) + ""
textc: "" + (LaTeX[round(10000 * sin(α + ((q + 1) / 6)°)) / 10000]) + ""
text3: "⇒sin" + (LaTeX[α]) + "" + (LaTeX[If[n ≟ 0, "", n + "\;'"]]) + "=" + (LaTeX[sin(α + (q / 6)°) + (n - 10 * q) / 10 * (sin(α + ((q + 1) / 6)°) - sin(α + (q / 6)°))]) + ""
text1: "\frac{x-\fgcolor{red}{" + (LaTeX[textb]) + "}}\fgcolor{blue}{{" + (LaTeX[textc]) + "-" + (LaTeX[textb]) + "}}=\fgcolor{green}{\frac{" + (LaTeX[textp]) + "-" + (LaTeX[texta]) + "}{" + (LaTeX[textd]) + "-" + (LaTeX[texta]) + "}}"
text2: "⇒x=\fgcolor{red}{" + (LaTeX[textb]) + "}+\fgcolor{green}{\frac{" + (LaTeX[n - 10 * q]) + "}{10}}×\fgcolor{blue}{" + (LaTeX[sin(α + ((q + 1) / 6)°) - sin(α + (q / 6)°)]) + "{"
d = LineBisector(D, A)
e = LineBisector(P, A)
E, F = Intersect(d, a)
G, H = Intersect(e, a)
f = CircleArc(F, D, A)
g = CircleArc(H, P, A)
h = CircleArc(E, B, C)
k = CircleArc(G, B, R)
text0: "$已知：\;sin" + (LaTeX[α]) + "" + (LaTeX[If[q ≟ 0, "", "" + (10 * q) + "'"]]) + "=" + (LaTeX[sin(α + (q / 6)°)]) + "，$
$sin" + (LaTeX[If[n ≥ 50, α + °, α]]) + "" + (LaTeX[If[n ≥ 50, "", "" + (10 * q + 10) + "'"]]) + "=" + (LaTeX[sin(α + ((q + 1) / 6)°)]) + "，$
$試求：\;sin" + (LaTeX[α]) + "" + (LaTeX[If[n ≟ 0, "", n + "\;'"]]) + "之值$"
K: Corner[4] - (-0.1, 2.2)
a_1, b, i, j, l = Polygon(K + (0, -0.1), K + (5.5, -0.1), K + (5.5, -0.5), K + (0, -0.5))
a_2, m, p, r, t = Polygon(K + (0, -0.62), K + (5.5, -0.62), K + (5.5, -1), K + (0, -1))
a_4, b_1, c_1, d_1, e_1 = Polygon(K + (3, -0.62), K + (5.5, -0.62), K + (5.5, -1), K + (3, -1))
a_3, f_1, g_1, h_1, i_1 = Polygon(K + (3, -0.5), K + (5.5, -0.5), K + (5.5, -0.1), K + (3, -0.1))
text11: "\frac{x-{ " + (LaTeX[textb]) + "}}{" + (LaTeX[textc]) + " -" + (LaTeX[textb]) + " }=\frac{ " + (LaTeX[textp]) + "- " + (LaTeX[texta]) + "}{" + (LaTeX[textd]) + " -" + (LaTeX[texta]) + " }"
poly2, a_5, b_2, r_1, p_1 = Polygon(A, B, R, P)