三角函數表
Author: 藍邦偉 老師

三角函數表:

顯示:控制滑桿

銳角三角函數的定義:

α = 1.1693705988362009 rad (slider from 0 to 1.5707963267948966, step 0.017453292519943295)
s = 0.3 (slider from 0.1 to 0.5, step 0.05)
k = 2 (slider from 1 to 5, step 1)
o: α / ° + k - 90.0
A = (3.503437209302333, 3.4637255813953463)
β = 20 (slider from 0 to 50, step 10)
list1 = Sequence(A + (0.0, s * i), i, -6.0 * k, 6.0 * k)
b_1 = Segment(A, A + (11.0, 0.0))
i = Segment(A + (0.0, -(6.0) * s * k - s), A + (0.0, 6.0 * s * k + s + 0.5))
e = Segment(A + (2.0, -(6.0) * s * k - s), A + (2.0, 6.0 * s * k + s + 0.5))
文字1 = Text("角度", A + (0.7, 6.0 * s * k + 0.5))
list3 = Sequence(Text["" + (Mod[6.0 * k - i, 6.0] * 10.0) + (If[Mod[6.0 * k - i, 6.0] ≟ 0.0, "0'", "'"]), A + (1.0, s * i - 0.1)], i, -(6.0 * k), 6.0 * k)
多邊形1, l, m, n, p = Polygon(A + (0.0, -(β - 5.0) / 10.0 * s), A + (8.0, -(β - 5.0) / 10.0 * s), A + (8.0, -(β + 5.0) / 10.0 * s), A + (0.0, -(β + 5.0) / 10.0 * s))
list2 = Sequence(Text["" + (α - i°), A + (0.5, s * 6.0 * i - 0.1)], i, -(k), k)
文字5: "現在角度θ=" + α + β + (If[β ≟ 0.0, "0'", "'"])
多邊形2, b_2, q, r, t = Polygon(A + (0.0, -(6.0) * s * k + 6.0 * If[o > 0.0, o] * s - 0.5 * s), A + (11.0, -(6.0) * s * k + 6.0 * If[o > 0.0, o] * s - 0.5 * s), A + (11.0, -(6.0) * s * k - s), A + (0.0, -(6.0) * s * k - s))
u: α / ° - k
多邊形3, a_1, c_1, d_1, e_1 = Polygon(A + (0.0, 6.0 * s * k + 6.0 * If[u < 0.0, u] * s + 0.5 * s), A + (11.0, 6.0 * s * k + 6.0 * If[u < 0.0, u] * s + 0.5 * s), A + (11.0, 6.0 * s * k + s), A + (0.0, 6.0 * s * k + s))
a_2 = false
f = Segment(A + (4.0, -(6.0) * s * k - s), A + (4.0, 6.0 * s * k + s + 0.5))
g = Segment(A + (6.0, -(6.0) * s * k - s), A + (6.0, 6.0 * s * k + s + 0.5))
list4 = Sequence(Text[floor(sin(α - (i / 6.0)°)) + If[floor(10000.0 * sin(α - (i / 6.0)°)) - 10000.0 * floor(sin(α - (i / 6.0)°)) > 1000.0, "." + (floor(10000.0 * sin(α - (i / 6.0)°)) - 10000.0 * floor(sin(α - (i / 6.0)°))), If[floor(10000.0 * sin(α - (i / 6.0)°)) - 10000.0 * floor(sin(α - (i / 6.0)°)) > 100.0, ".0" + (floor(10000.0 * sin(α - (i / 6.0)°)) - 10000.0 * floor(sin(α - (i / 6.0)°))), If[floor(10000.0 * sin(α - (i / 6.0)°)) - 10000.0 * floor(sin(α - (i / 6.0)°)) > 10.0, ".00" + (floor(10000.0 * sin(α - (i / 6.0)°)) - 10000.0 * floor(sin(α - (i / 6.0)°))), ".0000"]]], A + (2.6, s * i - 0.1)], i, -6.0 * k, 6.0 * k)
文字2 = Text("sin", A + (2.8, 6.0 * s * k + 0.5))
文字3 = Text("cos", A + (4.8, 6.0 * s * k + 0.5))
list5 = Sequence(Text[floor(cos(α - (i / 6.0)°)) + If[floor(10000.0 * cos(α - (i / 6.0)°)) - 10000.0 * floor(cos(α - (i / 6.0)°)) > 1000.0, "." + (floor(10000.0 * cos(α - (i / 6.0)°)) - 10000.0 * floor(cos(α - (i / 6.0)°))), If[floor(10000.0 * cos(α - (i / 6.0)°)) - 10000.0 * floor(cos(α - (i / 6.0)°)) > 100.0, ".0" + (floor(10000.0 * cos(α - (i / 6.0)°)) - 10000.0 * floor(cos(α - (i / 6.0)°))), If[floor(10000.0 * cos(α - (i / 6.0)°)) - 10000.0 * floor(cos(α - (i / 6.0)°)) > 10.0, ".00" + (floor(10000.0 * cos(α - (i / 6.0)°)) - 10000.0 * floor(cos(α - (i / 6.0)°))), ".0000"]]], A + (4.6, s * i - 0.1)], i, -6.0 * k, 6.0 * k)
list6 = Sequence(Text[If[lg(tan(α - (i / 6.0)°)) ≥ 2.0, floor(tan(α - (i / 6.0)°)) + "." + (floor(100.0 * tan(α - (i / 6.0)°) - 100.0 * floor(tan(α - (i / 6.0)°)))), If[lg(tan(α - (i / 6.0)°)) ≥ 1.0, floor(tan(α - (i / 6.0)°)) + If[floor(1000.0 * tan(α - (i / 6.0)°) - 1000.0 * floor(tan(α - (i / 6.0)°))) > 100.0, "." + (floor(1000.0 * tan(α - (i / 6.0)°) - 1000.0 * floor(tan(α - (i / 6.0)°)))), ".0" + (floor(1000.0 * tan(α - (i / 6.0)°) - 1000.0 * floor(tan(α - (i / 6.0)°))))], floor(tan(α - (i / 6.0)°)) + If[floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°)) > 1000.0, "." + (floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°))), If[floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°)) > 100.0, ".0" + (floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°))), If[floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°)) > 10.0, ".00" + (floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°))), If[floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°)) > 0.0, ".000" + (floor(10000.0 * tan(α - (i / 6.0)°)) - 10000.0 * floor(tan(α - (i / 6.0)°))), ".0000"]]]]]], A + (6.6, s * i - 0.1)], i, -6.0 * k, 6.0 * k)
文字4 = Text("tan", A + (6.8, 6.0 * s * k + 0.5))
h = Segment(A + (8.0, -(6.0) * s * k - s), A + (8.0, 6.0 * s * k + s + 0.5))
j = Segment(A + (0.0, 6.0 * s * k + s + 0.5), A + (8.0, 6.0 * s * k + s + 0.5))
c_2 = Segment(A + (0.0, 6.0 * s * k + s), A + (8.0, 6.0 * s * k + s))
d = Segment(A + (0.0, -(6.0) * s * k - s), A + (8.0, -(6.0) * s * k - s))
show = 1 (slider from 0 to 1, step 1)
B = (1.579716279069776, 1.0693069767441845)
f_1 = Line(B, xAxis)
C = (9.64297209302326, 6.185586046511625)
g_1 = OrthogonalLine(C, f_1)
D = Intersect(g_1, f_1)
c = Segment(B, C)
a = Segment(C, D)
b = Segment(D, B)
θ = Angle(D, B, C)
γ = Angle(C, D, B)
文字8: "\[\left\{\begin{array}sinθ= \frac{ 對邊a }{ 斜邊c} = \frac{ " + a + " }{ " + c + "}=" + (a / c) + "  \\ cosθ= \frac{ 鄰邊b }{斜邊c}= \frac{ " + b + " }{ " + c + "}=" + (b / c) + " \\ tanθ= \frac{對邊a }{ 鄰邊b}= \frac{ " + a + " }{" + b + "}=" + (a / b) + "  \\\end{array}\]"
文字6 = Text("θ=" + α + β + (If[β ≟ 0.0, "0'", "'"]), A + (-(1.6), -(β + 3.0) / 10.0 * s))
Q_1: A + (0.0, 2.0)
Q_2: A - (0.0, 1.6)
Q_3: A + (0.0, 0.2)
Q_4: Q_1 + (8.0, 0.0)
Q_5: Q_3 + (8.0, 0.0)
Q_6: Q_2 + (8.0, 0.0)
h_1 = Segment(Q_1, Q_4)
i_1 = Segment(Q_3, Q_5)
j_1 = Segment(Q_2, Q_6)
Q_7: A - (0.0, 3.4)
Q_8: Q_7 + (8.0, 0.0)
k_1 = Segment(Q_7, Q_8)