鏡射示例
Author: 藍邦偉  老師

$ O $

$鏡射直線 L:x=0 $

$鏡射直線L: y=0 $

$鏡射示例 $

$A'(x',y')$

1

$ 顯示相關三角函數值 $

$ sin\;0°=0 $
$cos\;0°=1$

$sin30°=\frac{1}{2}  $
$cos30°=\frac{\sqrt{3}}{2}$

$ sin60°=\frac{\sqrt{3}}{2} $
$cos60°=\frac{1}{2}$

$ sin90°=1 $
$cos90°=0$

$ sin120°=\frac{\sqrt{3}}{2} $
$cos120°=-\frac{1}{2}$

$ sin150°=\frac{1}{2} $
$cos150°=-\frac{\sqrt{3}}{2}$

$ sin180°=0 $
$cos180°=-1$

$ sin210°=-\frac{1}{2} $
$cos210°=-\frac{\sqrt{3}}{2}$

$ sin240°=-\frac{\sqrt{3}}{2} $
$cos240°=-\frac{1}{2}$

$ sin270°=-1 $
$cos270°=0$

$ sin300°=-\frac{\sqrt{3}}{2} $
$cos300°=\frac{1}{2}$

$ sin330°=-\frac{1}{2} $
$cos330°=\frac{\sqrt{3}}{2}$

$ sin360°=0 $
$cos360°=1

$⇒L：\; y=(\sqrt{3}-1)\;x $

$⇒L：\; y=\frac{1}{\sqrt{3}}\;x $

$⇒L：\; y=x $

$⇒L：\; y=\sqrt{3}\;x $

$⇒L：\; y=(\sqrt{3}+1)\;x $

$⇒L：\; y=(-\sqrt{3}-1)\;x $

$⇒L：\; y=-\sqrt{3}\;x $

$⇒L：\; y=-x $

$⇒L：\; y=-\frac{1}{\sqrt{3}}\;x $

$⇒L：\; y=(-\sqrt{3}+1)\;x $

$⇒L：\; y=0 $

C = (2.4752712214127266, 4.664584349353071)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
Q_2: 0.67 * Corner[1] + 0.33 * Corner[2]
list1 = Sequence(Sequence[(i, j), i, floor(x(Q_2)) + 1, floor(x(Corner[2]))], j, floor(y(Corner[1])), floor(y(Corner[3])))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
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])
n = 0 (slider from 0 to 12, step 1)
θ: 15° * n
L = Line((0, 0), (cos(θ), sin(θ)))
Q: (cos(θ), sin(θ))
α = Angle((1, 0), O, Q)
a = 5 (slider from -5 to 5, step 1)
P = DynamicCoordinates(C, floor(x(C)), floor(y(C)))
b = 1 (slider from -5 to 5, step 1)
P' = Mirror(P, L)
A = (-13.018874869826282, -0.6203732354973466)
c = true
B: A - (0, 2)
d = Segment(P', P)
β = Angle(d, L)
t_P: "$ A\; " + (LaTeX[P]) + "$"
List_1: {1.7320508075688772}
t_{L}: "$ 鏡射直線L:y=tan" + (LaTeX[θ]) + " x $"
D = (-15.168445287590979, -1.8504488465230964)
t_{Matrix}: "$ A'：\left [\begin{array}{cc} x' \\ y' \\ \end{array}   \right ]  $
$=\left [ \begin{array}{cc} cos\;" + (LaTeX[2 * θ]) + " & sin\;" + (LaTeX[2 * θ]) + " \\ sin\;" + (LaTeX[2 * θ]) + " & -cos\;" + (LaTeX[2 * θ]) + " \\ \end{array}  \right ]\left [ \begin{array}{cc} " + (LaTeX[x(P)]) + " \\ " + (LaTeX[y(P)]) + " \\ \end{array}  \right ]  $"