旋轉示例
Author: 藍邦偉  老師

$ O $

$θ=%v$

$ A'(x',y') $

$ sin30°=\frac{1}{2}$
$cos30°=\frac{\sqrt3}{2} $

$ sin15°=\frac{\sqrt{6}-\sqrt2}{4}$
$cos15°=\frac{\sqrt{6}-\sqrt{2}}{4} $

$ sin45°=\frac{\sqrt{2}}{2}$
$cos45°=\frac{\sqrt{2}}{2} $

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

$ sin75°=\frac{\sqrt{6}-\sqrt{2}}{4}$
$cos75°=\frac{\sqrt{6}-\sqrt{2}}{4} $

$ sin90°=1$
$cos90°=0 $

$sin105°=\frac{\sqrt{6}-\sqrt{2}}{4}$
$cos105°=-\frac{\sqrt{6}-\sqrt{2}}{4}$

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

$ sin135°=\frac{\sqrt{2}}{2} $
$cos135°=-\frac{\sqrt{2}}{2}$

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

$ sin165°=\frac{\sqrt{6}-\sqrt{2}}{4}$
$cos165°=-\frac{\sqrt{6}-\sqrt{2}}{4} $

$ sin180°=0$
$cos180°=-1 $

$ sin195°=-\frac{\sqrt{6}-\sqrt{2}}{4}$
$cos195°=-\frac{\sqrt{6}-\sqrt{2}}{4} $

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

$ sin225°=-\frac{\sqrt{2}}{2}$
$cos225°=-\frac{\sqrt{2}}{2} $

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

$ sin255°=-\frac{\sqrt{6}-\sqrt{2}}{4}$
$cos255°=-\frac{\sqrt{6}-\sqrt{2}}{4} $

$ sin270°=-1$
$cos270°=0 $

$ sin285°=-\frac{\sqrt{6}+\sqrt{2}}{4} $
$cos285°=\frac{\sqrt6-\sqrt{2}}{4}$

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

$ sin315°=-\frac{\sqrt{2}}{2}$
$cos315°=\frac{\sqrt{2}}{2} $

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

$ sin345°=-\frac{\sqrt{6}-\sqrt{2}}{4} $
$cos345°=\frac{\sqrt{6}+\sqrt{2}}{4}$

$ 線性變換示例  \;旋轉 $

$ sin0°=0 $
$cos0°=1$

1

$ 顯示對應三角函數值 $

C = (4.194177764549596, 1.3629826717480698)
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: 0.63 * Corner[1] + 0.37 * 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])
a = 2 (slider from -4 to 4, step 1)
b = 0 (slider from -4 to 4, step 1)
A = DynamicCoordinates(C, floor(x(C)), floor(y(C)))
e = 5.000000058430487E-8 (slider from -6.28318531 to 6.283185307179586, step 0.26179939)
A' = Rotate(A, e, O)
s = Angle(A, O, A')
t = Angle(A', O, A)
c = CircleArc(O, A, A')
d = CircleArc(O, A', A)
f = Segment(O, A)
g = Segment(O, A')
w: -t
t_A: "$ A" + (LaTeX[A]) + " $"
THETA: "$旋轉角度 θ=" + (LaTeX[If[e > 0, "", "-"]]) + " " + (LaTeX[If[e ≥ 0, s, t]]) + "$"
B = (-14.667135662450475, -2.5770491088247187)
k: (180 * e) / π
h = true
Main: "$ A'：\;\left [\begin{array}{cc} x' \\ y' \\ \end{array}   \right ]$
$\;\;\;=\left [ \begin{array}{cc} cos" + (LaTeX[If[e < 0, "(-"]]) + " " + (LaTeX[If[e ≥ 0, s, t]]) + "" + (LaTeX[If[e < 0, ")"]]) + "& -sin" + (LaTeX[If[e < 0, "(-"]]) + " " + (LaTeX[If[e ≥ 0, s, t]]) + "" + (LaTeX[If[e < 0, ")"]]) + "\\ sin" + (LaTeX[If[e < 0, "(-"]]) + "" + (LaTeX[If[e > 0, s, t]]) + " & cos" + (LaTeX[If[e < 0, "(-"]]) + " " + (LaTeX[If[e ≥ 0, s, t]]) + "" + (LaTeX[If[e < 0, ")"]]) + "\\ \end{array}  \right ] \left [  \begin{array}{cc} " + (LaTeX[x(A)]) + " \\ " + (LaTeX[y(A)]) + " \\ \end{array} \right ]   $"