複數的極式與極座標,直角座標的關係
Author: 藍邦偉老師

$%v$

$ 極座標轉換為直角座標 $

$sin15°=\frac{\sqrt6-\sqrt2}{4}$
$cos15°=\frac{\sqrt6+\sqrt2}{4}$

$sin75°=\frac{\sqrt6+\sqrt2}{4}$
$cos75°=\frac{\sqrt6-\sqrt2}{4}$

$sin105°=\frac{\sqrt6-\sqrt2}{4}$
$cos105°=-\frac{\sqrt6+\sqrt2}{4}$

$sin165°=\frac{\sqrt6-\sqrt2}{4}$
$cos165°=-\frac{\sqrt6+\sqrt2}{4}$

$sin195°=-\frac{\sqrt6-\sqrt2}{4}$
$cos195°=-\frac{\sqrt6+\sqrt2}{4}$

$sin255°=-\frac{\sqrt6-\sqrt2}{4}$
$cos255°=-\frac{\sqrt6+\sqrt2}{4}$

$sin285°=-\frac{\sqrt6-\sqrt2}{4}$
$cos285°=\frac{\sqrt6+\sqrt2}{4}$

$sin345°=-\frac{\sqrt6-\sqrt2}{4}$
$cos345°=\frac{\sqrt6+\sqrt2}{4}$

list1 = Sequence(Circle[(0, 0), r], r, 1, 10)
list5 = Sequence(Sequence[(r * sqrt(2) * cos(((k - 1) * 45)°), r * sqrt(2) * sin(((k - 1) * 45)°)), k, 1, 8], r, 1, 10)
list4 = Sequence(Sequence[(r * cos(((k - 1) * 15)°), r * sin(((k - 1) * 15)°)), k, 1, 24], r, 1, 10)
list6 = Union(list5, list4)
list2 = Sequence((cos(((k - 1) * 15)°), sin(((k - 1) * 15)°)), k, 1, 24)
A = Point(list6)
list3 = Sequence(Ray[(0, 0), (cos(((k - 1) * 15)°), sin(((k - 1) * 15)°))], k, 1, 24)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[3]))
poly1, a, q_2, q_3, b = Polygon(Corner[1], Q_2, Q_3, Corner[4])
c = Vector((0, 0), (x(Corner[2]), 0))
r: sqrt(x(A)^(2) + y(A)^(2))
θ = Angle((1, 0), (0, 0), A)
t2: "=(" + (LaTeX[SurdText[x(A)]]) + "," + (LaTeX[SurdText[y(A)]]) + ")"
B = (-14.986335332991313, 2.944882237542266)
t1: "$極座標為：\;[" + (LaTeX[SurdText[r]]) + "\;," + (LaTeX[θ]) + "]$
$直角座標為：\;$
$(" + (LaTeX[SurdText[r]]) + "cos" + (LaTeX[θ]) + "," + (LaTeX[SurdText[r]]) + "sin" + (LaTeX[θ]) + ")$"
t_A: "$ A(" + (LaTeX[SurdText[r]]) + " ," + (LaTeX[θ]) + ")$"