2D 座標架
Author: 藍邦偉  老師

$ O $

補角關係

$θ=%v$

$P(cosθ,sinθ)$

$R(r cos(-θ),r sin(-θ))$

$Q(rcos(180°-θ),rsin(180°-θ))$

$sin(180°-θ)=sinθ\;,\; cos(180°-θ)=-cosθ$ 
$tan(180°-θ)=\frac{sin(180°-θ)}{cos(180°-θ)}=\frac{sinθ}{-cosθ}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=-tanθ$

$4.\;sin(180°+θ)=sin(180°-(-θ))$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=sin(-θ)=-sinθ$
$\;\;\;\;cos(180°+θ)=cos(180°-(-θ))$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=-cos(-θ)=-cosθ$
$tan(180°+θ)=\frac{sin(180°+θ)}{cos(180°+θ)}=\frac{-sinθ}{-cosθ}$
$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;=tanθ$

1

顯示角度

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: 0.55 * Corner[1] + 0.45 * 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])
θ = 0 rad (slider from 0 to 6.283185307179586, step 0.017453292519943295)
r = 3
c: x^(2) + y^(2) = r^(2)
P: (r * cos(θ), r * sin(θ))
R: (r * cos(-θ), r * sin(-θ))
Q: (r * cos(180° - θ), r * sin(180° - θ))
T: (r, 0)
a_1 = Segment(O, ((r + 1) * cos(θ), (r + 1) * sin(θ)))
a_2 = Segment(O, ((r + 1) * cos(-θ), (r + 1) * sin(-θ)))
a_3 = Segment(O, ((r + 1) * cos(180° - θ), (r + 1) * sin(θ)))
a = true
t_P: "P(cos" + (LaTeX[If[a ≟ true, "" + θ, "θ"]]) + ",sin" + (LaTeX[If[a ≟ true, "" + θ, "θ"]]) + ")"
t_R: "R(cos" + (LaTeX[If[a ≟ true, "" + (-θ), "(-θ)"]]) + ",sin" + (LaTeX[If[a ≟ true, "" + (-θ), "(-θ)"]]) + ")"
t_Q: "Q(cos" + (LaTeX[If[a ≟ true, "" + (180° - θ), "(180°-θ)"]]) + ",sin" + (LaTeX[If[a ≟ true, "" + (180° - θ), "(180°-θ)"]]) + ")"
text1: "$1.標準位置角" + (LaTeX[If[a ≟ true, "" + θ, "θ"]]) + "與" + (LaTeX[If[a ≟ true, "-" + θ, "-θ"]]) + "\;的終邊對稱於\;x\;軸$
$2.而" + (LaTeX[If[a ≟ true, "180°-" + θ, "180°-θ"]]) + "=" + (LaTeX[If[a ≟ true, "-" + θ + "+180°", "-θ+180°"]]) + "故" + (LaTeX[If[a ≟ true, "-" + θ, "-θ"]]) + "的$
$\;\;\;終邊與" + (LaTeX[If[a ≟ true, "180°-" + θ, "180°-θ"]]) + "的終邊對稱於原點$
$3.所以" + (LaTeX[If[a ≟ true, "" + θ, "θ"]]) + "與" + (LaTeX[If[a ≟ true, "180°-" + θ, "180°-θ"]]) + "的終邊對稱於\;y\;軸$"