正切與直線的斜率
Author: 藍邦偉  老師
Date: 24 12 月 2012

$O$

$θ$

P(x,y)

$ 正切與直線斜率 $

O = (0, 0)
u = Vector((x(Corner[1]), y(O)), (x(Corner[3]), y(O)))
v = Vector((x(O), y(Corner[1])), (x(O), y(Corner[3])))
θ = 1.0995574287564276 rad (slider from 0*° to 6.283185307179586, step 0.1*°)
a: y - y(O) = tan(θ) * (x - x(O))
A: O + (1, 0)
B: O + (cos(θ), sin(θ))
c = CircleArc(O, A, B)
P: O + (3 * cos(θ), 3 * sin(θ))
text1: "$ 斜率\;m=\frac{\Delta y}{\Delta x}$
$\;\;\;\;\;\;\;\;\;\;\;\;=tanθ $
$\;\;\;\;\;\;\;\;\;\;\;\;=\frac{" + (LaTeX[y(P)]) + "}{" + (LaTeX[x(P)]) + "}$
$\;\;\;\;\;\;\;\;\;\;\;\;=tan" + (LaTeX[θ]) + "$
$\;\;\;\;\;\;\;\;\;\;\;\;=" + (LaTeX[FractionText[Slope[a]]]) + "$"
Q_2: 0.8 * Corner[1] + 0.2 * Corner[2]
Q_3: (x(Q_2), y(Corner[3]))
poly1, b, q_2, q_3, d = Polygon(Corner[1], Q_2, Q_3, Corner[4])
e = Segment(Q_3, Q_2)
text2: "$ P\; " + (LaTeX[P]) + "$"