直線斜率與正切函數的關係
Author: 藍邦偉  老師
Date: 15 1 月 2013

$O$

$θ=%v$

$P(x,y)$

$ 正切與直線斜率 $

$間隔$

$θ=%v$

O = (0, 0)
θ = 0 rad (slider from 0*° to 6.283185307179586, step k)
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 + (cos(θ), sin(θ))
list: {0.1*°, 1*°, 30*°}
n = 3 (slider from 1 to 3, step 1)
k = Element(list, n)
α = Angle((1, 0), O, P)
Q_2: 0.3 * Corner[2] + 0.7 * Corner[1]
Q_3: (x(Q_2), y(Corner[3]))
poly1, b, q_2, q_3, d = Polygon(Corner[1], Q_2, Q_3, Corner[4])
text1: "$m= \frac{y}{x}$
$\;\;\;\;=\frac{" + (LaTeX[SurdText[y(P)]]) + "}{" + (LaTeX[SurdText[x(P)]]) + "}$
$\;\;\;\;=\frac{sin" + (LaTeX[θ]) + "}{cos" + (LaTeX[θ]) + "} $
$\;\;\;\;=tan" + (LaTeX[θ]) + "$
$\;\;\;\;=" + (LaTeX[If[θ ≟ 90° ∨ θ ≟ 270°, "斜率不存在", SurdText[tan(θ)]]]) + "$"