餘弦定理(3)
Author: 藍邦偉  老師
Date: 7 1 月 2013

$C$

A(b,0)

B(x,y)

$ 餘弦定理 $

$\;\;\;\; B(x,y)=B[a,∠C]$
$=B(acosC,asinC)$

$ c^2=\overline{AB}^2 $
$=(acosC-b)²+(asinC-0)^2$

$ =a²cos²C+asinC-2abcosC+b² $
$=a²+b²-2abcosC$

$ \left\lbrace\begin{array}{ll} a^2=b^2+c^2-2bc\;cosA \ b^2=c^2+a^2-2ac\;cosB \ c^2=a^2+b^2-2ab\;cosC \end{array}   \right.\  $
$\left\lbrace \begin{array}{ll} cosA=\frac{b^2+c^2-a^2}{2bc} \ cosB=\frac{a^2+c^2-b^2}{2ac} \ cosC=\frac{a^2+b^2-c^2}{2ab} \end{array}  \right.\ $

E = (2.14, 4.14)
D = (6.42, -0.04)
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
C = (0, 0)
A = DynamicCoordinates(D, floor(x(D)), 0)
B = DynamicCoordinates(E, floor(x(E)), floor(y(E)))
a = Segment(B, C)
c = Segment(B, A)
α = Angle(A, C, B)
b = Segment(C, A)
r, c_1, a_1, b_2 = Polygon(C, A, B)
text4: "$ =" + (LaTeX[a]) + "^2+" + (LaTeX[b]) + "^2-2\times" + (LaTeX[a]) + "\times" + (LaTeX[b]) + "\;cos" + (LaTeX[α]) + " $"
text5: "$ =" + (LaTeX[c^(2)]) + " $
$⇒c=" + (LaTeX[c]) + "$"
text6: "$ a=" + (LaTeX[a]) + " $"
text7: "$ b=" + (LaTeX[b]) + " $"
text8: "$ c=" + (LaTeX[c]) + " $"
text9: "$ B" + (LaTeX[B]) + " $"
text10: "$ A" + (LaTeX[A]) + " $"
step = 5 (slider from 0 to 5, step 1)