餘弦定理
Author: kuanchangsou

阿壽工坊---http://120.101.70.8/longlife/

B(x,y)=(bcosθ,bsinθ)

A(a,0)

餘弦定理:

C = (0, 0)
B = (-1.76, 3.353333333333339)
A = Point(xAxis)
poly1, a, c, b = Polygon(C, A, B)
θ = Angle(A, C, B)
text1: "將三角形ABC的 \cr 
頂點C放在坐標軸原點上,\cr
頂點A放在x軸的正向上 \cr
則頂點B在θ角的邊上 \cr
因為:\textcolor{red}{ " + (LaTeX[TableText[{{"cos(θ)= \frac{ x }{b }"}, {"sin(θ)= \frac{ y }{b } "}}, "{"]]) + "} \cr 
⇒" + (LaTeX[TableText[{{"x=b·cos(θ)"}, {"y=b·sin(θ)"}}, "{"]]) + " \cr 
所以 \cr 
c²=(b·cosθ-a)²+(b·sinθ)² \cr 
\text{   }=b²cos²θ-2abcosθ+a²+b²sin²θ \cr 
\text{   }=a²+b²sin²θ+b²cos²θ-2abcosθ \cr 
\text{   }=a²+b²-2abcosθ \cr 
⇒cosθ=\textcolor{red}{\frac{ a²+b²-c² }{2ab }}"