三角方程式(3)
Author: 藍邦偉  老師

0°≤θ<360°

三角方程式(3)

m= \frac{  \sqrt{ 3 }  }{ 3} 

P

Q

P

Q

m=1

m=\sqrt{ 3 } 

Q

P

m=- \sqrt{ 3 } 

Q

P

m=- 1

P

Q

m=-  \frac{  \sqrt{ 3 }  }{3 } 

tanθ=  \frac{  \sqrt{ 3 }  }{ 3}  \rightarrow{}θ=?

tanθ= 1\rightarrow{}θ=?

tanθ= \sqrt{3 } \rightarrow{}θ=?

tanθ=- \sqrt{3} \rightarrow{}θ=?

tanθ=- 1 \rightarrow{}θ=?

tanθ=- \frac{ \sqrt{ 3 } }{3 }\rightarrow{}θ=? 

P

Q

O: 0.5 * (Corner[1.0] + Corner[3.0])
u = Vector((x(Corner[1.0]), y(O)), (x(Corner[3.0]), y(O)))
v = Vector((x(O), y(Corner[1.0])), (x(O), y(Corner[3.0])))
d = Circle(O, 1.0)
P: O + (1.0, 0.0)
n = 1 (slider from 0 to 6, step 1)
L_6: y = y(O) - sqrt(3.0) / 3.0 * (x - x(O))
L_5: y = y(O) - (x - x(O))
L_2: y = y(O) + x - x(O)
L_3: y = y(O) + sqrt(3.0) * (x - x(O))
L_4: y = y(O) - sqrt(3.0) * (x - x(O))
C, D = Intersect(d, L_2)
c = Segment(C, O)
e = Segment(O, D)
E, F = Intersect(d, L_3)
f = Segment(E, O)
g = Segment(O, F)
G, H = Intersect(d, L_4)
h = Segment(O, H)
i = Segment(O, G)
I, J = Intersect(d, L_5)
j = Segment(O, J)
k = Segment(O, I)
K, L = Intersect(d, L_6)
l = Segment(O, L)
m = Segment(O, K)
γ = Angle(P, O, C)
δ = Angle(P, O, D)
ε = Angle(P, O, E)
ζ = Angle(P, O, F)
η = Angle(P, O, H)
θ = Angle(P, O, G)
ι = Angle(P, O, J)
κ = Angle(P, O, I)
λ = Angle(P, O, L)
μ = Angle(P, O, K)
L_1: y - y(O) = 1.0 / sqrt(3.0) * (x - x(O))
A = Intersect(d, L_1, 2.0)
B = Intersect(d, L_1, 1.0)
α = Angle(P, O, A)
β = Angle(P, O, B)