Polarkurve

r(θ)

θ

θ

\frac{ \frac{r}{2}} { \frac{a}{2}}=cos(\theta)

Beweis

Spur P

a = 2 (slider from -5 to 5, step 0.05)
θ = 0.65 (slider from 0 to 10, step 0.01)
r(x) = a * cos(x)
K: (θ, r(θ))
P: (r(θ); θ)
Polarkurve = Locus(P, θ)
b = false
O = (0, 0)
c = Segment(O, P)
K_θ: (θ, 0)
d = Segment(K, K_θ)
E = (1, 0)
e = Segment(O, K_θ)
Text1: "r(x) = " + (LaTeX[r]) + ""
P': (-r(θ); θ)
α = Angle(E, O, P')
β = Angle(E, O, P)
f = Segment(O, P')
θ_g: θ / π * 180
g = OrthogonalLine(E, c)
M = Intersect(c, g)
Vieleck1, a_1, o, e_1 = Polygon(O, E, M)
h = false
i = Segment(E, P)
P_s: P
j = true