Cosinus "Pi"-Symmetrie

$\frac{\pi}{6}$

$\frac{\pi}{4}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$\pi$

$x$

$\textcolor{#339900}{\cos(x)}$

$\textcolor{#CC0000}{\pi - x}$

$\textcolor{#CC0000}{\cos(\pi - x)}$

$x$

$\frac{\pi}{2}$

$-\frac{\pi}{2}$

$\pi$

$0$

$x$

$x$

$x$

$\pi - x$

$\pi - x$

f(x) = cos(x)
X_{0}: (0, 0)
X_{pi6}: (π / 6, 0)
X_{pi4}: (π / 4, 0)
X_{pi3}: (π / 3, 0)
X_{pi2}: (π / 2, 0)
X_{pi}: (π, 0)
P_{x} = Point(xAxis)
P_{y}: (x(P_{x}), f(x(P_{x})))
P_{x2}: (π - x(P_{x}), 0)
P_{y2}: (x(P_{x2}), f(x(P_{x2})))
i = Segment(P_{x}, P_{y})
j = Segment(P_{x2}, P_{y2})
U = Point(xAxis)
l = Segment(X_{0}, P_{x})
Einheitskreis: (x - x(U))^(2) + y^(2) = 1
Y_{achse}: x = x(U)
B = Intersect(Einheitskreis, Y_{achse}, 1)
D = Intersect(Einheitskreis, Y_{achse}, 2)
C = Intersect(Einheitskreis, xAxis, 2)
A = Intersect(Einheitskreis, xAxis, 1)
Q = Point(Einheitskreis)
Q_{x}: (x(Q), 0)
Q_{2}: (x(U) + cos(x(P_{x2})), sin(x(P_{x2})))
m = Segment(U, Q)
n = Segment(Q_{2}, U)
p = Segment(Q_{x}, U)
q = Segment(Q_{x}, Q)
alpha = Angle(A, U, Q)
k = Segment(P_{x2}, X_{pi})
P_{null}: (0, y(P_{y}))
t = Segment(P_{null}, P_{y})
alpha2 = Angle(Q, U, A)
Q_{x2}: (x(Q_{2}), 0)
r = Segment(Q_{x2}, Q_{2})
a = Segment(Q_{x2}, U)
alpha_2 = Angle(A, U, Q_{2})
alpha2_{2} = Angle(Q_{2}, U, A)
Funktionsvorschrift: "\textcolor{blue}{\cos(\pi-x)=-" + (LaTeX[f]) + "}"
P_{null2}: (0, y(P_{y2}))
s = Segment(P_{null2}, P_{y2})
loops = 0 (slider from -5 to 5)
alpha_{full} = Angle(A, U, A - (0, 0.01))
alpha_{full2} = Angle(A, U, A - (0, 0.01))
alpha2_{full} = Angle(A, U, A - (0, 0.01))
alpha2_{full2} = Angle(A, U, A - (0, 0.01))