ω

φ

$g(x) = \cos(x)$

$f(x) = \sin(x)$

$\sin(x)$

$x$

f(x) = a sin(ω t)

g(x) = a cos(ω t)

$x$

P(\textcolor[rgb]{0.4,0.6,0}{\underbrace{r\cos(\omega t + \varphi)}_{x(t)}}|\textcolor[rgb]{0,0.6,1}{\underbrace{r\sin(\omega t + \varphi)}_{y(t)}})

$\cos(x)$

III

$\triangleright$

$\circ$

S

v: -3.2
M: (v, 0)
gL2: -1.5
gR2: 1.5
gU2: -1.5
gO2: 1.5
gL1: -1
gR1: 8
gU1: -1.5
gO1: 1.5
α = 2.5830872929516078 rad (slider from 0 to 360°, step 0.017453292519943295)
t = 0 (slider from 0 to tmax, step 0.01)
omega = 1 (slider from 0.5 to 4, step 0.5)
x0: t
r = 2 (slider from 0.5 to 2, step 0.5)
phi = 0 (slider from 0 to zweipi, step zweipi / 8)
g(x) = If[x ≥ 0, (r * cos((omega * x) + phi))]
f(x) = If[x ≥ 0, (r * sin((omega * x) + phi))]
P: (g(t), f(t)) + (v, 0)
Q: (x(P), 0)
sy = Segment(Q, P)
R: (g(0), f(0)) + (v, 0)
c = CircleArc(M, R, P)
aSin = true
bCos = false
X: (x0, 0)
w = Angle(R, M, P)
sP = Segment(M, P)
h = Segment(M, R)
S: (0, y(P)) + (v, 0)
sxk = Segment((0, 0), X)
sx = Segment(S, P)
Py: (x0, f(x0))
k = Circle(M, r)
i = Segment((v - r, 0), (v + r, 0))
j = Segment((v, (-r)), (v, r))
zweipi: (2 * pi)
vK: -0.7
K: (vK, y(P))
f0(t) = (r * sin((omega * t) + phi))
g0(t) = (r * cos((omega * t) + phi))
tmax: (2 * pi)
aV: -6.5
l1 = Sequence(Vector[(aV, i), (aV + 1, i)], i, -2, 2, 0.5)
Text3: "y(t) = " + (LaTeX[r]) + " \cdot \sin(" + (LaTeX[omega]) + " \cdot t + " + (LaTeX[phi]) + ") = " + (LaTeX[f0]) + ""
s(x) = If[x ≥ 0, (r * sin((omega * x) + phi))]
Px: (x0, s(x0))
S0: (vK, 0)
sa = Segment(S0, K)
s0(t) = (r * sin((omega * t) + phi))
Text4: "s(t) = " + (LaTeX[r]) + " \cdot \sin(" + (LaTeX[omega]) + " \cdot t + " + (LaTeX[phi]) + ") = " + (LaTeX[s0]) + ""