Étude A sin(b (x-h) ) + k
Author: Pierre Lantagne

y=sin(x)

\mbox{Étude de }

f(x)=a\,\sin(b\,[x-h])+k

\(a\):  \mbox{étirement et/ou réflexion}\ 
\(b\):  \mbox{pulsation}\ 
\(h\):\mbox{translation horizontale (déphasage)}\
\(k\):\mbox{translation verticale}

Valeurs initiales

y=cos(x)

$y=sin(x)$

Cosinus

y=tan(x)

Tangente

y=sec(x)

Sécante

Cotangente

y=csc(x)

Cosécante

\mbox{Étude de }

f(x)=a\,\cos(b\,[x-h])+k

\mbox{Étude de }

f(x)=a\,\tan(b\,[x-h])+k

\mbox{Étude de }

f(x)=a\,\cot(b\,[x-h])+k

\mbox{Étude de }

f(x)=a\,\sec(b\,[x-h])+k

\mbox{Étude de }

f(x)=a\,\csc(b\,[x-h])+k

\(\mbox{Modifications des paramètres}\)\ \mbox{   additifs et multiplicatifs}

\setlength{\fboxsep}{8pt}\setlength\fboxrule{1pt}\ovalbox{\mbox{Effets des paramètres multiplicatifs et additifs sur les fonctions trigonométriques}

y=cot(x)

\(y=\sin(x)\)

\(y=\cos(x)\)

\(y=\tan(x)\)

\(y=\cot(x)\)

\(y=\sec(x)\)

\(y=\csc(x)\)

a: 1
b: 1
h: 0
k: 0
f_1(x) = (a * sin((b * (x - h)))) + k
g_1(x) = sin(x)
A_1: (0.3, 6)
B: (7, 6)
C: (7, 4)
D: (0.3, 4)
E: (0.2, 7.5)
F: (9, 7.5)
G: (9, 6.5)
H: (0.2, 6.5)
I = (-9.80115465104304, 7.817178526695921)
J = (-3.3633156264148916, 7.813949127389957)
K = (-3.337521622256091, 3.3547659931003904)
L = (-9.775360646884241, 3.357995392406354)
f_2(x) = (a * cos((b * (x - h)))) + k
g_2(x) = cos(x)
a_{1}: false
b_{3}: false
f_3(x) = (a * tan((b * (x - h)))) + k
g_3(x) = tan(x)
c: false
f_5(x) = (a * sec((b * (x - h)))) + k
g_5(x) = sec(x)
d: false
e: false
f_6(x) = (a * csc((b * (x - h)))) + k
g_6(x) = csc(x)
f: false
amplitude: abs(a)
période: (2 * π / abs(b))
fréquence: abs(b) / 2 / π
A: 1
Tcos: "f(x)=" + (LaTeX[a]) + " \cos(" + (LaTeX[b]) + " (x-" + (LaTeX[h]) + " ))+" + (LaTeX[k]) + ""
Ttan: "f(x)=" + (LaTeX[a]) + "\tan(" + (LaTeX[b]) + "(x-" + (LaTeX[h]) + "))+" + (LaTeX[k]) + ""
Tsec: "f(x)=" + (LaTeX[a]) + " \cot( " + (LaTeX[b]) + "(x-" + (LaTeX[h]) + " ))+" + (LaTeX[k]) + ""
Tcot: "f(x)=" + (LaTeX[a]) + " \sec(" + (LaTeX[b]) + " (x-" + (LaTeX[h]) + " ))+" + (LaTeX[k]) + ""
Tcosec: "f(x)=" + (LaTeX[a]) + " \csc(" + (LaTeX[b]) + " (x- " + (LaTeX[h]) + "))+" + (LaTeX[k]) + ""
Tsin: "f(x)=" + (LaTeX[a]) + "\sin(" + (LaTeX[b]) + "(x−" + (LaTeX[h]) + "))+k"
f_4(x) = cot(x)
g_4(x) = (a * cot((b * (x - h)))) + k
Asymptan = Sequence(x = i, i, (-11 * π / 2), (11 * π / 2), π)
Asympcsc = Sequence(x = i, i, (-11 * π), (11 * π), π)
Asympcot = Sequence(x = i, i, (-6 * π), (6 * π), π)
Asympsec = Sequence(x = i, i, (-11 * π / 2), (11 * π / 2), π)