Fonctions trigonométriques 1 Fonction sinus et cosinus 2

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cos sin
cos : R→R
x7→ cos(x)sin : R→R x7→ sin(x)
2π x ∈R
cos(x+ 2π) = cos(x)
sin(x+ 2π) = sin(x)
cos sin
f x0f(x0+h)−f(x0)
h
h→0
sin(h)
hh→0
h∈0; π
2h T
(OI)I(OM)
IOM h
OAM h
OIT h
cos(h)≤sin(h)
h≤1 cos(h)
h > 0

cos(h)h
h−π
2; 0
cos(h)≤sin(h)
h≤1 cos(h)
h0=−h
(sin(0))0
cos(h)−1
hh→0
h∈0; π
2M h
[IM]IM h
p2(1 −cos(h)) ≤h
1−cos(h)≤h2
2
1−cos(h)
h−π
2; 0
cos(h)−1
h
(cos(0))0
lim
h→0
sin(h)
h= 1
lim
h→0
cos(h)−1
h= 0
sin sin0(0) = 1 cos
cos0(0) = 1
x∈R
h→0cos(x+h)−cos(x)
h
sin(x+h)−sin(x)
h
sin cos R
sin0(x) = cos(x)
cos0(x) = −sin(x)
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sin cos
[−π;π]
sin
x−π−π
2
π
2π
cos(x)
sin(x)
cos
x−π−π
2
π
2π
−sin(x)
cos(x)
π2π−π−2π
y= sin(x)y= cos(x)
cos sin
tan
f:−π
2;π 2→R
x7→ sin(x)
cos(x)
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f0(x) = 1
cos2(x)
f
x∈Rcos(x)6= 0 tan(x) = sin(x)
cos(x)π
tan
a, b ∈R
f:R→R
x7→ cos(ax +b)
g:R→R
x7→ sin(ax +b)
f g R
f0(x) = −asin(ax +b)
g0(x) = acos(ax +b)
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