Trigo1

RELATIONS TRIGONOMETRIQUES

M est un point du cercle de centre O et de rayon OA.

AM

= α. ( OA , OB ) = α (exprimé en radians)

Dans le repère (O; OA , OB ), M a pour coordonnées (cos α , sin α). soit x = cos α et y = sin α.

AT = tan α.

PROPRIETES :

-1
_cos α
1 -1
sin α
1 sin² α + cos² α = 1 α ∈  tan α = α α cos sin cotan α = α α sin cos = α tan 1 1 + tan² α = α 2 cos 1 1 + cotan² α = α 2 sin 1 . ANGLES PARTICULIERS : O /4 /3 /2 - /2 0 /6 π π π π π π x en rad 0 π_/6 π_/4 π_/3 π_/2 π _-π/2 x en degrés 0 30 45 60 90 180 270 sin x 0 2 1 2 2 2 3 1 0 -1 cos x 1 2 3 2 2 2 1 0 -1 0 tan x 0 3 3 1 3 0 SYMETRIES : x ∈ , k ∈ O 0 x -x /2-x /2+x -x +x π π π π

cos(x + 2kπ) = cos x sin(x + 2kπ) = sin x tan(x + 2kπ) = tan x cos(x + 2π) = cos x sin(x + 2π) = sin x tan(x + 2π) = tan x cos(-x) = cos x sin(-x) = - sin x tan(-x) = - tan x cos(π – x) = - cos x sin(π – x) = sin x tan(π – x) = - tan x cos(π + x) = - cos x sin(π + x) = - sin x tan(π + x) = tan x cos(π/2 – x) = sin x sin(π/2 – x) = cos x tan(π/2 – x) = cotan x cos(π/2 + x) = - sin x sin(π/2 + x) = cos x tan(π/2 + x) = - cotan x EQUATIONS FONDAMENTALES : cos a = cos b ⇔ a = b [2π] ou a = -b [2π] sin a = sin b ⇔ a = b [2π] ou a = π – b [2π] tan a = tan b ⇔ a = b [π] TRIANGLE RECTANGLE : cos A = AB AC = . hypo . adj é cot sin A = BA BC = . hypo . opp é cot . tan A = AC BC = . adj é cot . opp é cot A B C