Exo 2 : Résoudre sin x = - ½ dans R puis I = [ - 6π ; - (5/2)π ]. …

Résoudre sin x = - ½ dans R puis I = [ - 6π ; - (5/2)π ]. x1 x2

Résoudre sin x = - ½ dans R puis I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ π/6 x1 x2

Résoudre sin x = - ½ dans R puis I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ π/6 π 0 x1 x2

Résoudre sin x = - ½ dans R puis I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 π 0 x1 x2

Résoudre sin x = - ½ S = { 7π/6 + k2π ; - π/6 + k2π } dans R ; puis dans I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 π 0 x1 x2

Résoudre sin x = - ½ S = { 7π/6 + k2π ; - π/6 + k2π } dans R ; puis dans I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 - 6π = 0 – 3(2π) = 0 – 3 tours - 6π x1 x2

Résoudre sin x = - ½ S = { 7π/6 + k2π ; - π/6 + k2π } dans R ; puis dans I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 - 6π = 0 – 3(2π) = 0 – 3 tours Amplitude = (–(5/2)π) – (-6π) = 3,5π = 1,75 tour - 6π x1 x2 - (5/2)π

Résoudre sin x = - ½ S = { 7π/6 + k2π ; - π/6 + k2π } dans R ; puis dans I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 - 6π = 0 – 3(2π) = 0 – 3 tours Amplitude = (–(5/2)π) – (-6π) = 3,5π = 1,75 tour - 6π c a b x1 x2 - (5/2)π

Résoudre sin x = - ½ S = { 7π/6 + k2π ; - π/6 + k2π } dans R ; puis dans I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 - 6π = 0 – 3(2π) = 0 – 3 tours Amplitude = (–(5/2)π) – (-6π) = 3,5π = 1,75 tour - 6π a = - 6π + π + π/6 = - 29π/6 c a b x1 x2 - (5/2)π

Résoudre sin x = - ½ S = { 7π/6 + k2π ; - π/6 + k2π } dans R ; puis dans I = [ - 6π ; - (5/2)π ]. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 - 6π = 0 – 3(2π) = 0 – 3 tours Amplitude = (–(5/2)π) – (-6π) = 3,5π = 1,75 tour - 6π a = - 6π + π + π/6 = - 29π/6 c a b b = - 6π + π + 5π/6 = - 25π/6 x1 x2 - (5/2)π

Résoudre sin x = - ½ S = { 7π/6 + k2π ; - π/6 + k2π } dans R ; S = { - 29π/6 ; - 25π/6 ; - 17π/6 } dans I. Angle remarquable sin π/6 = + ½ x1 = π + π/6 = 7π/6 x2 = 0 - π/6 = - π/6 π/6 - 6π = 0 – 3(2π) = 0 – 3 tours Amplitude = (–(5/2)π) – (-6π) = 3,5π = 1,75 tour - 6π a = - 6π + π + π/6 = - 29π/6 c a b b = - 6π + π + 5π/6 = - 25π/6 x1 x2 c = a + 2π = - 17π/6 - (5/2)π