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Phoebeliwel
@Phoebeliwel
May 2019
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Besoin d'aide pour une question qui pose problème en maths :p Merci pour l'aide! Voici l'énoncé:
Quel est l'ensemble des solutions sur ]-
;
[ de sin(x)-
cos(x)=0
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scoladan
Verified answer
Bonjour,
sin(x) - √3cos(x) = 0 (E)
⇔ sin(x) = √3cos(x)
⇔ sin(x)/cos(x) = √3
SI
cox(x) ≠ 0 (E')
Si cos(x) = 0, (E) ⇔ sin(x) = 0 ⇒ sin(x) = cos(x) = 0 impossible
(E') ⇔ tan(x) = √3
⇔ x = π/3 + kπ ,avec k ∈ Z
2 solutions sur [-π;π] :
k = 0 ⇒ x = π/3
k = -1 ⇒ x = π/3 - π = -2π/3
1 votes
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Lista de comentários
Verified answer
Bonjour,sin(x) - √3cos(x) = 0 (E)
⇔ sin(x) = √3cos(x)
⇔ sin(x)/cos(x) = √3 SI cox(x) ≠ 0 (E')
Si cos(x) = 0, (E) ⇔ sin(x) = 0 ⇒ sin(x) = cos(x) = 0 impossible
(E') ⇔ tan(x) = √3
⇔ x = π/3 + kπ ,avec k ∈ Z
2 solutions sur [-π;π] :
k = 0 ⇒ x = π/3
k = -1 ⇒ x = π/3 - π = -2π/3