bonsoir quelquun pourrait tˆik mˆaider ?

x désigne un nombre réel de l'intervalle (-pi/2;0)


tel que cos(x) = racine carree de 5 /3
Déterminer sin2 (x) puis en
déduire la valeur exacte de sin(x).

By: USER3615
26 Agustus 2025 mathematiques 5 minutes
4.5
245 views 245 comments 13 shares

Question

Grade: Education Subject: mathematiques
bonsoir quelquun pourrait tˆik mˆaider ?

x désigne un nombre réel de l'intervalle (-pi/2;0)


tel que cos(x) = racine carree de 5 /3
Déterminer sin2 (x) puis en
déduire la valeur exacte de sin(x).
Asked by:
245 Viewed 245 Answers

Answer (245)

Best Answer
(186)

Selon le théorème de pythagore : cos(x)²+sin(x)²=1 donc sin(x)² = 1-5/9 = 4/9

d'où : ║sin(x)║ = sqrt(sin(x)²) = 2/3 et pour x∈[-pi/2, 0] sin(x)≤0

donc : sin(x) = -2/3

Answered on 26 Agustus 2025

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