Quiz : Maîtrisez la trigonométrie en 10 questions !

Question 1 sur 10 10:00

[{"id":20448,"question":"Quelle est la valeur de sin(30°) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(30°) = 1\/2, c'est une valeur remarquable à connaître.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20449,"question":"L'équation sin(x) = 0 admet-elle des solutions dans l'intervalle [0, 2π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions sont x = 0, π et 2π dans cet intervalle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20450,"question":"Quelle identité trigonométrique est toujours vraie ?","option_a":"sin²x + cos²x = 1","option_b":"sinx + cosx = 1","option_c":"tanx = sinx + cosx","option_d":"sin²x - cos²x = 1","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'identité fondamentale sin²x + cos²x = 1 est toujours vérifiée.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20451,"question":"La fonction tangente est-elle périodique ? Si oui, quelle est sa période ?","option_a":"Non","option_b":"Oui, période π","option_c":"Oui, période 2π","option_d":"Oui, période π\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction tangente a une période de π, car tan(x + π) = tan(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20452,"question":"Quelle est la valeur de cos(π\/3) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"D","explication":"cos(π\/3) = √3\/2, valeur remarquable à retenir.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20453,"question":"L'équation cos(x) = -1 admet-elle une solution dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La solution est x = π, qui n'est pas dans l'intervalle [0, π[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20454,"question":"Quelle est la relation entre sin(x) et cos(π\/2 - x) ?","option_a":"sin(x) = cos(π\/2 - x)","option_b":"sin(x) = -cos(π\/2 - x)","option_c":"sin(x) = 2cos(π\/2 - x)","option_d":"Aucune relation","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une identité trigonométrique fondamentale : sin(x) = cos(π\/2 - x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20455,"question":"La fonction sinus est-elle paire ou impaire ?","option_a":"Paire","option_b":"Impaire","option_c":"Ni l'une ni l'autre","option_d":"Les deux","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction sinus est impaire car sin(-x) = -sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20456,"question":"Quelle est la valeur de tan(45°) ?","option_a":"0","option_b":"1","option_c":"√2","option_d":"√3","option_e":"","option_f":"","bonne_reponse":"B","explication":"tan(45°) = 1, car sin(45°) = cos(45°) = √2\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":20457,"question":"L'équation sin(2x) = 1 admet-elle des solutions dans l'intervalle [0, π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions sont x = π\/4 et x = 5π\/4, mais seule x = π\/4 est dans [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]