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[{"id":79312,"question":"Quelle est la période de la fonction f(x) = sin(2x) ?","option_a":"π","option_b":"2π","option_c":"π\/2","option_d":"4π","option_e":"","option_f":"","bonne_reponse":"C","explication":"La période de sin(kx) est 2π\/k. Ici, k=2, donc la période est 2π\/2 = π.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79313,"question":"L'équation cos(x) = 1\/2 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 = π\/3 et x = 5π\/3 dans [0, 2π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79314,"question":"Quelle est la dérivée de la fonction f(x) = cos(x) ?","option_a":"sin(x)","option_b":"-sin(x)","option_c":"cos(x)","option_d":"-cos(x)","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée de cos(x) est -sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79315,"question":"La fonction tangente est-elle définie pour tout x réel ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction tangente n'est pas définie pour x = π\/2 + kπ, où k est un entier.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79316,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(π\/6) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79317,"question":"La fonction f(x) = sin(x) est-elle paire ou impaire ?","option_a":"Paire","option_b":"Impaire","option_c":"Ni paire ni impaire","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":79318,"question":"Résoudre l'équation tan(x) = √3 dans l'intervalle [0, π].","option_a":"π\/3","option_b":"π\/6","option_c":"2π\/3","option_d":"π\/4","option_e":"","option_f":"","bonne_reponse":"A","explication":"tan(π\/3) = √3, donc la solution est x = π\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79319,"question":"La dérivée de la fonction f(x) = tan(x) est-elle sec²(x) ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de tan(x) est bien sec²(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79320,"question":"Quelle est la valeur maximale de la fonction f(x) = cos(x) ?","option_a":"0","option_b":"1","option_c":"-1","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction cosinus atteint sa valeur maximale de 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":79321,"question":"La fonction f(x) = sin(x) + cos(x) 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":"C","explication":"La somme de deux fonctions périodiques de même période est périodique de cette période. Ici, sin(x) et cos(x) ont une période de 2π.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]