Quiz : Maîtrisez la trigonométrie pour le Bac !

Question 1 sur 10 10:00

[{"id":56111,"question":"Quelle est la période de la fonction f(x) = sin(3x) ?","option_a":"2π","option_b":"π\/3","option_c":"2π\/3","option_d":"π","option_e":"","option_f":"","bonne_reponse":"C","explication":"La période d'une fonction sin(kx) est 2π\/k. Ici, k=3, donc la période est 2π\/3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56112,"question":"L'égalité sin²x + cos²x = 1 est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette identité trigonométrique fondamentale est valable pour tout réel x. Elle découle du théorème de Pythagore dans le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56113,"question":"Quelle est la dérivée de la fonction f(x) = cos(2x) ?","option_a":"-2sin(2x)","option_b":"-sin(2x)","option_c":"2sin(2x)","option_d":"sin(2x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de cos(u) est -u'·sin(u). Ici, u=2x, donc u'=2. Ainsi, f'(x) = -2sin(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56114,"question":"L'équation sin(x) = 0,5 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":"Oui, les solutions sont x = π\/6 et x = 5π\/6 dans l'intervalle [0, 2π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56115,"question":"Quelle formule permet d'exprimer sin(a+b) en fonction de sin(a), sin(b), cos(a) et cos(b) ?","option_a":"sin(a)cos(b) + cos(a)sin(b)","option_b":"sin(a)sin(b) + cos(a)cos(b)","option_c":"cos(a)cos(b) - sin(a)sin(b)","option_d":"sin(a)cos(b) - cos(a)sin(b)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule d'addition pour le sinus est sin(a+b) = sin(a)cos(b) + cos(a)sin(b).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56116,"question":"La fonction f(x) = tan(x) 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":"Non, la fonction tangente n'est pas définie pour x = π\/2 + kπ (k ∈ ℤ), car cos(x) = 0 à ces points.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56117,"question":"Quelle est la valeur de cos(π\/3) ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"A","explication":"cos(π\/3) = 1\/2. Cette valeur est à connaître par cœur dans le cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56118,"question":"L'équation cos(2x) = 1\/2 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":"Oui, les solutions sont x = π\/6 et x = 5π\/6 dans [0, π].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56119,"question":"Quelle est la formule de duplication pour sin(2a) ?","option_a":"2sin(a)cos(a)","option_b":"sin²(a) - cos²(a)","option_c":"cos²(a) - sin²(a)","option_d":"sin(a) + cos(a)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La formule de duplication pour sin(2a) est sin(2a) = 2sin(a)cos(a).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":56120,"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) pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]