Quiz — C-EX13-TRM-CA.pdf

Question 1 sur 10 20:00

[{"id":9863,"question":"Quelle est la valeur de sin(π\/6) ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. √2\/2","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(π\/6) = 1\/2, car π\/6 correspond à 30° et sin(30°) = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 0\", \"b\": \"B. 1\/2\", \"c\": \"C. √2\/2\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":9864,"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":"Vrai, car cos(2π\/3) = cos(4π\/3) = -1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":9865,"question":"Quelle identité trigonométrique est correcte parmi les suivantes ?","option_a":"A. sin²(x) + cos²(x) = 1","option_b":"B. tan(x) = sin(x) + cos(x)","option_c":"C. sin(2x) = 2sin(x)","option_d":"D. cos(2x) = sin²(x) - cos²(x)","option_e":"","option_f":"","bonne_reponse":"a","explication":"L'identité fondamentale est sin²(x) + cos²(x) = 1, valable pour tout x réel.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. sin²(x) + cos²(x) = 1\", \"b\": \"B. tan(x) = sin(x) + cos(x)\", ","_debug_options_count":4},{"id":9866,"question":"La fonction f(x) = sin(x) est-elle périodique ? Si oui, quelle est sa période ?","option_a":"A. Non, elle n'est pas périodique","option_b":"B. Oui, période = π","option_c":"C. Oui, période = 2π","option_d":"D. Oui, période = π\/2","option_e":"","option_f":"","bonne_reponse":"c","explication":"La fonction sin(x) est périodique de période 2π, car sin(x + 2π) = sin(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"A. Non, elle n'est pas périodique\", \"b\": \"B. Oui, période = π\"","_debug_options_count":4},{"id":9867,"question":"L'inégalité sin(x) \u003E 0 est-elle vraie pour x ∈ ]π, 2π[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux, car sin(x) est négatif dans l'intervalle ]π, 2π[.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":9868,"question":"Quelle est la dérivée de f(x) = cos(3x) ?","option_a":"A. 3cos(3x)","option_b":"B. -3sin(3x)","option_c":"C. -sin(3x)","option_d":"D. 3sin(3x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La dérivée de cos(u) est -u' sin(u), donc f'(x) = -3 sin(3x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"A. 3cos(3x)\", \"b\": \"B. -3sin(3x)\", \"c\": \"C. -sin(3x)\", \"d\": \"D. 3","_debug_options_count":4},{"id":9869,"question":"Dans un triangle rectangle, si l'angle α a pour cosinus 3\/5, quel est son sinus ?","option_a":"A. 4\/5","option_b":"B. 3\/4","option_c":"C. 5\/3","option_d":"D. 1\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"D'après le théorème de Pythagore, sin²(α) = 1 - cos²(α) = 1 - 9\/25 = 16\/25, donc sin(α) = 4\/5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. 4\/5\", \"b\": \"B. 3\/4\", \"c\": \"C. 5\/3\", \"d\": \"D. 1\/2\"}}","_debug_options_count":4},{"id":9870,"question":"L'équation tan(x) = √3 admet-elle une solution dans l'intervalle ]0, π\/2[ ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai, car tan(π\/3) = √3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":9871,"question":"Quelle formule permet d'exprimer sin(a + b) ?","option_a":"A. sin(a)cos(b) + cos(a)sin(b)","option_b":"B. sin(a)cos(b) - cos(a)sin(b)","option_c":"C. cos(a)cos(b) - sin(a)sin(b)","option_d":"D. cos(a)cos(b) + sin(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,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"A. sin(a)cos(b) + cos(a)sin(b)\", \"b\": \"B. sin(a)cos(b) - cos(a)si","_debug_options_count":4},{"id":9872,"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":"Faux, car tan(x) n'est pas définie pour x = π\/2 + kπ (k ∈ ℤ), où cos(x) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]