Quiz — Exercices - Fonctions circulaires.pdf

Question 1 sur 10 20:00

[{"id":84830,"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) = sin(30°) = 1\/2, valeur à connaître par cœur.","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":84831,"question":"L'équation sin 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 = 7π\/6 et x = 11π\/6 dans [0, 2π].","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":84832,"question":"Quelle identité trigonométrique est toujours vraie ?","option_a":"A. sin²x + cos²x = 0","option_b":"B. sin²x + cos²x = 1","option_c":"C. sin²x - cos²x = 1","option_d":"D. 2sinx = sin(2x)","option_e":"","option_f":"","bonne_reponse":"b","explication":"L'identité fondamentale est sin²x + cos²x = 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\": \"b\", \"options\": {\"a\": \"A. sin²x + cos²x = 0\", \"b\": \"B. sin²x + cos²x = 1\", \"c\": \"C. ","_debug_options_count":4},{"id":84833,"question":"La fonction tangente est-elle définie pour x = π\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"tan(π\/2) n'est pas défini car cos(π\/2) = 0, et tan x = sin x \/ cos x.","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":84834,"question":"Quelle est la période de la fonction cosinus ?","option_a":"A. π\/2","option_b":"B. π","option_c":"C. 2π","option_d":"D. 4π","option_e":"","option_f":"","bonne_reponse":"c","explication":"La fonction cosinus a une période de 2π, car cos(x + 2π) = cos 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. π\/2\", \"b\": \"B. π\", \"c\": \"C. 2π\", \"d\": \"D. 4π\"}}","_debug_options_count":4},{"id":84835,"question":"L'équation cos(2x) = 0 admet-elle des solutions dans [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 = 3π\/4 dans [0, π].","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":84836,"question":"Quelle est la valeur de cos(π\/3) ?","option_a":"A. 0","option_b":"B. 1\/2","option_c":"C. √3\/2","option_d":"D. 1","option_e":"","option_f":"","bonne_reponse":"b","explication":"cos(π\/3) = cos(60°) = 1\/2, valeur fondamentale à retenir.","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. √3\/2\", \"d\": \"D. 1\"}}","_debug_options_count":4},{"id":84837,"question":"La fonction sinus est-elle paire ou impaire ?","option_a":"A. Paire","option_b":"B. Impaire","option_c":"C. Ni paire ni impaire","option_d":"D. Les deux","option_e":"","option_f":"","bonne_reponse":"b","explication":"sin(-x) = -sin x, donc la fonction sinus est impaire.","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. Paire\", \"b\": \"B. Impaire\", \"c\": \"C. Ni paire ni impaire\", \"d\":","_debug_options_count":4},{"id":84838,"question":"Quelle est la solution générale de l'équation sin x = 1 ?","option_a":"A. x = π\/2 + 2kπ","option_b":"B. x = π\/2 + kπ","option_c":"C. x = kπ","option_d":"D. x = π + 2kπ","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les solutions sont x = π\/2 + 2kπ, où k est un entier relatif.","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. x = π\/2 + 2kπ\", \"b\": \"B. x = π\/2 + kπ\", \"c\": \"C. x = kπ\",","_debug_options_count":4},{"id":84839,"question":"L'identité 1 + tan²x = 1\/cos²x est-elle toujours vraie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette identité découle de sin²x + cos²x = 1 et est valable pour tout x 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\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]