Quiz — Sommes trigonométriques.pdf

Question 1 sur 10 20:00

[{"id":10773,"question":"Quelle est la valeur de sin(π\/6) + cos(π\/3) ?","option_a":"1","option_b":"0.5","option_c":"1.5","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"sin(π\/6) = 0.5 et cos(π\/3) = 0.5, donc leur somme est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"1\", \"b\": \"0.5\", \"c\": \"1.5\", \"d\": \"√3\/2\"}}","_debug_options_count":4},{"id":10774,"question":"L'identité sin²(x) + cos²(x) = 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 est une propriété fondamentale de la trigonométrie, valable pour tout réel x.","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":10775,"question":"Quelle formule permet d'exprimer sin(a)cos(b) en fonction de sin(a+b) et sin(a-b) ?","option_a":"sin(a)cos(b) = [sin(a+b) + sin(a-b)]\/2","option_b":"sin(a)cos(b) = [sin(a+b) - sin(a-b)]\/2","option_c":"sin(a)cos(b) = [cos(a+b) + cos(a-b)]\/2","option_d":"sin(a)cos(b) = [cos(a+b) - cos(a-b)]\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte est sin(a)cos(b) = [sin(a+b) + sin(a-b)]\/2, issue des identités trigonométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"sin(a)cos(b) = [sin(a+b) + sin(a-b)]\/2\", \"b\": \"sin(a)cos(b) = [si","_debug_options_count":4},{"id":10776,"question":"La somme cos(π\/4) + cos(3π\/4) est-elle égale à 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"cos(π\/4) = √2\/2 et cos(3π\/4) = -√2\/2, donc leur somme est 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},{"id":10777,"question":"Quelle est la valeur de sin(π\/3)cos(π\/6) + cos(π\/3)sin(π\/6) ?","option_a":"1","option_b":"0.5","option_c":"√3\/2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"Cette expression correspond à sin(π\/3 + π\/6) = sin(π\/2) = 1, d'après la formule sin(a+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\": \"1\", \"b\": \"0.5\", \"c\": \"√3\/2\", \"d\": \"0\"}}","_debug_options_count":4},{"id":10778,"question":"L'identité cos(2a) = 1 - 2sin²(a) est-elle correcte ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"C'est une forme valide de l'identité de duplication pour le cosinus, équivalente à cos(2a) = cos²(a) - sin²(a).","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":10779,"question":"Quelle formule permet d'exprimer cos(a)cos(b) en fonction de cos(a+b) et cos(a-b) ?","option_a":"cos(a)cos(b) = [cos(a+b) + cos(a-b)]\/2","option_b":"cos(a)cos(b) = [cos(a+b) - cos(a-b)]\/2","option_c":"cos(a)cos(b) = [sin(a+b) + sin(a-b)]\/2","option_d":"cos(a)cos(b) = [sin(a+b) - sin(a-b)]\/2","option_e":"","option_f":"","bonne_reponse":"a","explication":"La formule correcte est cos(a)cos(b) = [cos(a+b) + cos(a-b)]\/2, issue des identités trigonométriques.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"cos(a)cos(b) = [cos(a+b) + cos(a-b)]\/2\", \"b\": \"cos(a)cos(b) = [co","_debug_options_count":4},{"id":10780,"question":"La somme sin(π\/2) + sin(3π\/2) est-elle égale à 0 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"sin(π\/2) = 1 et sin(3π\/2) = -1, donc leur somme est 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},{"id":10781,"question":"Quelle est la valeur de sin(π\/4)cos(π\/4) ?","option_a":"0.5","option_b":"√2\/2","option_c":"1","option_d":"0","option_e":"","option_f":"","bonne_reponse":"a","explication":"sin(π\/4) = cos(π\/4) = √2\/2, donc leur produit est (√2\/2)² = 0.5.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0.5\", \"b\": \"√2\/2\", \"c\": \"1\", \"d\": \"0\"}}","_debug_options_count":4},{"id":10782,"question":"L'identité tan(a+b) = (tan(a) + tan(b))\/(1 - tan(a)tan(b)) est-elle toujours définie ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Cette identité n'est pas définie lorsque 1 - tan(a)tan(b) = 0, c'est-à-dire lorsque tan(a)tan(b) = 1.","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}]