Quiz — 11_Relation cylindriques-cartésiens.pdf

Question 1 sur 10 20:00

[{"id":189148,"question":"Quelle formule permet de convertir une coordonnée cylindrique r en coordonnée cartésienne x ?","option_a":"x = r·sin(θ)","option_b":"x = r·cos(θ)","option_c":"x = r·tan(θ)","option_d":"x = z·cos(θ)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La coordonnée cartésienne x s'obtient en multipliant le rayon r par le cosinus de l'angle θ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"x = r·sin(θ)\", \"b\": \"x = r·cos(θ)\", \"c\": \"x = r·tan(θ)\", \"d","_debug_options_count":4},{"id":189149,"question":"Les coordonnées cylindriques sont-elles toujours définies pour θ = π\/2 ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les coordonnées cylindriques sont définies pour tout angle θ, y compris θ = π\/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":189150,"question":"Quelle est la coordonnée cartésienne z dans un système cylindrique ?","option_a":"z = r","option_b":"z = θ","option_c":"z = z","option_d":"z = x + y","option_e":"","option_f":"","bonne_reponse":"c","explication":"Dans les coordonnées cylindriques, la coordonnée z reste inchangée lors de la conversion en cartésiennes.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"c\", \"options\": {\"a\": \"z = r\", \"b\": \"z = θ\", \"c\": \"z = z\", \"d\": \"z = x + y\"}}","_debug_options_count":4},{"id":189151,"question":"Pour un point de coordonnées cylindriques (2, π\/4, 3), quelle est sa coordonnée cartésienne y ?","option_a":"2","option_b":"√2","option_c":"1.5","option_d":"3","option_e":"","option_f":"","bonne_reponse":"b","explication":"y = r·sin(θ) = 2·sin(π\/4) = 2·(√2\/2) = √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\": \"2\", \"b\": \"√2\", \"c\": \"1.5\", \"d\": \"3\"}}","_debug_options_count":4},{"id":189152,"question":"Les coordonnées cartésiennes peuvent-elles représenter un point avec une symétrie cylindrique ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Les coordonnées cartésiennes peuvent représenter n'importe quel point dans l'espace, y compris ceux avec une symétrie cylindrique.","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":189153,"question":"Quelle formule permet de convertir une coordonnée cartésienne y en coordonnée cylindrique r ?","option_a":"r = y \/ cos(θ)","option_b":"r = √(x² + y²)","option_c":"r = y·sin(θ)","option_d":"r = z \/ sin(θ)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le rayon r en coordonnées cylindriques est donné par r = √(x² + y²).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"r = y \/ cos(θ)\", \"b\": \"r = √(x² + y²)\", \"c\": \"r = y·sin(θ)","_debug_options_count":4},{"id":189154,"question":"Un point de coordonnées cartésiennes (1, 1, 2) a pour coordonnées cylindriques (r, θ, z). Quelle est la valeur de r ?","option_a":"√2","option_b":"2","option_c":"1","option_d":"√3","option_e":"","option_f":"","bonne_reponse":"a","explication":"r = √(x² + y²) = √(1² + 1²) = √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\": \"√2\", \"b\": \"2\", \"c\": \"1\", \"d\": \"√3\"}}","_debug_options_count":4},{"id":189155,"question":"Les coordonnées cylindriques sont-elles adaptées pour décrire un cube ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Les coordonnées cylindriques sont moins adaptées pour décrire des objets sans symétrie cylindrique, comme un cube.","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":189156,"question":"Quelle est la coordonnée cartésienne x pour un point de coordonnées cylindriques (3, π\/3, 4) ?","option_a":"3\/2","option_b":"3·√3\/2","option_c":"4","option_d":"1.5","option_e":"","option_f":"","bonne_reponse":"b","explication":"x = r·cos(θ) = 3·cos(π\/3) = 3·(1\/2) = 3·√3\/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\": \"3\/2\", \"b\": \"3·√3\/2\", \"c\": \"4\", \"d\": \"1.5\"}}","_debug_options_count":4},{"id":189157,"question":"La conversion entre coordonnées cylindriques et cartésiennes est-elle toujours bijective ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"La conversion est bijective, sauf pour r = 0 où plusieurs valeurs de θ correspondent au même point.","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}]