Quiz : Maîtrisez les fonctions trigonométriques en Terminale Math

Question 1 sur 10 10:00

[{"id":49771,"question":"Quelle est la dérivée de la fonction f(x) = sin(x) ?","option_a":"cos(x)","option_b":"sin(x)","option_c":"-cos(x)","option_d":"-sin(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de sin(x) est cos(x), une propriété fondamentale à retenir pour l'étude des variations.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49772,"question":"L'équation cos(x) = 1 admet-elle une solution dans l'intervalle [0, 2π] ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. La solution est x = 0 (ou x = 2π), car cos(0) = 1 et cos(2π) = 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49773,"question":"Quelle est la valeur de tan(π\/4) ?","option_a":"0","option_b":"1","option_c":"√2","option_d":"1\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"tan(π\/4) = 1, car sin(π\/4) = cos(π\/4) = √2\/2, donc leur rapport est 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49774,"question":"La fonction f(x) = cos(x) est-elle périodique ? Si oui, quelle est sa période ?","option_a":"Non","option_b":"Oui, période π","option_c":"Oui, période 2π","option_d":"Oui, période π\/2","option_e":"","option_f":"","bonne_reponse":"C","explication":"La fonction cos(x) est périodique de période 2π, car cos(x + 2π) = cos(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49775,"question":"L'équation sin(x) = 2 admet-elle des solutions réelles ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"Faux. La fonction sinus prend ses valeurs dans l'intervalle [-1, 1], donc sin(x) = 2 n'a pas de solution réelle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49776,"question":"Quelle est la dérivée de la fonction g(x) = tan(x) ?","option_a":"1 + tan²(x)","option_b":"1\/(1 + x²)","option_c":"sin(x)\/cos(x)","option_d":"cos(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée de tan(x) est 1 + tan²(x), ce qui équivaut à 1\/cos²(x) (formule à connaître).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49777,"question":"Dans un triangle rectangle, si un angle mesure 30°, quel est le rapport entre le côté opposé et l'hypoténuse ?","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1\/√3","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle rectangle, sin(30°) = côté opposé \/ hypoténuse = 1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49778,"question":"La fonction f(x) = sin(2x) a-t-elle une période de π ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Vrai. La période de sin(2x) est π, car sin(2(x + π)) = sin(2x + 2π) = sin(2x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49779,"question":"Quelle est la solution générale de l'équation cos(x) = √3\/2 ?","option_a":"x = π\/6 + 2kπ ou x = 11π\/6 + 2kπ, k ∈ ℤ","option_b":"x = π\/3 + 2kπ ou x = 5π\/3 + 2kπ, k ∈ ℤ","option_c":"x = π\/4 + kπ, k ∈ ℤ","option_d":"x = π\/2 + kπ, k ∈ ℤ","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les solutions sont x = π\/6 + 2kπ ou x = 11π\/6 + 2kπ (car cos(π\/6) = √3\/2 et cos(11π\/6) = √3\/2).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49780,"question":"La fonction f(x) = cos(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":"A","explication":"La fonction cos(x) est paire, car cos(-x) = cos(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]