Quiz : Maîtrisez la trigonométrie en 3ème année secondaire

Question 1 sur 10 10:00

[{"id":17958,"question":"Quelle est la valeur de sin(30°) ?","option_a":"0","option_b":"1\/2","option_c":"√2\/2","option_d":"√3\/2","option_e":"","option_f":"","bonne_reponse":"B","explication":"La valeur de sin(30°) est 1\/2, valeur fondamentale à retenir pour les angles remarquables.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17959,"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, appelée relation fondamentale de la trigonométrie, est valable pour tout angle x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17960,"question":"Résoudre l'équation sin(x) = √3\/2 pour x ∈ [0, 360°].","option_a":"30° et 150°","option_b":"60° et 120°","option_c":"45° et 315°","option_d":"0° et 180°","option_e":"","option_f":"","bonne_reponse":"B","explication":"Les solutions de sin(x) = √3\/2 dans [0, 360°] sont 60° et 120° car sin(60°) = sin(120°) = √3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17961,"question":"La tangente d'un angle est-elle définie pour tout angle ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La tangente n'est pas définie pour les angles où cos(x) = 0, c'est-à-dire 90° + k×180° (k ∈ ℤ).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17962,"question":"Simplifier l'expression sin(x)cos(x) + cos(x)sin(x).","option_a":"sin(2x)","option_b":"2sin(x)cos(x)","option_c":"cos(2x)","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'expression se simplifie en 2sin(x)cos(x) grâce à l'identité sin(2x) = 2sin(x)cos(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17963,"question":"Quelle identité permet d'exprimer cos(2x) en fonction de sin(x) ?","option_a":"cos(2x) = 1 - 2sin²(x)","option_b":"cos(2x) = 2cos²(x) - 1","option_c":"cos(2x) = sin²(x) - cos²(x)","option_d":"cos(2x) = 2sin(x)cos(x)","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'identité cos(2x) = 1 - 2sin²(x) permet d'exprimer cos(2x) uniquement en fonction de sin(x).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17964,"question":"Résoudre cos(x) = -1\/2 pour x ∈ [0, 360°].","option_a":"120° et 240°","option_b":"60° et 300°","option_c":"150° et 210°","option_d":"30° et 330°","option_e":"","option_f":"","bonne_reponse":"A","explication":"Les solutions de cos(x) = -1\/2 dans [0, 360°] sont 120° et 240° car cos(120°) = cos(240°) = -1\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17965,"question":"L'identité tan(x) = sin(x)\/cos(x) est-elle valable pour x = 90° ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"L'identité n'est pas valable pour x = 90° car cos(90°) = 0, ce qui rend tan(90°) indéfinie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17966,"question":"Calculer sin(45°) + cos(45°).","option_a":"√2","option_b":"1","option_c":"2","option_d":"0","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(45°) = cos(45°) = √2\/2, donc sin(45°) + cos(45°) = √2\/2 + √2\/2 = √2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":17967,"question":"Quelle est la période de la fonction sin(x) ?","option_a":"π","option_b":"2π","option_c":"π\/2","option_d":"4π","option_e":"","option_f":"","bonne_reponse":"B","explication":"La fonction sin(x) est périodique de période 2π, c'est-à-dire sin(x + 2π) = sin(x) pour tout x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]