Trigonométrie et Algèbre — 3ème Année Secondaire

Question 1 sur 10 10:00

[{"id":49241,"question":"Dans un triangle rectangle ABC avec un angle de 30°, si l'hypoténuse mesure 10 cm, quelle est la longueur du côté opposé à l'angle de 30° ?","option_a":"5 cm","option_b":"5√3 cm","option_c":"10\/√3 cm","option_d":"10 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"Le côté opposé à un angle de 30° dans un triangle rectangle est égal à la moitié de l'hypoténuse (sin 30° = 0.5).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49242,"question":"La formule cos²(x) + sin²(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 trigonométrique fondamentale est vraie pour tout angle réel x.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49243,"question":"Résolvez l'équation : 2x² - 8x + 6 = 0.","option_a":"x = 1 ou x = 3","option_b":"x = -1 ou x = -3","option_c":"x = 2 ou x = 4","option_d":"x = 0 ou x = 4","option_e":"","option_f":"","bonne_reponse":"A","explication":"En factorisant : 2(x² - 4x + 3) = 0 → (x-1)(x-3)=0 → x=1 ou x=3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49244,"question":"Si tan(θ) = √3, alors θ est égal à :","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"C","explication":"tan(60°) = √3, donc θ = 60°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49245,"question":"L'identité (a + b)² = a² + 2ab + b² est-elle correcte ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Cette identité est correcte et fait partie des identités remarquables.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49246,"question":"Calculez sin(45°) :","option_a":"1\/2","option_b":"√2\/2","option_c":"√3\/2","option_d":"1","option_e":"","option_f":"","bonne_reponse":"B","explication":"sin(45°) = √2\/2, une valeur fondamentale en trigonométrie.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49247,"question":"Un triangle rectangle a un angle de 45°. Si l'un des côtés adjacents mesure 5 cm, quelle est la longueur de l'hypoténuse ?","option_a":"5√2 cm","option_b":"10 cm","option_c":"5 cm","option_d":"5\/√2 cm","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans un triangle rectangle isocèle (45°), l'hypoténuse = côté × √2 → 5√2 cm.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49248,"question":"La formule a² - b² = (a - b)(a + b) est-elle une identité remarquable ?","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Oui, c'est une identité remarquable utilisée pour factoriser des différences de carrés.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49249,"question":"Résolvez l'équation trigonométrique : 2cos(x) = √2.","option_a":"x = 30°","option_b":"x = 45°","option_c":"x = 60°","option_d":"x = 90°","option_e":"","option_f":"","bonne_reponse":"B","explication":"cos(x) = √2\/2 → x = 45° (ou 315° dans [0°, 360°]).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":49250,"question":"Si sin(θ) = 0.5, alors θ peut être égal à :","option_a":"30°","option_b":"45°","option_c":"60°","option_d":"90°","option_e":"","option_f":"","bonne_reponse":"A","explication":"sin(30°) = 0.5, donc θ = 30° (ou 150° dans [0°, 360°]).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]