Quiz — حلول تمارين الزوايا الموجهة. 2020_2.pdf

Question 1 sur 5 10:00

[{"id":288,"question":"Quelle est la mesure principale de l'angle orienté -7π\/4 radians ?","option_a":"π\/4 radians","option_b":"-3π\/4 radians","option_c":"π\/4 radians (positif)","option_d":"5π\/4 radians","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour trouver la mesure principale, on ajoute ou soustrait 2π jusqu'à obtenir une valeur entre 0 et 2π. Ici, -7π\/4 + 2π = -7π\/4 + 8π\/4 = π\/4.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":289,"question":"Si sin(θ) = -√3\/2 et cos(θ) = -1\/2, dans quel quadrant se trouve l'angle θ ?","option_a":"Premier quadrant","option_b":"Deuxième quadrant","option_c":"Troisième quadrant","option_d":"Quatrième quadrant","option_e":"","option_f":"","bonne_reponse":"C","explication":"Un angle dont le sinus et le cosinus sont tous deux négatifs se situe dans le troisième quadrant du cercle trigonométrique.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":290,"question":"Quelle est la valeur de tan(π\/3) ?","option_a":"1\/2","option_b":"√3\/2","option_c":"√3","option_d":"1","option_e":"","option_f":"","bonne_reponse":"C","explication":"tan(π\/3) = sin(π\/3)\/cos(π\/3) = (√3\/2)\/(1\/2) = √3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":291,"question":"Un angle orienté a pour mesure 5π\/6 radians. Quelle est sa mesure en degrés ?","option_a":"75°","option_b":"120°","option_c":"150°","option_d":"210°","option_e":"","option_f":"","bonne_reponse":"C","explication":"Pour convertir des radians en degrés, on multiplie par 180\/π. Ainsi, 5π\/6 × (180\/π) = 150°.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":292,"question":"Si cos(θ) = 0,5 et que θ est un angle orienté du premier quadrant, quelle est la valeur de sin(θ) ?","option_a":"√3\/2","option_b":"1\/2","option_c":"-√3\/2","option_d":"-1\/2","option_e":"","option_f":"","bonne_reponse":"A","explication":"Dans le premier quadrant, sin(θ) est positif. D'après le théorème de Pythagore, sin²(θ) + cos²(θ) = 1, donc sin(θ) = √(1 - 0,5²) = √3\/2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]