{"common":{"save":0,"post_id":"7044","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"4825","post_id":"7044","mon_id":"1158924","chapter_id":"1159141","question":"<p>Cho <span class=\"math-tex\">$cos\\alpha=\\dfrac{3}{7}$<\/span> và <span class=\"math-tex\">$\\dfrac{3\\pi}{2}< \\alpha < 2\\pi$<\/span>. Khi \u0111ó sinα b\u1eb1ng:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{4}{7}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$-\\dfrac{4}{7}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$-\\dfrac{2\\sqrt{10}}{7}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{2\\sqrt{10}}{7}$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Áp d\u1ee5ng công th\u1ee9c:<\/p><p>sin²α = 1 – cos²α = <span class=\"math-tex\">$1-\\dfrac{9}{49}$<\/span> = <span class=\"math-tex\">$\\dfrac{40}{49}$<\/span><\/p><p>Vì <span class=\"math-tex\">$\\dfrac{3\\pi}{2}< \\alpha < 2\\pi$<\/span> nên sinα < 0. <\/p><p>Do \u0111ó sinα = <span class=\"math-tex\">$-\\dfrac{2\\sqrt{10}}{7}$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$-\\dfrac{2\\sqrt{10}}{7}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-03 03:25:04","option_type":"math","len":0},{"id":"4826","post_id":"7044","mon_id":"1158924","chapter_id":"1159141","question":"<p>Cho cosa = <span class=\"math-tex\">$\\dfrac{1}{3}$<\/span>. Khi \u0111ó giá tr\u1ecb cos2a b\u1eb1ng:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{8}{9}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$-\\dfrac{7}{9}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$-\\dfrac{8}{9}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{7}{9}$<\/span>"],"correct":"2","level":"3","hint":"","answer":"<p>Ta có:<\/p><p>cos2a = 2cos²a – 1 = 2 . <span class=\"math-tex\">$\\dfrac{1}{9}$<\/span> – 1 = <span class=\"math-tex\">$-\\dfrac{7}{9}$<\/span><\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$-\\dfrac{7}{9}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-03 03:29:08","option_type":"math","len":0},{"id":"4829","post_id":"7044","mon_id":"1158924","chapter_id":"1159141","question":"<p>G\u1ecdi M, m l\u1ea7n l\u01b0\u1ee3t là giá tr\u1ecb l\u1edbn nh\u1ea5t và nh\u1ecf nh\u1ea5t c\u1ee7a hàm s\u1ed1 <span class=\"math-tex\">$y=5sin\\bigg(x+\\dfrac{\\pi}{6}\\bigg)+9$<\/span>. Tính t\u1ed5ng T = M + m.<\/p>","options":["<strong>A.<\/strong> T = 18","<strong>B.<\/strong> T = 14","<strong>C.<\/strong> T = 19","<strong>D.<\/strong> T = 16"],"correct":"1","level":"3","hint":"","answer":"<p>V\u1edbi m\u1ecdi x ∈ R, ta có <span class=\"math-tex\">$-1 \\le sin\\bigg(x+\\dfrac{\\pi}{6}\\bigg) \\le 1$<\/span><\/p><p> Suy ra <span class=\"math-tex\">$4\\le 5sin\\bigg(x+\\dfrac{\\pi}{6}\\bigg)+9 \\le 14$<\/span><\/p><p> hay <span class=\"math-tex\">$4\\le y \\le 14$<\/span><\/p><p>Giá tr\u1ecb l\u1edbn nh\u1ea5t c\u1ee7a hàm s\u1ed1 là M = 14 khi <span class=\"math-tex\">$sin\\bigg(x+\\dfrac{\\pi}{6}\\bigg) =1\\Leftrightarrow x=\\dfrac{\\pi}{3}+k2\\pi, (k\\in Z)$<\/span><\/p><p>Giá tr\u1ecb nh\u1ecf nh\u1ea5t c\u1ee7a hàm s\u1ed1 là m = 4 khi <span class=\"math-tex\">$sin\\bigg(x+\\dfrac{\\pi}{6}\\bigg) =-1\\Leftrightarrow x=-\\dfrac{2\\pi}{3}+k2\\pi, (k\\in Z)$<\/span><\/p><p>V\u1eady T = M + m = 14 + 4 = 18<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> T = 18<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-12-03 03:39:33","option_type":"txt","len":0}]}