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HomeLớp 11Toán lớp 11 - Sách kết nối tri thứcBài 4. Phương trình lượng giác cơ bảnBài tập trung bình
{"common":{"save":0,"post_id":"7040","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"4753","post_id":"7040","mon_id":"1158924","chapter_id":"1159141","question":"<p>V\u1edbi <span class=\"math-tex\">$x \\in [0 ; 2\\pi]$<\/span> , ph\u01b0\u01a1ng trình <span class=\"math-tex\">$sin2x-cos2x+3sinx-cosx-1=0$<\/span> có bao nhiêu nghi\u1ec7m?<\/p>","options":["<strong>A.<\/strong> 1","<strong>B.<\/strong> 3","<strong>C.<\/strong> 2","<strong>D.<\/strong> 4"],"correct":"3","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$sin2x-cos2x+3sinx-cosx-1=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$2sinxcosx+2sin^2x-1+3sinx-cosx-1=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$(2sin^2x+3sinx-2)+(2sinxcosx-cosx)=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$(2sinx-1)(sinx+2)+cosx(2sinx-1) = 0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$(2sinx-1)(sinx+cosx+2)=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$2sinx-1=0$<\/span> ho\u1eb7c <span class=\"math-tex\">$sinx+cosx+2=0$<\/span><\/p><p>Tr\u01b0\u1eddng h\u1ee3p 1: <span class=\"math-tex\">$2sinx-1=0$<\/span> ⇔ <span class=\"math-tex\">$sinx=\\dfrac{1}{2}$<\/span> <\/p><p>⇔ <span class=\"math-tex\">$x=\\dfrac{\\pi}{6}+k2\\pi$<\/span> ho\u1eb7c <span class=\"math-tex\">$x=\\dfrac{5\\pi}{6}+k2\\pi$<\/span> , k ∈ Z .<\/p><p>Vì <span class=\"math-tex\">$x \\in[0;2\\pi]$<\/span> nên ph\u01b0\u01a1ng trình có 2 nghi\u1ec7m là <span class=\"math-tex\">$x=\\dfrac{\\pi}{6};x=\\dfrac{5\\pi}{6}$<\/span> .<\/p><p>Tr\u01b0\u1eddng h\u1ee3p 2: <span class=\"math-tex\">$sinx+cosx+2=0$<\/span> ⇔ <span class=\"math-tex\">$\\sqrt{2}sin\\bigg(x+\\dfrac{\\pi}{4}\\bigg)+2=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$sin\\bigg(x+\\dfrac{\\pi}{4}\\bigg)=-\\sqrt{2}$<\/span> . Do \u0111ó ph\u01b0\u01a1ng trình vô nghi\u1ec7m.<\/p><p>V\u1eady trên <span class=\"math-tex\">$[0;2\\pi]$<\/span> , ph\u01b0\u01a1ng trình \u0111ã cho có hai nghi\u1ec7m.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 2.<\/span><\/p>","type":"choose","extra_type":"shape2","user_id":"131","test":"0","date":"2023-11-19 09:32:09","option_type":"txt","len":0},{"id":"4756","post_id":"7040","mon_id":"1158924","chapter_id":"1159141","question":"<p>Nghi\u1ec7m c\u1ee7a ph\u01b0\u01a1ng trình <span class=\"math-tex\">$sin\\bigg(\\dfrac{\\pi}{3}-x\\bigg).cos\\bigg(x-\\dfrac{\\pi}{3}\\bigg)+\\dfrac{1}{2}=0$<\/span> là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x=\\dfrac{7\\pi}{12}+k\\pi$<\/span> , k ∈ Z.","<strong>B.<\/strong> <span class=\"math-tex\">$x=\\dfrac{7\\pi}{12}+k\\dfrac{\\pi}{2}$<\/span> , k ∈ Z.","<strong>C.<\/strong> <span class=\"math-tex\">$x=-\\dfrac{7\\pi}{6}+k\\pi$<\/span> , k ∈ Z.","<strong>D.<\/strong> <span class=\"math-tex\">$x=\\dfrac{5\\pi}{6}+k2\\pi$<\/span> , k ∈ Z."],"correct":"1","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$sin\\bigg(\\dfrac{\\pi}{3}-x\\bigg)cos\\bigg(x-\\dfrac{\\pi}{3}\\bigg)+\\dfrac{1}{2}=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$-sin\\bigg(x-\\dfrac{\\pi}{3}\\bigg)cos\\bigg(x-\\dfrac{\\pi}{3}\\bigg)+\\dfrac{1}{2}=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$-\\dfrac{1}{2}sin\\bigg(2x-\\dfrac{2\\pi}{3}\\bigg)+\\dfrac{1}{2}=0$<\/span><\/p><p>⇔ <span class=\"math-tex\">$sin\\bigg(2x-\\dfrac{2\\pi}{3}\\bigg)=1$<\/span><\/p><p>⇔ <span class=\"math-tex\">$2x-\\dfrac{2\\pi}{3}=\\dfrac{\\pi}{2}+k2\\pi$<\/span><\/p><p>⇔ <span class=\"math-tex\">$x=\\dfrac{7\\pi}{12}+k\\pi$<\/span> , k ∈ Z<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$x=\\dfrac{7\\pi}{12}+k\\pi$<\/span> , k ∈ Z.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-19 09:50:44","option_type":"math","len":0},{"id":"4759","post_id":"7040","mon_id":"1158924","chapter_id":"1159141","question":"<p>Ph\u01b0\u01a1ng trình <span class=\"math-tex\">$2sinx+\\sqrt{3}=0$<\/span> có t\u1ed5ng nghi\u1ec7m d\u01b0\u01a1ng nh\u1ecf nh\u1ea5t và nghi\u1ec7m âm l\u1edbn nh\u1ea5t b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{4\\pi}{3}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$2\\pi$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{\\pi}{3}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\pi$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p><span class=\"math-tex\">$2sinx+\\sqrt{3}=0$<\/span> ⇔ <span class=\"math-tex\">$sinx=-\u200b\\dfrac{\\sqrt{3}}{2}\u200b$<\/span> <\/p><p>⇔ <span class=\"math-tex\">$sinx=sin\\bigg(-\\dfrac{\\pi}{3}\\bigg)$<\/span> <\/p><p>⇔ <span class=\"math-tex\">$x=-\\dfrac{\\pi}{3}+k2\\pi$<\/span> ho\u1eb7c <span class=\"math-tex\">$x=\\dfrac{4\\pi}{3}+k2\\pi$<\/span> , k ∈ Z.<\/p><p>Xét <span class=\"math-tex\">$x=-\\dfrac{\\pi}{3}+k2\\pi$<\/span> , k ∈ Z, ta \u0111\u01b0\u1ee3c nghi\u1ec7m d\u01b0\u01a1ng nh\u1ecf nh\u1ea5t là <span class=\"math-tex\">$x_1=\\dfrac{5\\pi}{3}\u200b\u200b$<\/span> và nghi\u1ec7m âm l\u1edbn nh\u1ea5t <span class=\"math-tex\">$x_2=-\\dfrac{\\pi}{3}$<\/span> .<\/p><p>Xét <span class=\"math-tex\">$x=\\dfrac{4\\pi}{3}+k2\\pi$<\/span> , k ∈ Z, ta \u0111\u01b0\u1ee3c nghi\u1ec7m d\u01b0\u01a1ng nh\u1ecf nh\u1ea5t là <span class=\"math-tex\">$x_3=\\dfrac{4\\pi}{3}\u200b\u200b$<\/span> và nghi\u1ec7m âm l\u1edbn nh\u1ea5t <span class=\"math-tex\">$x_4=-\\dfrac{2\\pi}{3}$<\/span> .<\/p><p>V\u1eady t\u1ed5ng nghi\u1ec7m d\u01b0\u01a1ng nh\u1ecf nh\u1ea5t và nghi\u1ec7m âm l\u1edbn nh\u1ea5t c\u1ee7a ph\u01b0\u01a1ng trình \u0111ã cho b\u1eb1ng <span class=\"math-tex\">$\\pi$<\/span> .<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$\\pi$<\/span> .<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-11-19 10:09:17","option_type":"math","len":0}]}