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添加关联题24594

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wangweiye7840 2024-02-19 13:54:08 +08:00
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题库0.3/Problems.json
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@ -584606,7 +584606,9 @@
"20230209\t王伟叶"
],
"same": [],
"related": [],
"related": [
"024594"
],
"remark": "",
"space": "",
"unrelated": []
@ -667164,6 +667166,31 @@
"space": "4em",
"unrelated": []
},
"024594": {
"id": "024594",
"content": "根据下列条件, 分别写出角$x$的集合:\\\\\n(1) $\\sin x=\\dfrac{\\sqrt{2}}{2}$, $x$的集合为\\blank{100};\\\\\n(2) $\\cos x=-\\dfrac{1}{2}$, $x$的集合为\\blank{100};\\\\\n(3) $\\cot x=-\\sqrt{3}$, $x$的集合为\\blank{100};\\\\\n(4) $\\sin (x-\\dfrac{2 \\pi}{3})=\\dfrac{1}{2}$, $x$的集合为\\blank{100};\\\\\n(5) $\\cos (5 x+\\dfrac{\\pi}{4})=-\\dfrac{\\sqrt{3}}{2}$, $x$的集合为\\blank{100};\\\\\n(6) $\\sin (\\dfrac{4 x+7 \\pi}{2})=\\dfrac{\\sqrt{2}}{2}$, $x$的集合为\\blank{100}.",
"objs": [],
"tags": [
"第三单元"
],
"genre": "",
"ans": "(1) $\\{x | x=k \\pi+ (-1)^k \\cdot \\dfrac{\\pi}{4},\\ k \\in \\mathbf{Z}\\}$;\\\\\n(2) $\\{x | x=2k \\pi \\pm \\dfrac{2\\pi}{3},\\ k \\in \\mathbf{Z}\\}$;\\\\\n(3) $\\{x | x=k \\pi + \\dfrac{5\\pi}{6},\\ k \\in \\mathbf{Z}\\}$;\\\\\n(4) $\\{x | x=2k \\pi + \\dfrac{5\\pi}{6}$ 或$x=2k \\pi + \\dfrac{3\\pi}{2} ,\\ k \\in \\mathbf{Z}\\}$;\\\\\n第二种写法: $\\{x | x=k \\pi+ (-1)^k \\cdot \\dfrac{\\pi}{6}+\\dfrac{2\\pi}{3},\\ k \\in \\mathbf{Z}\\}$;\\\\\n(5) $\\{x | x=\\dfrac{2k \\pi}{5} + \\dfrac{7\\pi}{60}$ 或$ x=\\dfrac{2k \\pi}{5} - \\dfrac{13\\pi}{60} ,\\ k \\in \\mathbf{Z}\\}$;\\\\\n(6) $\\{x | x=k \\pi - \\dfrac{5\\pi}{8}$ 或$x=k \\pi - \\dfrac{3\\pi}{8} ,\\ k \\in \\mathbf{Z}\\}$",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一下校本作业-20240219修改",
"edit": [
"20230209\t王伟叶",
"20240219\t王伟叶"
],
"same": [],
"related": [
"021529"
],
"remark": "",
"space": "",
"unrelated": []
},
"030001": {
"id": "030001",
"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",