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收录I20260201新题

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weiye.wang 2024-02-17 17:01:34 +08:00
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题库0.3/Problems.json
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@ -96356,7 +96356,9 @@
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@ -666955,6 +666966,200 @@
"space": "4em",
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"024585": {
"id": "024585",
"content": "计算:\\\\\n(1) $6 \\cos 270^{\\circ}+10 \\sin 0^{\\circ}-4 \\tan 180^{\\circ}+5 \\cos 360^{\\circ}=$\\blank{50}.\\\\\n(2) $\\sin ^2 \\dfrac{\\pi}{4}-\\cos ^2 \\dfrac{\\pi}{2}+2 \\tan ^3 \\dfrac{\\pi}{4}=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240217\t王伟叶"
],
"same": [],
"related": [
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"remark": "",
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},
"024586": {
"id": "024586",
"content": "已知一个扇形的圆心角是 $\\dfrac{\\pi}{3}$, 弧长等于 $\\pi \\mathrm{cm}$, 则这个扇形的半径是\\blank{50}cm.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240217\t王伟叶"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024587": {
"id": "024587",
"content": "若 $\\dfrac{\\cos \\alpha}{\\sin \\alpha}=2$, 则 $\\dfrac{3 \\sin \\alpha-2 \\cos \\alpha}{2 \\sin \\alpha-3 \\cos \\alpha}$ 的值是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
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"same": [],
"related": [
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"remark": "",
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"024588": {
"id": "024588",
"content": "若 $\\tan \\beta=-\\dfrac{\\sqrt{3}}{3}$, 且 $\\dfrac{\\pi}{2}<\\beta<\\pi$, 则 $\\beta=$\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240217\t王伟叶"
],
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"024589": {
"id": "024589",
"content": "若 $\\sin \\theta \\geq 0$ 且 $\\tan \\theta \\leq 0$, 请用集合的形式表达 $\\theta$ 的范围是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
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],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024590": {
"id": "024590",
"content": "已知 $\\sin \\alpha+\\cos \\alpha=\\dfrac{1}{5}$, $0<\\alpha<\\pi$, 则 $\\sin \\alpha-\\cos \\alpha$ 的值是\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
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"024591": {
"id": "024591",
"content": "下面命题中, 正确的命题序号是\\blank{50}.\\\\\n\\textcircled{1} 与 $-\\dfrac{\\pi}{3}$ 终边相同的角的集合是 $\\{\\alpha | \\alpha=k \\cdot 360^{\\circ}-60^{\\circ}\\}$;\\\\\n\\textcircled{2} 若 $A=\\{\\alpha | \\alpha=\\dfrac{k \\pi}{6}, k \\in \\mathbf{Z}\\}$, $B=\\{\\beta | \\beta=\\dfrac{k \\pi}{2}$ 或 $\\dfrac{k \\pi}{2}\\pm \\dfrac{5 \\pi}{6}, k \\in \\mathbf{Z}\\}$, $C=\\{\\gamma | \\gamma=-\\dfrac{k \\pi}{6}, k \\in \\mathbf{Z}\\}$, 则 $A=B=C$;\\\\\n\\textcircled{3} 若 $\\alpha$ 在第三象限, 则 $\\dfrac{\\alpha}{3}$ 一定不在第三象限;\\\\\n\\textcircled{4} ``$\\alpha$ 是锐角''是``$2 \\alpha$ 是第一、二象限的角''的充分不必要条件.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
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],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"024592": {
"id": "024592",
"content": "已知角 $\\alpha$ 的顶点与坐标原点 $O$ 重合, 始边在 $x$ 轴的正半轴上, 终边上有一点 $P(1+m, 1-m)$, 并且 $\\sin \\alpha=-\\dfrac{\\sqrt{5}}{5}$. 求 $m$ 的值及 $\\cos \\alpha$、$\\tan\\alpha$ 的值.",
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"genre": "解答题",
"ans": "",
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"duration": -1,
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},
"024593": {
"id": "024593",
"content": "已知 $\\tan ^2 \\alpha=2 \\tan ^2 \\beta+1$, 求 $\\sin ^2 \\beta-2 \\sin ^2 \\alpha-1$ 的值.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
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"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.",
@ -725027,7 +725232,9 @@
"20230224\t王伟叶"
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@ -725049,7 +725256,9 @@
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