From 4cf9fb18d79ea6dc7bdc4c1a158b9731c2c3bfaf Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 10:53:59 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A22=E6=96=B0=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 200 +++++++++++++++++++++++++++++++ 2 files changed, 203 insertions(+) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index 76edd777..6151de94 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -64,3 +64,6 @@ 20240125-105050 023779:023788 +20240125-105348 +023789:023798 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index c023ed8b..8b09236f 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -642205,6 +642205,206 @@ "space": "4em", "unrelated": [] }, + "023789": { + "id": "023789", + "content": "若 $\\tan \\alpha=2$, 且 $\\alpha$ 为第三象限的角, 则 $\\sin \\alpha=$\\blank{50}, $\\cos \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023790": { + "id": "023790", + "content": "若 $1+\\cos ^2 \\theta=3 \\sin \\theta \\cos \\theta$, 则 $\\tan \\theta$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023791": { + "id": "023791", + "content": "若 $\\sin \\theta \\cos \\theta=\\dfrac{1}{8}$, $\\theta \\in(\\dfrac{\\pi}{4}, \\dfrac{\\pi}{2})$, 则 $\\cos \\theta-\\sin \\theta=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023792": { + "id": "023792", + "content": "若 $\\dfrac{2 \\cos x+3 \\sin x}{\\sin x-2 \\cos x}=7$, 则 $\\tan x=$\\blank{50}, $\\cos ^2 x-5 \\sin ^2 x-2=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023793": { + "id": "023793", + "content": "若 $f(\\alpha)=\\dfrac{2 \\sin (\\pi+\\alpha) \\cos (\\pi-\\alpha)-\\cos (\\pi+\\alpha)}{1+\\sin ^2 \\alpha+\\cos (\\dfrac{3 \\pi}{2}+\\alpha)-\\sin ^2(\\dfrac{\\pi}{2}+\\alpha)}$($1+2 \\sin \\alpha \\neq 0$), 则$f(-\\dfrac{23 \\pi}{6})=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023794": { + "id": "023794", + "content": "若 $\\dfrac{\\sin \\alpha+3 \\cos \\alpha}{3 \\cos \\alpha-\\sin \\alpha}=5$, 则 $\\cos ^2 \\alpha+\\dfrac{1}{2}\\sin 2 \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023795": { + "id": "023795", + "content": "若 $\\sin \\alpha=\\dfrac{k-3}{k+5}$, $\\cos \\alpha=\\dfrac{4-2 k}{k+5}$, $\\dfrac{\\pi}{2}<\\alpha<\\pi$, 则 $\\tan \\alpha=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023796": { + "id": "023796", + "content": "已知 $\\cos \\alpha=\\dfrac{4}{5}$, 则 $\\dfrac{\\cos (\\alpha-\\dfrac{\\pi}{2})+2 \\sin (3 \\pi-\\alpha)}{2 \\tan (3 \\pi+\\alpha)+\\cot (\\dfrac{\\pi}{2}+\\alpha)}$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023797": { + "id": "023797", + "content": "已知 $\\sin \\theta+\\cos \\theta=-\\dfrac{1}{5}$ 且 $\\theta \\in(0, \\pi)$, 则 $\\tan \\theta$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023798": { + "id": "023798", + "content": "已知 $\\tan x-\\dfrac{1}{\\cos x}=\\sqrt{\\dfrac{1-\\sin x}{1+\\sin x}}$, 求 $x$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "4em", + "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