From 69c13e796d0c4d6e5d65357034ef511488ef78bf Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Fri, 5 May 2023 19:59:59 +0800 Subject: [PATCH] =?UTF-8?q?=E6=B7=BB=E5=8A=A0=E9=AB=98=E4=B8=89=E6=98=93?= =?UTF-8?q?=E9=94=99=E9=A2=984=E8=AF=BE=E5=89=8D=E4=BD=BF=E7=94=A8?= =?UTF-8?q?=E6=95=B0=E6=8D=AE?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/修改题目数据库.py | 2 +- .../小闲平台作业测验数据导入_2023届.ipynb | 6 +- 工具/文本文件/metadata.txt | 1646 ++++------------- 题库0.3/Problems.json | 198 +- 4 files changed, 525 insertions(+), 1327 deletions(-) diff --git a/工具/修改题目数据库.py b/工具/修改题目数据库.py index ed2cb685..21f7196a 100644 --- a/工具/修改题目数据库.py +++ b/工具/修改题目数据库.py @@ -1,6 +1,6 @@ import os,re,json """这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭, 随后运行第二个代码块""" -problems = "13921" +problems = "015121" def generate_number_set(string,dict): string = re.sub(r"[\n\s]","",string) diff --git a/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb b/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb index 7a54461d..8d8cbfd5 100644 --- a/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb +++ b/工具/分年级专用工具/小闲平台作业测验数据导入_2023届.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -14,7 +14,7 @@ "filepath = \"数据导入作业文件\"\n", "\n", "# date = str(time.localtime().tm_year)+str(time.localtime().tm_mon).zfill(2)+str(time.localtime().tm_mday).zfill(2)\n", - "date = \"20230419\"\n", + "date = \"20230420\"\n", "\n", "#生成文件名tex_file和zip_file\n", "files = [os.path.join(filepath,f) for f in os.listdir(filepath)]\n", @@ -108,7 +108,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.15" + "version": "3.9.15" }, "orig_nbformat": 4, "vscode": { diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index c80f68b0..ab0cee67 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,1478 +1,506 @@ -ans +usages -021441 -错误, 正确, 错误, 错误 +000363 +20230420 2023届高三10班 0.833 +000625 +20230420 2023届高三10班 0.733 -021442 -D +002372 +20230420 2023届高三10班 0.867 +003421 +20230420 2023届高三10班 1.000 -021443 -C +010951 +20230420 2023届高三10班 0.700 +012255 +20230420 2023届高三10班 0.767 -021444 -A +013097 +20230420 2023届高三10班 0.567 +013118 +20230420 2023届高三10班 0.767 -021445 -C +031387 +20230420 2023届高三10班 0.600 +031323 +20230420 2023届高三10班 0.867 -021446 -D +031386 +20230420 2023届高三10班 0.233 +008866 +20230420 2023届高三10班 0.900 -021447 -$-390^\circ$ +012199 +20230420 2023届高三10班 0.867 0.600 +013134 +20230420 2023届高三10班 0.967 0.800 0.500 -021448 -$304^\circ$, $-56^\circ$ +000363 +20230420 2023届高三11班 0.870 +000625 +20230420 2023届高三11班 0.826 -021449 -$-144^\circ$ +002372 +20230420 2023届高三11班 1.000 +003421 +20230420 2023届高三11班 0.783 -021450 -二, 四 +010951 +20230420 2023届高三11班 0.696 +012255 +20230420 2023届高三11班 0.696 -021451 -(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$ +013097 +20230420 2023届高三11班 0.522 +013118 +20230420 2023届高三11班 0.522 -021452 -\begin{tikzpicture}[>=latex] -\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle; -\draw (30:2) -- (0,0) -- (60:2); -\draw [->] (-2,0) -- (2,0) node [below] {$x$}; -\draw [->] (0,-2) -- (0,2) node [left] {$y$}; -\draw (0,0) node [below left] {$O$}; -\end{tikzpicture} +031387 +20230420 2023届高三11班 0.522 +031323 +20230420 2023届高三11班 0.783 -021453 -$-1290^{\circ}$;第二象限 +031386 +20230420 2023届高三11班 0.261 +008866 +20230420 2023届高三11班 1.000 -021454 -(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. +012199 +20230420 2023届高三11班 1.000 0.652 +013134 +20230420 2023届高三11班 1.000 0.826 0.217 -021455 -(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\ -(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. +000363 +20230420 2023届高三12班 1.000 +000625 +20230420 2023届高三12班 0.809 -021456 -C +002372 +20230420 2023届高三12班 0.905 +003421 +20230420 2023届高三12班 0.857 -021457 -B +010951 +20230420 2023届高三12班 0.714 +012255 +20230420 2023届高三12班 0.762 -021458 -$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$ +013097 +20230420 2023届高三12班 0.762 +013118 +20230420 2023届高三12班 0.619 -021459 -(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$ +031387 +20230420 2023届高三12班 0.476 +031323 +20230420 2023届高三12班 0.809 -021460 -$\sqrt{3}$ +031386 +20230420 2023届高三12班 0.524 +008866 +20230420 2023届高三12班 0.905 -021461 -(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ +012199 +20230420 2023届高三12班 0.952 0.619 +013134 +20230420 2023届高三12班 0.952 0.667 0.714 -021462 -(1)$16\pi+\frac{2\pi}{3}$,二;\\ -(2)$-18\pi+\frac{4\pi}{3}$,三;\\ -(3)$-2\pi+\frac{7\pi}{5}$,三;\\ -(4)$-2\pi+\frac{3\pi}{4}$,二. +000363 +20230420 2023届高三01班 0.905 +000625 +20230420 2023届高三01班 1.000 -021463 -$\frac{1}{2}$ +002372 +20230420 2023届高三01班 0.905 +003421 +20230420 2023届高三01班 1.000 -021464 -(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. +010951 +20230420 2023届高三01班 0.905 +012255 +20230420 2023届高三01班 1.000 -021465 -(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ -(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\ -(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\ -(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. +013097 +20230420 2023届高三01班 1.000 +013118 +20230420 2023届高三01班 1.000 -021466 -(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. +031387 +20230420 2023届高三01班 1.000 +031323 +20230420 2023届高三01班 0.952 -021467 -(1) 第四象限；第四象限；\\ -(2) 第二象限或者第四象限；第一象限或第二象限或者$y$轴正半轴. +031386 +20230420 2023届高三01班 0.619 +008866 +20230420 2023届高三01班 1.000 -021468 -$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ +012199 +20230420 2023届高三01班 0.952 0.809 +013134 +20230420 2023届高三01班 1.000 0.905 0.809 -021469 -\begin{tabular}{|c|c|c|c|c|c|} -\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\ -\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\ -\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\ -\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\ -\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\ -\hline -\end{tabular} +000363 +20230420 2023届高三02班 0.774 +000625 +20230420 2023届高三02班 0.677 -021470 -$2\sqrt{5}$ +002372 +20230420 2023届高三02班 0.871 +003421 +20230420 2023届高三02班 0.871 -021471 -$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ +010951 +20230420 2023届高三02班 0.935 +012255 +20230420 2023届高三02班 0.452 -021472 -$ \left( -2,\frac{2}{3} \right)$ +013097 +20230420 2023届高三02班 0.677 +013118 +20230420 2023届高三02班 0.871 -021473 -$<$ +031387 +20230420 2023届高三02班 0.452 +031323 +20230420 2023届高三02班 0.935 -021474 -5 +031386 +20230420 2023届高三02班 0.484 +008866 +20230420 2023届高三02班 0.968 -021475 -2 +012199 +20230420 2023届高三02班 0.935 0.516 +013134 +20230420 2023届高三02班 1.000 0.839 0.645 -021476 -当$t=\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha =- \frac{\sqrt{15}}{3}$;\\ -当$t=-\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha = \frac{\sqrt{15}}{3}$;\\ -当$t=0$时, $\cos \alpha=-1$, $\tan \alpha = 0$. +000363 +20230420 2023届高三03班 0.875 +000625 +20230420 2023届高三03班 0.875 -021477 -当$\alpha$在第二象限时，$ \sin \alpha =\frac{4}{5}$, $\tan \alpha=-\frac{4}{3}$;\\ -当$\alpha$在第三象限时，$ \sin \alpha =-\frac{4}{5}$, $\tan \alpha=\frac{4}{3}$. +002372 +20230420 2023届高三03班 0.792 +003421 +20230420 2023届高三03班 0.750 -021478 -$-\frac{\sqrt{3}}{4}$ +010951 +20230420 2023届高三03班 0.875 +012255 +20230420 2023届高三03班 0.708 -021479 -(1) 第四象限； (2) 第一、四象限；(3)第一、三象限；(4)第一、三象限. +013097 +20230420 2023届高三03班 0.458 +013118 +20230420 2023届高三03班 0.708 -021480 -$A=\left\{ -2,-0,4 \right\}$ +031387 +20230420 2023届高三03班 0.458 +031323 +20230420 2023届高三03班 0.875 -021481 -(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ -(2) $[0,3)$ +031386 +20230420 2023届高三03班 0.292 +008866 +20230420 2023届高三03班 0.917 -021482 -\begin{center} -\begin{tabular}{|c|c|c|c|c|c|} -\hline$\alpha$&$\dfrac{\pi}{3}$&$\dfrac{7 \pi}{4}$&$\dfrac{2021 \pi}{2}$&$-\dfrac{\pi}{6}$&$-\dfrac{22 \pi}{3}$\\ -\hline$\sin \alpha$& $\frac{\sqrt{3}}{2}$ &$-\frac{\sqrt{2}}{2}$ & $1$&$-\frac{1}{2}$ &$\frac{\sqrt{3}}{2}$ \\ -\hline$\cos \alpha$&$\frac{1}{2}$ &$\frac{\sqrt{2}}{2}$ & $0$&$\frac{\sqrt{3}}{2}$ &$-\frac{1}{2}$ \\ -\hline$\tan \alpha$&$\sqrt{3}$ &$-1$ & 不存在 &$-\frac{\sqrt{3}}{3}$ &$-\sqrt{3}$\\ -\hline$\cot \alpha$&$\frac{\sqrt{3}}{3}$ &$-1$ & $ 0$&$-\sqrt{3}$ &$-\frac{\sqrt{3}}{3}$ \\ -\hline -\end{tabular} -\end{center} +012199 +20230420 2023届高三03班 0.958 0.750 +013134 +20230420 2023届高三03班 0.958 0.833 0.542 -021483 -(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\ -(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$ +000363 +20230420 2023届高三04班 0.769 +000625 +20230420 2023届高三04班 0.923 -021484 -$-\frac{2\sqrt{5}}{5}$;$2$ +002372 +20230420 2023届高三04班 0.846 +003421 +20230420 2023届高三04班 0.923 -021485 -\textcircled{2} \textcircled{4} +010951 +20230420 2023届高三04班 0.615 +012255 +20230420 2023届高三04班 0.769 -021486 -当$\alpha$在第一象限时，$ \sin \alpha =\frac{3\sqrt{10}}{10}$, $\cos \alpha =\frac{\sqrt{10}}{10}$,$\tan \alpha=3$;\\ -当$\alpha$在第三象限时，$ \sin \alpha =-\frac{3\sqrt{10}}{10}$,$\cos \alpha =-\frac{\sqrt{10}}{10}$, $\tan \alpha=3$. +013097 +20230420 2023届高三04班 0.615 +013118 +20230420 2023届高三04班 0.692 -021487 -$\sin k\pi =0$;\\$\cos k\pi=\left\{ - \begin{array}{lc} - $1$, & k=2n \\ - $ -1$ , &k=2n-1\\ - \end{array} -\right.$ ($n \in \mathbf{Z}$). +031387 +20230420 2023届高三04班 0.308 +031323 +20230420 2023届高三04班 0.769 -021488 -(1) $\{\theta | 2k \pi+\dfrac{\pi}{3}<\theta<2k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$;\\ -(2) $\{\theta | k \pi-\dfrac{\pi}{2}<\theta \le k \pi-\dfrac{\pi}{6},\ k \in \mathbf{Z} \}$;\\ -(3) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. +031386 +20230420 2023届高三04班 0.538 +008866 +20230420 2023届高三04班 1.000 -021489 -第二象限 +012199 +20230420 2023届高三04班 0.846 0.615 +013134 +20230420 2023届高三04班 1.000 0.615 0.615 -021490 -(1) 当$\dfrac{\alpha}{2}$在第二象限时，点$P$在第四象限；\\ -当$\dfrac{\alpha}{2}$在第四象限时，点$P$在第二象限.\\ -(2) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ +000363 +20230420 2023届高三05班 0.914 +000625 +20230420 2023届高三05班 0.943 -021491 -当$m=0$时，$ \cos (\alpha+1905^{\circ})=-1$,$\tan (\alpha-615^{\circ})=0$;\\ -当$m=\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=-\frac{\sqrt{15}}{3}$;\\ -当$m=-\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=\frac{\sqrt{15}}{3}$. +002372 +20230420 2023届高三05班 0.829 +003421 +20230420 2023届高三05班 0.886 -021492 -$-\dfrac{3}{8}$ +010951 +20230420 2023届高三05班 0.771 +012255 +20230420 2023届高三05班 0.886 -021493 -$-\dfrac{1}{20}$ +013097 +20230420 2023届高三05班 0.429 +013118 +20230420 2023届高三05班 0.657 -021494 -$\dfrac{7\sqrt{2}}{4}$ +031387 +20230420 2023届高三05班 0.571 +031323 +20230420 2023届高三05班 0.800 -021495 -$\dfrac{3\sqrt{5}}{5}$ +031386 +20230420 2023届高三05班 0.543 +008866 +20230420 2023届高三05班 0.886 -021496 -$11$ +012199 +20230420 2023届高三05班 1.000 0.771 +013134 +20230420 2023届高三05班 0.943 0.914 0.571 -021497 -$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ +000363 +20230420 2023届高三06班 0.900 +000625 +20230420 2023届高三06班 0.875 -021498 -$\sin ^2 \alpha$ +002372 +20230420 2023届高三06班 0.900 +003421 +20230420 2023届高三06班 0.900 -021499 -$1$ +010951 +20230420 2023届高三06班 0.850 +012255 +20230420 2023届高三06班 0.950 -021502 -$-\dfrac{12}{5}$ +013097 +20230420 2023届高三06班 0.650 +013118 +20230420 2023届高三06班 0.925 -021503 -$-\dfrac{\sqrt{3}}{2}$ +031387 +20230420 2023届高三06班 0.900 +031323 +20230420 2023届高三06班 0.850 -021504 -$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ +031386 +20230420 2023届高三06班 0.525 +008866 +20230420 2023届高三06班 0.950 -021505 -$-\dfrac{\sqrt{11}}{3}$ +012199 +20230420 2023届高三06班 0.975 0.725 +013134 +20230420 2023届高三06班 0.975 0.825 0.475 -021506 -$\dfrac{\pi}{3}$ +000363 +20230420 2023届高三07班 0.815 +000625 +20230420 2023届高三07班 0.741 -021507 -$\left[ 0,\pi \right )$ +002372 +20230420 2023届高三07班 0.815 +003421 +20230420 2023届高三07班 0.889 -021508 -$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$ +010951 +20230420 2023届高三07班 0.741 +012255 +20230420 2023届高三07班 0.556 -021509 -$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$ +013097 +20230420 2023届高三07班 0.593 +013118 +20230420 2023届高三07班 0.630 -021510 -$\cot \alpha$ +031387 +20230420 2023届高三07班 0.481 +031323 +20230420 2023届高三07班 0.926 -021511 -$-1$ +031386 +20230420 2023届高三07班 0.259 +008866 +20230420 2023届高三07班 0.741 -021512 -$-1$ +012199 +20230420 2023届高三07班 0.926 0.556 +013134 +20230420 2023届高三07班 0.926 0.815 0.407 -021513 -$ \sin 2-\cos 2$ +000363 +20230420 2023届高三08班 0.964 +000625 +20230420 2023届高三08班 0.964 -021514 -$0$ +002372 +20230420 2023届高三08班 0.786 +003421 +20230420 2023届高三08班 0.964 -021515 -$0$ +010951 +20230420 2023届高三08班 0.536 +012255 +20230420 2023届高三08班 0.929 -021516 -$-\dfrac{\sqrt{1-a^2}}{a}$ +013097 +20230420 2023届高三08班 0.536 +013118 +20230420 2023届高三08班 0.679 -021517 -$-\dfrac{2+\sqrt{3}}{3}$ +031387 +20230420 2023届高三08班 0.607 +031323 +20230420 2023届高三08班 0.964 -021518 -(1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$. +031386 +20230420 2023届高三08班 0.393 +008866 +20230420 2023届高三08班 0.893 -021519 -(1) $-\dfrac{2}{3}$; \\ -(2) $\dfrac{2}{3}$; \\ -(3) $-\dfrac{\sqrt{5}}{3}$;\\ -(4) $\dfrac{\sqrt{5}}{2}$. +012199 +20230420 2023届高三08班 0.964 0.714 +013134 +20230420 2023届高三08班 1.000 0.786 0.321 -021520 -(1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ; -(3) $-\tan \dfrac{\pi}{9}$; (4) $\cot \dfrac{7\pi}{15}$. +000363 +20230420 2023届高三09班 0.786 +000625 +20230420 2023届高三09班 0.786 -021521 -$\dfrac{2}{5}$ +002372 +20230420 2023届高三09班 0.786 +003421 +20230420 2023届高三09班 0.929 -021522 -$(3,4)$ +010951 +20230420 2023届高三09班 0.643 +012255 +20230420 2023届高三09班 0.786 -021523 -$0$ +013097 +20230420 2023届高三09班 0.714 +013118 +20230420 2023届高三09班 0.786 -021524 -$\sin \alpha$ +031387 +20230420 2023届高三09班 0.714 +031323 +20230420 2023届高三09班 0.857 -021525 -$-\dfrac{1}{5}$ +031386 +20230420 2023届高三09班 0.357 +008866 +20230420 2023届高三09班 1.000 -021526 -(1) $\dfrac{\sqrt{6}}{6}-\sqrt{3}$;\\ -(2) $-\dfrac{\sqrt{6}}{3}$;\\ -(3) $1$ - - -021527 -(1) $\dfrac{6 \pi}{5}$; (2) $\dfrac{4 \pi}{5}$; (3) $\dfrac{13 \pi}{10}$; (4) $\dfrac{17 \pi}{10}$. - - -021528 -(1) 当$\alpha$在第一象限时, $\sin (2 \pi-\alpha)=-\dfrac{\sqrt{3}}{2}$; -当$\alpha$在第三象限时, $\sin (2 \pi-\alpha)=\dfrac{\sqrt{3}}{2}$.\\ -(2) 当$\alpha$在第一象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=-\sqrt{3}$; -当$\alpha$在第四象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=\sqrt{3}$. - - -021529 -(1) $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\ -(2) $\{x | x=2k \pi \pm \dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\ -(3) $\{x | x=k \pi + \dfrac{5\pi}{6},\ k \in \mathbf{Z}\}$;\\ -(4) $\{x | x=2k \pi + \dfrac{5\pi}{6}$ 或$x=2k \pi + \dfrac{3\pi}{2} ,\ k \in \mathbf{Z}\}$;\\ -第二种写法： $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{6}+\dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\ -(5) $\{x | x=k \pi - \arctan \dfrac{\sqrt{3}}{2}+ \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\ -(6) $\{x | x=\dfrac{2k \pi}{5} + \dfrac{7\pi}{60}$ 或$ x=\dfrac{2k \pi}{5} - \dfrac{13\pi}{60} ,\ k \in \mathbf{Z}\}$;\\ -(7) $\{x | x=k \pi - \dfrac{5\pi}{8}$ 或$x=k \pi - \dfrac{3\pi}{8} ,\ k \in \mathbf{Z}\}$; - - -021530 -(1) $\{ \dfrac{\pi}{12},\dfrac{17\pi}{12} \}$;\\ -(2) $\{ \dfrac{5\pi}{6} \}$;\\ -(3) $\{ \dfrac{\pi}{12},\dfrac{5\pi}{12} \}$;\\ -(4) $\{ \dfrac{5\pi}{6} \}$. - - -021531 -(1) $\{x | x= \dfrac{2k \pi}{5} ,\ k \in \mathbf{Z}\}$;\\ -(2) $\{x | x= \dfrac{2k \pi}{3} +\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\ -(3) $\{x | x= 2k \pi$ 或$x=k \pi +(-1)^k \cdot \dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\ -(4) $\{x | x= k \pi+\dfrac{ \pi}{3}$ 或$x=k \pi -\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$. - - -021532 -$\dfrac{3+4\sqrt{3}}{10}$ - - -021533 -$-1$ - - -021534 -$-\dfrac{33}{50}$ - - -021535 -(1) $\dfrac{\sqrt{6}-\sqrt{2}}{4}$; -(2) $\dfrac{\sqrt{6}+\sqrt{2}}{4}$; -(3) $0$. - - -021536 -(1) $\sqrt{3} \sin \alpha$; -(2) $\cos(\alpha-2\beta)$. - - -021537 -$\dfrac{140}{221}$ - - -021538 -$\dfrac{2\sqrt{6}-1}{6}$ - - -021539 -证明略 - - -021540 -C - - -021541 -A - - -021542 -$\dfrac{3\sqrt{10}+6\sqrt{2}+2\sqrt{14}-\sqrt{70}}{24}$ - - -021543 -$\dfrac{8\sqrt{3}-21}{20}$ - - -021544 -$\dfrac{\pi}{2}$ - - -040018 -(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\pi}{6}$; (3) $\dfrac{\pi}{10}$; (4) $\dfrac{\pi}{3}$; (5) $\dfrac{5\pi}{12}$; (6) $\dfrac{\pi}{15}$ - - -040019 -(1) $60^{\circ}$; (2) $36^{\circ}$; (3) $45^{\circ}$; (4) $75^{\circ}$; (5) $40^{\circ}$; (6) $54^{\circ}$ - - -040020 -(1) $2k\pi+\dfrac{\pi}{2}$; (2) $2k\pi+\dfrac{3\pi}{2}$; (3) $2k\pi+\dfrac{7\pi}{6}$; (4) $k\pi+\dfrac{\pi}{4}$; (5) $\dfrac{k\pi}{2}+\dfrac{\pi}{6}$ - - -040021 -(1) $k \times 360^{\circ}+60^{\circ}$;\\ -(2) $k \times 360^{\circ}+330^{\circ}$; \\ -(3) $k \times 360^{\circ}-210^{\circ}$; \\ -(4) $k \times 180^{\circ}-45^{\circ}$; \\ -(5) $k \times 90^{\circ}+50^{\circ}$ - - -040022 -(1) $330^{\circ}$; (2) $240^{\circ}$; (3) $210^{\circ}$; (4) $300^{\circ}$ - - -040023 -(1) $\dfrac{4\pi}{3}$; (2) $\dfrac{11\pi}{6}$; (3) $10-2\pi$; (4) $-10+4\pi$ - - -040024 -$18$ - - -040025 -$3$,$-2$ - - -040026 -(1) $1037$; (2) $-4k+53$; (3) $500$ - - -040027 -$-2n+10$ - - -040028 -15 - - -040029 -$7$ - - -040030 -$(4,\dfrac{14}{3}]$ - - -040031 -$2n-1$ - - -040032 -$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$ - - -040033 -$200$ - - -040034 -略 - - -040035 -$a_n=\begin{cases}1, & n=1,\\ 2n, & n=2k, \\ 2n-2, & n=2k+1\end{cases}$($k\in \mathbf{N}$, $k\ge 1$) - - -040036 -$6n-3$ - - -040057 -$\dfrac{19}{28}\sqrt{7}$ - - -040058 -$\dfrac{79}{156}$ - - -040059 -$2$ - - -040060 -$-\dfrac{\sqrt{1-m^2}}{m}$ - - -040061 -$-\dfrac{1}{5}, \dfrac{1}{5}$ - - -040062 -$-\dfrac{1}{3}, 3$ - - -040063 -$\dfrac{1}{2}, -2$ - - -040064 -$\dfrac{\sqrt{6}}{3}$ - - -040065 -$\dfrac{1}{3}, -\dfrac{9}{4}$ - - -040066 -$\dfrac{1}{3}, \dfrac{7}{9}$ - - -040067 -$\pm\dfrac{\sqrt{2}}{3}$ - - -040068 -$\dfrac{1}{4}, \dfrac{2}{5}$ - - -040069 -$\dfrac{1-\sqrt{17}}{4}$ - - -040070 -(1) 三； (2) 三 - - -040071 -(1) $[-\dfrac{1}{2},\dfrac{1}{2})\cup\{1\}$; (2) $[-\dfrac{\pi}{3},\dfrac{\pi}{3})$; (3) $\{-\dfrac{1}{2}\}$ - - -040072 -(1) $-\tan \alpha-\cot \alpha$; (2) $-\dfrac{\sqrt{2}}{\sin \alpha}$; (3) $-1$; (4) $0$ - - -040073 -略 - - -040074 -$-\dfrac{10}{9}$ - - -040075 -$a_n=\dfrac{1}{3n-2}$ - - -040076 -$a_n=\dfrac{1}{n}$ - - -040077 -$(n-\dfrac{4}{5})5^n$ - - -040078 -$2^{n+1}-3$ - - -040079 -$1078$ - - -040080 -$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$ - - -040081 -(1) 略； (2) $n^2$ - - -040082 -(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$ - - -040083 -$\dfrac{\sqrt{3}}{2}$ - - -040084 -$0$ - - -040085 -$\{0,-2\pi\}$ - - -040086 -$-\dfrac{\pi}6,\dfrac 56\pi$ - - -040087 -$\cot \alpha$ - - -040088 -$7+4\sqrt{3}$ - - -040089 -$\dfrac{\sqrt{2}-\sqrt{6}}{4}$ - - -040090 -$\dfrac{\sqrt{3}+\sqrt{35}}{12}$ - - -040091 -$\dfrac 12$ - - -040092 -$5$ - - -040093 -$-\dfrac 12$ - - -040094 -$\dfrac{\pi}{12}$ - - -040095 -$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$ - - -040096 -$\dfrac 43 \pi$ - - -040097 -$\textcircled{4}$ - - -040098 -C - - -040099 -$\dfrac{-2\sqrt{2}-\sqrt{3}}6$ - - -040100 -$-\dfrac 7{25}$ - - -040101 -$-\dfrac {\pi}3$ - - -040102 -$(-\dfrac {12}{13}, \dfrac{5}{13})$ - - -040103 -$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$ - - -040104 -略 - - -040105 -$\dfrac {171} {221}, -\dfrac {21} {221}$ - - -040106 -$\{-\pi\}$ - - -040107 -$\dfrac{8\sqrt{2}-3}{15}$ - - -040108 -$\sin \theta$ - - -040109 -$-\dfrac{56}{65}$ - - -040110 -$\dfrac {\pi}4$ - - -040111 -略 - - -040112 -略 - - -040181 -$\dfrac 7{25}$ - - -040182 -$-\dfrac{\pi}3+2k\pi,k \in \mathbf{Z}$ - - -040183 -$\dfrac{4\sqrt{3}-3}{10}$ - - -040184 -$\dfrac 17$ - - -040185 -$4\sqrt{2} \sin(\alpha+\dfrac {7}{4}\pi))$ - - -040186 -$3$ - - -040187 -$\dfrac 32$ - - -040188 -$\sqrt{3}$ - - -040189 -$2$ - - -040190 -$\dfrac {13}{18}$ - - -040191 -$\dfrac{7}{4}\pi$ - - -040192 -$\dfrac{64}{25}$ - - -040193 -C - - -040194 -A - - -040195 -B - - -040196 -C - - -040197 -$-\dfrac{\pi}6$ - - -040198 -$\dfrac 23 \pi$ - - -040199 -$\dfrac 32$ - - -040200 -$\sqrt{1-k}$ - - -040201 -$-\dfrac{484}{729}$ - - -040131 -$-\dfrac{25}{12}$ - - -040132 -$\dfrac 52$ - - -040133 -$-\dfrac{\pi}4$ - - -040134 -$-\dfrac 12$ - - -040135 -$\dfrac 6{19}$ - - -040136 -$-\dfrac {\sqrt{3}}3$ - - -040137 -$\dfrac 3{22}$ - - -040138 -$4$ - - -040139 -$-\dfrac{63}{65}$ - - -040226 -$\dfrac 49 \sqrt{2}$ - - -040227 -$\sin \theta \cos \theta$ - - -040228 -$-\dfrac1{16}$ - - -040229 -$\dfrac 32$ - - -040230 -$\dfrac{13}{18}$ - - -040231 -$-2-\sqrt{7}$ - - -040232 -$\sin{\dfrac{\alpha}2}$ - - -040233 -$0$ - - -040234 -$\dfrac{120}{169}$ - - -040235 -$3$或$5$ - - -040236 -$\pi-\arcsin{\dfrac{24}{25}}$ - - -040237 -$\arcsin{\dfrac{3\sqrt{10}}{10}}$或$\arcsin{\dfrac{\sqrt{10}}{10}}$ - - -040238 -$60^{\circ}$或$120^{\circ}$ - - -040239 -$\dfrac 23 \pi$ - - -040240 -$8$ - - -040241 -\textcircled{4} - - -040242 -$\dfrac 35$或$\dfrac{24}{25}$或$\dfrac{3\sqrt{10}}{10}$或$\dfrac{\sqrt{10}}{10}$ - - -040243 -(1)$\angle A=75^{\circ}, \angle B=45^{\circ}, a=\sqrt{2}+\sqrt{6}$\\ -(2) $\angle B=60^{\circ}, \angle C=75^{\circ}, c=\sqrt{6}+3\sqrt{2}$或 -$\angle B=120^{\circ}, \angle C=15^{\circ}, c=3\sqrt{2} - \sqrt{6}$ - - -040244 -$\dfrac 12$ - - -040245 -$\dfrac 12 \pm \dfrac{\sqrt{6}}5$ - - -040246 -$-\dfrac7{25}$ - - -040247 -$\dfrac {\sqrt{2}} 2 +\dfrac 14$ - - -040248 -$90^\circ$ - - -040249 -$\dfrac 1{a}$ - - -040250 -$-\dfrac{16}{65}$ - - -040251 -$\dfrac{24}{13}$ - - -040252 -$\dfrac{\sqrt{11}}{6}$ - - -040253 -直角三角形 - - -040254 -$120^\circ$ - - -040255 -$-\dfrac{48}{49}$ - - -040256 -等边三角形 - - -040257 -等腰三角形 - - -040258 -等腰或直角三角形 - - -040259 -$30^\circ$ - - -040260 -$30^\circ$或$90^\circ$或$150^\circ$ - - -040261 -$2\sqrt{7}$ - - -040262 -$\dfrac 12$ - - -040263 -$(0,\dfrac{\pi}4]$ - - -040264 -(1) $\dfrac 23 \pi$; (2) 等腰钝角三角形 - - -040265 -(1) $\dfrac{\sqrt{3}}6$; (2) $\dfrac{\sqrt{39}+\sqrt{3}}2$ - - -040266 -$\{x|\dfrac{\pi}6+2k\pi \le x \le \dfrac 56 \pi+2k\pi, k \in \mathbb{Z} \}$ - - -040267 -$[0,3)$ - - -040268 -$4$ - - -040269 -$\pi$ - - -040270 -$\pi$ - - -040271 -$\dfrac{\pi}{2}$ - - -040272 -$-\sin{\dfrac 12 -1}$ - - -040273 -\textcircled{2}\textcircled{3}\textcircled{5} - - -040274 -等腰直角三角形 - - -040275 -$\{x|\dfrac{\pi}4+2k\pi \le x \le \dfrac 45 \pi+2k\pi, k \in \mathbb{Z} \}$ - - -040276 -$4\pi$ - - -040277 -$\dfrac{\pi}{2}$ - - -040278 -$\sqrt{5}$ - - -040279 -$12$ - - -040280 -$6+\sqrt{15}$ - - -040281 -\textcircled{3} \textcircled{4} - - -040282 -$(1)b=1,c=\sqrt{13}$;\\ -$(2)$等腰三角形或直角三角形 - - -040396 -$\{x|2k\pi+\dfrac{\pi}4