From 67a56736c03e74148a92172db744835e2965109b Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Wed, 21 Jun 2023 12:47:29 +0800 Subject: [PATCH] =?UTF-8?q?=E5=BD=95=E5=85=A52025=E5=B1=8A=E9=AB=98?= =?UTF-8?q?=E4=B8=80=E9=83=A8=E5=88=86=E5=B9=B3=E6=97=B6=E4=BD=9C=E4=B8=9A?= =?UTF-8?q?=E7=AD=94=E6=A1=88?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具/文本文件/metadata.txt | 4390 +++++++++++++++--------------------- 工具/答案metadata生成.py | 2 +- 题库0.3/Problems.json | 116 +- 3 files changed, 1924 insertions(+), 2584 deletions(-) diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 4e35ea62..56a270e7 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,3788 +1,3128 @@ -usages +ans -021909 -20230616 2025届高一11班 0.667 0.967 0.967 1.000 +021441 +错误, 正确, 错误, 错误 -021910 -20230616 2025届高一11班 0.933 -021911 -20230616 2025届高一11班 0.900 +021442 +D -021912 -20230616 2025届高一11班 0.950 -021913 -20230616 2025届高一11班 0.933 +021443 +C -021914 -20230616 2025届高一11班 0.767 -021915 -20230616 2025届高一11班 0.767 +021444 +A -021916 -20230616 2025届高一11班 0.867 -021917 -20230616 2025届高一11班 0.967 +021445 +C -021918 -20230616 2025届高一11班 0.933 -021919 -20230616 2025届高一11班 0.933 +021446 +D -021920 -20230616 2025届高一11班 0.967 -021921 -20230616 2025届高一11班 1.000 1.000 +021447 +$-390^\circ$ -021922 -20230616 2025届高一11班 0.800 0.967 0.967 0.900 -021923 -20230616 2025届高一11班 0.833 0.533 +021448 +$304^\circ$, $-56^\circ$ -021909 -20230616 2025届高一12班 0.818 0.818 0.970 1.000 -021910 -20230616 2025届高一12班 0.985 +021449 +$-144^\circ$ -021911 -20230616 2025届高一12班 0.909 -021912 -20230616 2025届高一12班 0.970 +021450 +二, 四 -021913 -20230616 2025届高一12班 0.970 -021914 -20230616 2025届高一12班 0.697 +021451 +(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$ -021915 -20230616 2025届高一12班 0.727 -021916 -20230616 2025届高一12班 0.788 +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} -021917 -20230616 2025届高一12班 0.970 -021918 -20230616 2025届高一12班 0.909 +021453 +$-1290^{\circ}$;第二象限 -021919 -20230616 2025届高一12班 0.879 -021920 -20230616 2025届高一12班 0.970 +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) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. -021921 -20230616 2025届高一12班 1.000 1.000 -021922 -20230616 2025届高一12班 0.773 0.894 0.985 1.000 +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) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. -021923 -20230616 2025届高一12班 0.742 0.500 -021909 -20230616 2025届高一01班 0.576 0.849 0.909 0.909 +021456 +C -021910 -20230616 2025届高一01班 0.849 -021911 -20230616 2025届高一01班 0.894 +021457 +B -021912 -20230616 2025届高一01班 0.879 -021913 -20230616 2025届高一01班 0.879 +021458 +$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$ -021914 -20230616 2025届高一01班 0.849 -021915 -20230616 2025届高一01班 0.515 +021459 +(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$ -021916 -20230616 2025届高一01班 0.515 -021917 -20230616 2025届高一01班 0.879 +021460 +$\sqrt{3}$ -021918 -20230616 2025届高一01班 0.909 -021919 -20230616 2025届高一01班 0.849 +021461 +(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ -021920 -20230616 2025届高一01班 0.758 -021921 -20230616 2025届高一01班 0.970 0.939 +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. -021922 -20230616 2025届高一01班 0.651 0.894 0.939 0.909 -021923 -20230616 2025届高一01班 0.909 0.909 +021463 +$\frac{1}{2}$ -021909 -20230616 2025届高一04班 0.567 0.900 0.900 0.900 -021910 -20230616 2025届高一04班 0.933 +021464 +(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. -021911 -20230616 2025届高一04班 0.900 -021912 -20230616 2025届高一04班 0.933 +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) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. -021913 -20230616 2025届高一04班 0.933 -021914 -20230616 2025届高一04班 0.833 +021466 +(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. -021915 -20230616 2025届高一04班 0.500 -021916 -20230616 2025届高一04班 0.500 +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. -021917 -20230616 2025届高一04班 1.000 -021918 -20230616 2025届高一04班 0.867 +021468 +$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ -021919 -20230616 2025届高一04班 0.867 -021920 -20230616 2025届高一04班 0.933 +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} -021921 -20230616 2025届高一04班 0.933 0.967 -021922 -20230616 2025届高一04班 0.433 0.900 0.967 0.933 +021470 +$2\sqrt{5}$ -021923 -20230616 2025届高一04班 0.733 0.133 -021909 -20230616 2025届高一05班 0.469 0.781 1.000 0.969 +021471 +$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ -021910 -20230616 2025届高一05班 0.859 -021911 -20230616 2025届高一05班 0.875 +021472 +$ \left( -2,\frac{2}{3} \right)$ -021912 -20230616 2025届高一05班 0.891 -021913 -20230616 2025届高一05班 0.938 +021473 +$<$ -021914 -20230616 2025届高一05班 0.750 -021915 -20230616 2025届高一05班 0.438 +021474 +5 -021916 -20230616 2025届高一05班 0.594 -021917 -20230616 2025届高一05班 0.969 +021475 +2 -021918 -20230616 2025届高一05班 0.938 -021919 -20230616 2025届高一05班 0.844 +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, $\cos \alpha=-1$, $\tan \alpha = 0$. -021920 -20230616 2025届高一05班 0.969 -021921 -20230616 2025届高一05班 1.000 0.938 +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}$, $\tan \alpha=\frac{4}{3}$. -021922 -20230616 2025届高一05班 0.359 0.844 0.969 0.938 -021923 -20230616 2025届高一05班 0.781 0.109 +021478 +$-\frac{\sqrt{3}}{4}$ -021909 -20230616 2025届高一06班 0.545 0.879 0.879 0.849 -021910 -20230616 2025届高一06班 0.879 +021479 +(1) 第四象限； (2) 第一、四象限；(3)第一、三象限；(4)第一、三象限. -021911 -20230616 2025届高一06班 0.955 -021912 -20230616 2025届高一06班 0.939 +021480 +$A=\left\{ -2,-0,4 \right\}$ -021913 -20230616 2025届高一06班 0.939 -021914 -20230616 2025届高一06班 0.697 +021481 +(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $[0,3)$ -021915 -20230616 2025届高一06班 0.515 -021916 -20230616 2025届高一06班 0.394 +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} -021917 -20230616 2025届高一06班 0.939 -021918 -20230616 2025届高一06班 0.879 +021483 +(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\ +(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$ -021919 -20230616 2025届高一06班 0.909 -021920 -20230616 2025届高一06班 0.667 +021484 +$-\frac{2\sqrt{5}}{5}$;$2$ -021921 -20230616 2025届高一06班 0.909 0.909 -021922 -20230616 2025届高一06班 0.455 0.894 0.849 0.849 +021485 +\textcircled{2} \textcircled{4} -021923 -20230616 2025届高一06班 0.818 0.788 -021909 -20230616 2025届高一08班 0.586 0.966 0.931 0.793 +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}$, $\tan \alpha=3$. -021910 -20230616 2025届高一08班 0.914 -021911 -20230616 2025届高一08班 0.914 +021487 +$\sin k\pi =0$; $\cos k\pi=\begin{cases}1, & k=2n, \\ -1, & k=2n-1\end{cases}$($n \in \mathbf{Z}$). -021912 -20230616 2025届高一08班 0.914 -021913 -20230616 2025届高一08班 0.759 +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) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. -021914 -20230616 2025届高一08班 0.586 -021915 -20230616 2025届高一08班 0.621 +021489 +第二象限 -021916 -20230616 2025届高一08班 0.655 -021917 -20230616 2025届高一08班 1.000 +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) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ -021918 -20230616 2025届高一08班 0.897 -021919 -20230616 2025届高一08班 0.724 +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}$. -021920 -20230616 2025届高一08班 0.724 -021921 -20230616 2025届高一08班 0.897 0.862 +021492 +$-\dfrac{3}{8}$ -021922 -20230616 2025届高一08班 0.897 0.914 1.000 1.000 -021923 -20230616 2025届高一08班 1.000 0.948 +021493 +$-\dfrac{1}{20}$ -021909 -20230616 2025届高一09班 0.394 0.849 0.849 0.849 -021910 -20230616 2025届高一09班 0.894 +021494 +$\dfrac{7\sqrt{2}}{4}$ -021911 -20230616 2025届高一09班 0.955 -021912 -20230616 2025届高一09班 0.939 +021495 +$\dfrac{3\sqrt{5}}{5}$ -021913 -20230616 2025届高一09班 0.667 -021914 -20230616 2025届高一09班 0.697 +021496 +$11$ -021915 -20230616 2025届高一09班 0.455 -021916 -20230616 2025届高一09班 0.667 +021497 +$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ -021917 -20230616 2025届高一09班 0.970 -021918 -20230616 2025届高一09班 0.788 +021498 +$\sin ^2 \alpha$ -021919 -20230616 2025届高一09班 0.727 -021920 -20230616 2025届高一09班 0.818 +021499 +$1$ -021921 -20230616 2025届高一09班 0.970 0.894 -021922 -20230616 2025届高一09班 0.394 0.697 0.909 0.894 +021502 +$-\dfrac{12}{5}$ -021923 -20230616 2025届高一09班 0.591 0.515 -021924 -20230616 2025届高一11班 0.853 +021503 +$-\dfrac{\sqrt{3}}{2}$ -021925 -20230616 2025届高一11班 0.971 -021926 -20230616 2025届高一11班 0.882 +021504 +$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ -021927 -20230616 2025届高一11班 0.824 -021928 -20230616 2025届高一11班 0.824 +021505 +$-\dfrac{\sqrt{11}}{3}$ -021929 -20230616 2025届高一11班 1.000 -021930 -20230616 2025届高一11班 0.618 +021506 +$\dfrac{\pi}{3}$ -021931 -20230616 2025届高一11班 0.794 0.574 -021932 -20230616 2025届高一11班 0.691 +021507 +$\left[ 0,\pi \right )$ -021933 -20230616 2025届高一11班 0.897 -021934 -20230616 2025届高一11班 0.912 +021508 +$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$ -021935 -20230616 2025届高一11班 0.676 -021936 -20230616 2025届高一11班 0.456 +021509 +$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$ -021937 -20230616 2025届高一11班 0.456 -021924 -20230616 2025届高一12班 0.902 +021510 +$\cot \alpha$ -021925 -20230616 2025届高一12班 1.000 -021926 -20230616 2025届高一12班 0.976 +021511 +$-1$ -021927 -20230616 2025届高一12班 0.707 -021928 -20230616 2025届高一12班 0.805 +021512 +$-1$ -021929 -20230616 2025届高一12班 0.976 -021930 -20230616 2025届高一12班 0.512 +021513 +$ \sin 2-\cos 2$ -021931 -20230616 2025届高一12班 0.902 0.585 -021932 -20230616 2025届高一12班 0.598 +021514 +$0$ -021933 -20230616 2025届高一12班 0.963 -021934 -20230616 2025届高一12班 0.976 +021515 +$0$ -021935 -20230616 2025届高一12班 0.829 -021936 -20230616 2025届高一12班 0.549 +021516 +$-\dfrac{\sqrt{1-a^2}}{a}$ -021937 -20230616 2025届高一12班 0.354 -021924 -20230616 2025届高一01班 0.784 +021517 +$-\dfrac{2+\sqrt{3}}{3}$ -021925 -20230616 2025届高一01班 0.865 -021926 -20230616 2025届高一01班 0.622 +021518 +(1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$. -021927 -20230616 2025届高一01班 0.351 -021928 -20230616 2025届高一01班 0.784 +021519 +(1) $-\dfrac{2}{3}$; \\ +(2) $\dfrac{2}{3}$; \\ +(3) $-\dfrac{\sqrt{5}}{3}$;\\ +(4) $\dfrac{\sqrt{5}}{2}$. -021929 -20230616 2025届高一01班 0.865 -021930 -20230616 2025届高一01班 0.270 +021520 +(1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ; +(3) $-\tan \dfrac{\pi}{9}$; (4) $\cot \dfrac{7\pi}{15}$. -021931 -20230616 2025届高一01班 0.811 0.540 -021932 -20230616 2025届高一01班 0.473 +021521 +$\dfrac{2}{5}$ -021933 -20230616 2025届高一01班 0.797 -021934 -20230616 2025届高一01班 0.784 +021522 +$(3,4)$ -021935 -20230616 2025届高一01班 0.757 -021936 -20230616 2025届高一01班 0.230 +021523 +$0$ -021937 -20230616 2025届高一01班 0.135 -021924 -20230616 2025届高一02班 0.824 +021524 +$\sin \alpha$ -021925 -20230616 2025届高一02班 0.882 -021926 -20230616 2025届高一02班 0.647 +021525 +$-\dfrac{1}{5}$ -021927 -20230616 2025届高一02班 0.882 -021928 -20230616 2025届高一02班 0.471 +021526 +(1) $\dfrac{\sqrt{6}}{6}-\sqrt{3}$;\\ +(2) $-\dfrac{\sqrt{6}}{3}$;\\ +(3) $1$ -021929 -20230616 2025届高一02班 0.882 -021930 -20230616 2025届高一02班 0.588 +021527 +(1) $\dfrac{6 \pi}{5}$; (2) $\dfrac{4 \pi}{5}$; (3) $\dfrac{13 \pi}{10}$; (4) $\dfrac{17 \pi}{10}$. -021931 -20230616 2025届高一02班 0.897 0.456 -021932 -20230616 2025届高一02班 0.912 +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, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=\sqrt{3}$. -021933 -20230616 2025届高一02班 0.824 -021934 -20230616 2025届高一02班 0.853 +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$x=k \pi - \dfrac{3\pi}{8} ,\ k \in \mathbf{Z}\}$; -021935 -20230616 2025届高一02班 0.500 -021936 -20230616 2025届高一02班 0.279 +021530 +(1) $\{ \dfrac{\pi}{12},\dfrac{17\pi}{12} \}$;\\ +(2) $\{ \dfrac{5\pi}{6} \}$;\\ +(3) $\{ \dfrac{\pi}{12},\dfrac{5\pi}{12} \}$;\\ +(4) $\{ \dfrac{5\pi}{6} \}$. -021937 -20230616 2025届高一02班 0.176 -021924 -20230616 2025届高一04班 0.938 +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$x=k \pi -\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$. -021925 -20230616 2025届高一04班 0.812 -021926 -20230616 2025届高一04班 0.875 +021532 +$\dfrac{3+4\sqrt{3}}{10}$ -021927 -20230616 2025届高一04班 0.719 -021928 -20230616 2025届高一04班 0.750 +021533 +$-1$ -021929 -20230616 2025届高一04班 0.938 -021930 -20230616 2025届高一04班 0.531 +021534 +$-\dfrac{33}{50}$ -021931 -20230616 2025届高一04班 0.906 0.562 -021932 -20230616 2025届高一04班 0.766 +021535 +(1) $\dfrac{\sqrt{6}-\sqrt{2}}{4}$; +(2) $\dfrac{\sqrt{6}+\sqrt{2}}{4}$; +(3) $0$. -021933 -20230616 2025届高一04班 0.859 -021934 -20230616 2025届高一04班 0.500 +021536 +(1) $\sqrt{3} \sin \alpha$; +(2) $\cos(\alpha-2\beta)$. -021935 -20230616 2025届高一04班 0.125 -021936 -20230616 2025届高一04班 1.000 +021537 +$\dfrac{140}{221}$ -021937 -20230616 2025届高一04班 1.000 -021924 -20230616 2025届高一05班 0.882 +021538 +$\dfrac{2\sqrt{6}-1}{6}$ -021925 -20230616 2025届高一05班 0.912 -021926 -20230616 2025届高一05班 0.882 +021539 +证明略 -021927 -20230616 2025届高一05班 0.765 -021928 -20230616 2025届高一05班 0.882 +021540 +C -021929 -20230616 2025届高一05班 0.882 -021930 -20230616 2025届高一05班 0.706 +021541 +A -021931 -20230616 2025届高一05班 0.868 0.529 -021932 -20230616 2025届高一05班 0.824 +021542 +$\dfrac{3\sqrt{10}+6\sqrt{2}+2\sqrt{14}-\sqrt{70}}{24}$ -021933 -20230616 2025届高一05班 0.926 -021934 -20230616 2025届高一05班 0.471 +021543 +$\dfrac{8\sqrt{3}-21}{20}$ -021935 -20230616 2025届高一05班 0.147 -021936 -20230616 2025届高一05班 1.000 +021544 +$\dfrac{\pi}{2}$ -021937 -20230616 2025届高一05班 1.000 -021924 -20230616 2025届高一06班 0.919 +021545 +$-\dfrac{2+\sqrt{15}}{6}$ -021925 -20230616 2025届高一06班 0.811 -021926 -20230616 2025届高一06班 0.703 +021546 +$-\dfrac{\sqrt{2}}{2}$ -021927 -20230616 2025届高一06班 0.622 -021928 -20230616 2025届高一06班 0.676 +021547 +$\sin 2\beta$ -021929 -20230616 2025届高一06班 0.973 -021930 -20230616 2025届高一06班 0.405 +021548 +$0$ -021931 -20230616 2025届高一06班 0.851 0.460 -021932 -20230616 2025届高一06班 0.527 +021549 +$2-\sqrt{3}$ -021933 -20230616 2025届高一06班 0.730 -021934 -20230616 2025届高一06班 0.622 +021550 +$\dfrac{16}{65}$ -021935 -20230616 2025届高一06班 0.568 -021936 -20230616 2025届高一06班 0.243 +021551 +$-\dfrac{7}{25}$ -021937 -20230616 2025届高一06班 0.297 -021924 -20230616 2025届高一08班 0.909 +021552 +$-\dfrac{4\sqrt{14}+3\sqrt{2}}{20}$ -021925 -20230616 2025届高一08班 0.879 -021926 -20230616 2025届高一08班 0.849 +021553 +$(\dfrac{4\sqrt{3}+3}{2},\dfrac{3\sqrt{3}-4}{2})$ -021927 -20230616 2025届高一08班 0.727 -021928 -20230616 2025届高一08班 0.727 +021554 +$-\dfrac{33}{65}$或$\dfrac{63}{65}$ -021929 -20230616 2025届高一08班 0.970 -021930 -20230616 2025届高一08班 0.545 +021555 +B -021931 -20230616 2025届高一08班 0.939 0.576 -021932 -20230616 2025届高一08班 0.727 +021556 +C -021933 -20230616 2025届高一08班 0.788 -021934 -20230616 2025届高一08班 0.485 +021557 +$-\dfrac{56}{65}$ -021935 -20230616 2025届高一08班 0.151 -021936 -20230616 2025届高一08班 0.591 +021558 +$-3$ -021937 -20230616 2025届高一08班 0.576 -021924 -20230616 2025届高一09班 0.912 +021559 +$\dfrac{3}{4}$ -021925 -20230616 2025届高一09班 0.971 -021926 -20230616 2025届高一09班 0.735 +021560 +$\dfrac{-6+5\sqrt{3}}{3}$ -021927 -20230616 2025届高一09班 0.794 -021928 -20230616 2025届高一09班 0.588 +021561 +$\tan \alpha$ -021929 -20230616 2025届高一09班 1.000 -021930 -20230616 2025届高一09班 0.441 +021562 +$\sqrt{3}$ -021931 -20230616 2025届高一09班 0.912 0.382 -021932 -20230616 2025届高一09班 0.809 +021563 +$-\dfrac{\sqrt{3}}{3}$ -021933 -20230616 2025届高一09班 0.971 -021934 -20230616 2025届高一09班 0.853 +021564 +A -021935 -20230616 2025届高一09班 0.235 -021936 -20230616 2025届高一09班 0.897 +021565 +$-\dfrac{17}{31}$ -021937 -20230616 2025届高一09班 0.853 -021938 -20230616 2025届高一11班 0.974 +021566 +$\dfrac{\pi}{4}$ -021939 -20230616 2025届高一11班 0.868 -021940 -20230616 2025届高一11班 0.974 +021567 +(1) $\dfrac{1}{3}$; +(2) $\dfrac{1}{7}$ -021941 -20230616 2025届高一11班 0.789 -021942 -20230616 2025届高一11班 0.526 +021568 +$-\dfrac{1}{5}$ -021943 -20230616 2025届高一11班 0.947 -021944 -20230616 2025届高一11班 0.947 +021569 +当$CD = 1.4$米时，$\tan \angle ACB$最大 -021945 -20230616 2025届高一11班 0.816 -021946 -20230616 2025届高一11班 1.000 1.000 +021570 +(1) $2 \sin (\alpha+\dfrac{\pi}{6})$; +(2) $\sqrt{2} \sin (\alpha+\dfrac{7\pi}{4})$. -021947 -20230616 2025届高一11班 0.921 -021948 -20230616 2025届高一11班 0.855 +021571 +$6\cos(\alpha+\dfrac{\pi}{3})$ -021949 -20230616 2025届高一11班 0.763 -021950 -20230616 2025届高一11班 0.882 0.947 +021572 +$2k \pi-\dfrac{\pi}{3}(k\in \mathbf{Z} )$ -021938 -20230616 2025届高一12班 1.000 -021939 -20230616 2025届高一12班 1.000 +021573 +B -021940 -20230616 2025届高一12班 0.923 -021941 -20230616 2025届高一12班 0.795 +021574 +$\dfrac{1}{3}$ -021942 -20230616 2025届高一12班 0.667 -021943 -20230616 2025届高一12班 1.000 +021575 +$\dfrac{\pi}{12}$或$\dfrac{5\pi}{12}$ -021944 -20230616 2025届高一12班 0.949 -021945 -20230616 2025届高一12班 0.718 +021576 +$5$ -021946 -20230616 2025届高一12班 0.987 0.949 -021947 -20230616 2025届高一12班 0.987 +021577 +$\dfrac{13}{3}$ -021948 -20230616 2025届高一12班 0.769 -021949 -20230616 2025届高一12班 0.731 +021578 +$-\dfrac{p}{1+q}$ -021950 -20230616 2025届高一12班 0.962 0.987 -021938 -20230616 2025届高一01班 0.947 +021579 +$\dfrac{3}{5}$ -021939 -20230616 2025届高一01班 0.868 -021940 -20230616 2025届高一01班 0.947 +021580 +$\dfrac{24}{7}$ -021941 -20230616 2025届高一01班 0.816 -021942 -20230616 2025届高一01班 0.368 +021581 +$-\dfrac{24}{25}$ -021943 -20230616 2025届高一01班 0.974 -021944 -20230616 2025届高一01班 0.658 +021582 +$-\dfrac{15}{17}$ -021945 -20230616 2025届高一01班 0.368 -021946 -20230616 2025届高一01班 0.868 0.789 +021583 +$\sin 2 \varphi=\dfrac{4\sqrt{2}}{9}$; +$\cos 2 \varphi=-\dfrac{7}{9}$; +$\tan 2 \varphi=-\dfrac{4\sqrt{2}}{7}$. -021947 -20230616 2025届高一01班 0.908 -021948 -20230616 2025届高一01班 0.750 +021584 +$\dfrac{24}{25}$; $\dfrac{7}{25}$; $\dfrac{24}{7}$ -021949 -20230616 2025届高一01班 0.711 -021950 -20230616 2025届高一01班 0.947 0.895 +021585 +(1) $-\dfrac{\sqrt{3}}{3}$;\\ +(2) $\dfrac{3}{4}$. -021938 -20230616 2025届高一02班 0.914 -021939 -20230616 2025届高一02班 0.857 +021586 +$\dfrac{7}{24}$ -021940 -20230616 2025届高一02班 0.943 -021941 -20230616 2025届高一02班 0.943 +021587 +$-\dfrac{2\sqrt{10}}{5}$ -021942 -20230616 2025届高一02班 0.571 -021943 -20230616 2025届高一02班 0.886 +021588 +$1$ -021944 -20230616 2025届高一02班 0.886 -021945 -20230616 2025届高一02班 0.514 +021590 +$1$或$\dfrac{7}{25}$ -021946 -20230616 2025届高一02班 0.943 0.871 -021947 -20230616 2025届高一02班 0.986 +021591 +$-\dfrac{\sqrt{2-2a}}{2}$ -021948 -20230616 2025届高一02班 0.857 -021949 -20230616 2025届高一02班 0.614 +021592 +第三象限 -021950 -20230616 2025届高一02班 0.971 0.971 -021938 -20230616 2025届高一04班 0.781 +021593 +当$\dfrac{\theta}{2}$在第二象限时， +$\sin \dfrac{\theta}{2}=\dfrac{\sqrt{3}}{3}$, +$\cos \dfrac{\theta}{2}=-\dfrac{\sqrt{6}}{3}$, +$\tan \dfrac{\theta}{2}=-\dfrac{\sqrt{2}}{2}$;\\ +当$\dfrac{\theta}{2}$在第四象限时， +$\sin \dfrac{\theta}{2}=-\dfrac{\sqrt{3}}{3}$, +$\cos \dfrac{\theta}{2}=\dfrac{\sqrt{6}}{3}$, +$\tan \dfrac{\theta}{2}=-\dfrac{\sqrt{2}}{2}$. -021939 -20230616 2025届高一04班 0.594 -021940 -20230616 2025届高一04班 0.781 +021594 +$\dfrac{3}{5}$;$\dfrac{4}{5}$ -021941 -20230616 2025届高一04班 0.719 -021942 -20230616 2025届高一04班 0.438 +021596 +$\dfrac{2}{3}$ -021943 -20230616 2025届高一04班 0.969 -021944 -20230616 2025届高一04班 0.875 +021597 +$\cos \alpha-\sin \alpha$ -021945 -20230616 2025届高一04班 0.250 -021946 -20230616 2025届高一04班 0.938 0.719 +021598 +$\sin \dfrac{ \alpha}{2}$ -021947 -20230616 2025届高一04班 0.844 -021948 -20230616 2025届高一04班 0.609 +021599 +(1) $\tan \dfrac{\theta}{2}$; (2) $\sin \alpha$. -021949 -20230616 2025届高一04班 0.453 -021950 -20230616 2025届高一04班 0.953 0.906 +021600 +$\dfrac{\sqrt{6}}{2}$ -021938 -20230616 2025届高一05班 0.914 -021939 -20230616 2025届高一05班 0.886 +021601 +$30^{\circ}$或$90^{\circ}$ -021940 -20230616 2025届高一05班 0.914 -021941 -20230616 2025届高一05班 0.886 +021602 +$\sqrt{6}$ -021942 -20230616 2025届高一05班 0.629 -021943 -20230616 2025届高一05班 0.971 +021603 +$55$ -021944 -20230616 2025届高一05班 0.886 -021945 -20230616 2025届高一05班 0.200 +021604 +$\dfrac{\pi}{3}$或$\dfrac{2\pi}{3}$ -021946 -20230616 2025届高一05班 0.900 0.886 -021947 -20230616 2025届高一05班 0.971 +021605 +$1: \sqrt{3}: 2$ -021948 -20230616 2025届高一05班 0.743 -021949 -20230616 2025届高一05班 0.771 +021606 +$2$ -021950 -20230616 2025届高一05班 0.971 0.914 -021938 -20230616 2025届高一06班 0.974 +021607 +$\dfrac{5}{8}$ -021939 -20230616 2025届高一06班 0.974 -021940 -20230616 2025届高一06班 0.921 +021608 +等腰 -021941 -20230616 2025届高一06班 0.658 -021942 -20230616 2025届高一06班 0.447 +021609 +$\dfrac{3\sqrt{2}}{2}$ -021943 -20230616 2025届高一06班 0.947 -021944 -20230616 2025届高一06班 0.842 +021610 +$\sqrt{3}$ -021945 -20230616 2025届高一06班 0.184 -021946 -20230616 2025届高一06班 0.684 0.684 +021611 +$\dfrac{7\pi}{12}$ -021947 -20230616 2025届高一06班 0.776 -021948 -20230616 2025届高一06班 0.618 +021612 +$\dfrac{2\pi}{3}$ -021949 -20230616 2025届高一06班 0.553 -021950 -20230616 2025届高一06班 0.947 0.868 +021613 +(1) $\left( 0,9 \right)$; \\ +(2) $\{9\} \cup \left[18,+ \infty \right)$;\\ +(3) $\left( 9,18 \right)$. -021938 -20230616 2025届高一08班 1.000 -021939 -20230616 2025届高一08班 0.824 +021614 +$\dfrac{3\sqrt{7}}{8}$ -021940 -20230616 2025届高一08班 0.912 -021941 -20230616 2025届高一08班 0.912 +021615 +$\sqrt{17}$或$\sqrt{65}$ -021942 -20230616 2025届高一08班 0.588 -021943 -20230616 2025届高一08班 0.941 +021616 +$\dfrac{\pi}{4}$ -021944 -20230616 2025届高一08班 0.912 -021945 -20230616 2025届高一08班 0.235 +021617 +\textcircled{1}；\textcircled{2} -021946 -20230616 2025届高一08班 0.853 0.750 -021947 -20230616 2025届高一08班 0.941 +021618 +$a>3$ -021948 -20230616 2025届高一08班 0.794 -021949 -20230616 2025届高一08班 0.721 +021619 +$a=\sqrt{21}$和$\sin B=\dfrac{5\sqrt{7}}{14}$ -021950 -20230616 2025届高一08班 0.897 0.868 -021938 -20230616 2025届高一09班 0.969 +021620 +$\dfrac{2\pi}{3}$ -021939 -20230616 2025届高一09班 1.000 -021940 -20230616 2025届高一09班 0.969 +021621 +$c=\sqrt{6}+\sqrt{2}$;$C=75^\circ$. -021941 -20230616 2025届高一09班 0.875 -021942 -20230616 2025届高一09班 0.594 +021622 +$\dfrac{\sqrt{19}}{2}$ -021943 -20230616 2025届高一09班 1.000 -021944 -20230616 2025届高一09班 0.969 +021623 +周长的最小值为$12$,此时三角形为正三角形；\\ +面积最大值为$4\sqrt{3}$,此时三角形为正三角形. -021945 -20230616 2025届高一09班 0.281 -021946 -20230616 2025届高一09班 0.859 0.797 +021624 +$\dfrac{\sqrt{5}}{5}$ -021947 -20230616 2025届高一09班 0.953 -021948 -20230616 2025届高一09班 0.766 +021625 +$\dfrac{2\sqrt{5}}{5}$或$-\dfrac{2\sqrt{5}}{25}$ -021949 -20230616 2025届高一09班 0.766 -021950 -20230616 2025届高一09班 0.969 1.000 +021626 +$\dfrac{\sqrt{5}}{5}$或$\dfrac{11\sqrt{5}}{25}$ -021951 -20230616 2025届高一11班 1.000 -021952 -20230616 2025届高一11班 0.949 +021627 +$\left ( 2,2\sqrt{2} \right )$ -021953 -20230616 2025届高一11班 0.923 -021954 -20230616 2025届高一11班 0.897 +021628 +(1) 以$C$为直角的直角三角形；\\ +(2) 以$A$为顶角的等腰三角形；\\ +(3) 以$A$为直角的直角三角形. -021955 -20230616 2025届高一11班 0.769 -021956 -20230616 2025届高一11班 0.949 +021629 +$a=\sqrt{13}$;$R=\dfrac{\sqrt{39}}{3}$. -021957 -20230616 2025届高一11班 1.000 -021958 -20230616 2025届高一11班 1.000 +021630 +$6\sqrt{19}$ -021959 -20230616 2025届高一11班 0.769 -021960 -20230616 2025届高一11班 0.936 +021631 +(1) $x=\arcsin \dfrac{2}{5}$或$\pi-\arcsin \dfrac{2}{5}$;\\ +(2) $x=\pi-\arccos \dfrac{2}{3}$或$\pi+\arccos \dfrac{2}{3}$;\\ +(3) $x=k\pi- \arctan \dfrac{1}{2},k \in \mathbf{Z}$. -021961 -20230616 2025届高一11班 0.987 -021962 -20230616 2025届高一11班 0.859 +021632 +$300\sqrt{3}$ -021963 -20230616 2025届高一11班 0.821 -021964 -20230616 2025届高一11班 0.897 0.923 +021633 +证明略 -021965 -20230616 2025届高一11班 0.974 0.949 -021951 -20230616 2025届高一12班 0.950 +021634 +$\theta=\dfrac{\pi}{12}$;塔高为$1.5$千米. -021952 -20230616 2025届高一12班 0.875 -021953 -20230616 2025届高一12班 0.912 +021635 +$64.81$米 -021954 -20230616 2025届高一12班 0.850 -021955 -20230616 2025届高一12班 0.825 +021636 +(1) $3.9$千米;(2) $4.0$千米. -021956 -20230616 2025届高一12班 0.775 -021957 -20230616 2025届高一12班 1.000 +021637 +$2.4$千米 -021958 -20230616 2025届高一12班 0.975 -021959 -20230616 2025届高一12班 0.400 +021638 +$\dfrac{\pi}{2}$ -021960 -20230616 2025届高一12班 0.875 -021961 -20230616 2025届高一12班 1.000 +021639 +B -021962 -20230616 2025届高一12班 0.812 -021963 -20230616 2025届高一12班 0.725 +021640 +(1) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-4,0) -- (4,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw (-pi,0.1) -- (-pi,0) node [below left] {$-\pi$}; +\draw (-0.5*pi,0.1) -- (-0.5*pi,0) node [below] {$-\frac{\pi}{2}$}; +\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\frac{\pi}{2}$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (0.1,1) -- (0,1) node [left] {$1$}; +\draw (0.1,-1) -- (0,-1) node [left] {$-1$}; +\draw [domain = -pi:pi,samples = 100] plot (\x,{sin(\x/pi*180)+1}); +\end{tikzpicture}\\ +(2) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (0,0) -- (7,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw (pi/2,0.1) -- (pi/2,0) node [below] {$\frac{\pi}{2}$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (1.5*pi,0.1) -- (1.5*pi,0) node [below] {$\frac{3\pi}{2}$}; +\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\pi$}; +\draw (0.1,1) -- (0,1) node [left] {$1$}; +\draw (0.1,-1) -- (0,-1) node [left] {$-1$}; +\draw [domain = 0:2*pi,samples = 100] plot (\x,{-cos(\x/pi*180)}); +\end{tikzpicture} -021964 -20230616 2025届高一12班 0.700 0.875 -021965 -20230616 2025届高一12班 0.912 0.838 +021641 +(1) 定义域为$\left \{x|x \neq-\dfrac{\pi}{2}+2k\pi,k \in \mathbf{Z} \right \}$;\\ +(2) 定义域为$\left \{x|\dfrac{\pi}{2}+2k\pi \leq x \leq \dfrac{3\pi}{2}+2k\pi,k \in \mathbf{Z} \right \}$. -021951 -20230616 2025届高一01班 0.947 -021952 -20230616 2025届高一01班 0.895 +021642 +$\left \{x|\dfrac{\pi}{6} \leq x \leq \dfrac{5\pi}{6},k \in \mathbf{Z} \right \}$ -021953 -20230616 2025届高一01班 0.816 -021954 -20230616 2025届高一01班 0.947 +021643 +$2\pi$ -021955 -20230616 2025届高一01班 0.500 -021956 -20230616 2025届高一01班 0.789 +021644 +C -021957 -20230616 2025届高一01班 1.000 -021958 -20230616 2025届高一01班 1.000 +021645 +C -021959 -20230616 2025届高一01班 0.632 -021960 -20230616 2025届高一01班 0.921 +021646 +(1) 当$a \in (-\infty，-\dfrac{\sqrt{2}}{2})\cup (1,+\infty)$ 时，方程实数解个数为$0$个；\\ +当$a \in [-\dfrac{\sqrt{2}}{2},0)\cup \{1\}$ 时，方程实数解个数为$1$个；\\ +当$a \in [0,1)$时，方程实数解个数为$2$个.\\ +(2) 当$a \in (-\infty，-1)\cup (1,+\infty)$ 时，方程实数解个数为$0$个；\\ +当$a \in (0,1]$时，方程实数解个数为$1$个;\\ +当$a \in \{0,-1\}$时，方程实数解个数为$2$个;\\ +当$a \in (-1,0)$时，方程实数解个数为$3$个. -021961 -20230616 2025届高一01班 0.947 -021962 -20230616 2025届高一01班 0.855 +021647 +(1) $8\pi$; +(2) $\pi$;(3) $\pi$;(4) $2\pi$. -021963 -20230616 2025届高一01班 0.395 -021964 -20230616 2025届高一01班 0.763 0.737 +021648 +$3$ -021965 -20230616 2025届高一01班 0.842 0.737 -021951 -20230616 2025届高一02班 0.946 +021649 +A -021952 -20230616 2025届高一02班 0.892 -021953 -20230616 2025届高一02班 0.919 +021650 +C -021954 -20230616 2025届高一02班 0.919 -021955 -20230616 2025届高一02班 0.838 +021651 +(1) 假;(1) 假;(3) 真. -021956 -20230616 2025届高一02班 0.946 -021957 -20230616 2025届高一02班 0.973 +021652 +D -021958 -20230616 2025届高一02班 0.946 -021959 -20230616 2025届高一02班 0.730 +021653 +(1) $\pi$; (2) $\pi$; (3) $\dfrac{\pi}{2}$; (4) $\dfrac{\pi}{|a|}$. -021960 -20230616 2025届高一02班 0.919 -021961 -20230616 2025届高一02班 0.824 +021654 +$4\sin(\dfrac{\pi x}{2})-2$ -021962 -20230616 2025届高一02班 0.743 -021963 -20230616 2025届高一02班 0.662 +021655 +B -021964 -20230616 2025届高一02班 0.905 0.865 -021965 -20230616 2025届高一02班 0.811 0.608 +021656 +A -021951 -20230616 2025届高一04班 0.824 -021952 -20230616 2025届高一04班 0.765 +021657 +(1) $f(3)=-1$; $f(5)=1$; $f(7)=-1$;\\ +(2) $T=4$. -021953 -20230616 2025届高一04班 0.882 -021954 -20230616 2025届高一04班 0.794 +021658 +$\left [2,4\right] $ -021955 -20230616 2025届高一04班 0.382 -021956 -20230616 2025届高一04班 0.382 +021659 +$\left [-2,2\right] $ -021957 -20230616 2025届高一04班 0.941 -021958 -20230616 2025届高一04班 0.824 +021660 +$ [-\dfrac{3}{2},3] $ -021959 -20230616 2025届高一04班 0.735 -021960 -20230616 2025届高一04班 0.941 +021661 +$ (-\dfrac{\sqrt{3}}{2},1] $ -021961 -20230616 2025届高一04班 0.721 -021962 -20230616 2025届高一04班 0.765 +021662 +$3$; $\left \{x|x=-\dfrac{\pi}{2}+2k\pi,k \in \bf{Z} \right\}$ -021963 -20230616 2025届高一04班 0.559 -021964 -20230616 2025届高一04班 0.618 0.735 +021663 +$-3$; $\left \{x|x=-\dfrac{\pi}{12}+k\pi,k \in \bf{Z} \right\}$ -021965 -20230616 2025届高一04班 0.824 0.794 -021951 -20230616 2025届高一05班 0.892 +021664 +当$x=\dfrac{\pi}{2}-\arcsin \dfrac{3\sqrt{13}}{13}+2k\pi,k \in \bf{Z}$时，函数的最大值为$\sqrt{13}$;\\ +当$x=-\dfrac{\pi}{2}-\arcsin \dfrac{3\sqrt{13}}{13}+2k\pi,k \in \bf{Z}$时，函数的最小值为$-\sqrt{13}$. -021952 -20230616 2025届高一05班 0.730 -021953 -20230616 2025届高一05班 0.892 +021665 +D -021954 -20230616 2025届高一05班 0.838 -021955 -20230616 2025届高一05班 0.486 +021666 +C -021956 -20230616 2025届高一05班 0.595 -021957 -20230616 2025届高一05班 0.973 +021667 +当$\alpha=\dfrac{\pi}{2}-\theta$时，竹竿的影子最长，最长为$\dfrac{\sin(\alpha+\theta)}{\sin \theta}*l$. -021958 -20230616 2025届高一05班 0.973 -021959 -20230616 2025届高一05班 0.838 +021668 +$[-1,1]$ -021960 -20230616 2025届高一05班 0.838 -021961 -20230616 2025届高一05班 0.649 +021669 +$\{x|x\neq 2k\pi,k \in \bf{Z}\}$;$(-\infty,0]$ -021962 -20230616 2025届高一05班 0.824 -021963 -20230616 2025届高一05班 0.554 +021670 +$k=3$或$-3$;$b=-1$ -021964 -20230616 2025届高一05班 0.622 0.932 -021965 -20230616 2025届高一05班 0.730 0.770 +021671 +当$x=0$时，函数$y$取到最大值，最大值为$0$;\\ +当$x=\dfrac{\pi}{4}$时，函数$y$取到最小值，最小值为$-1$. -021951 -20230616 2025届高一06班 0.853 -021952 -20230616 2025届高一06班 0.794 +021672 +$f(a)=\begin{cases} +a^2+2a+2, & a\leq -1,\\ +1, & -1=latex, scale = 0.7] +\draw [->] (-4,0) -- (4,0) node [below] {$x$}; +\draw [->] (0,-1.5) -- (0,2) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw ({-pi/12},0.1) -- ({-pi/12},0) node [below left] {$-\frac{\pi}{12}$}; +\draw ({pi/6},0.1) -- ({pi/6},0) node [below] {$\frac{\pi}{6}$}; +\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\frac{5\pi}{12}$}; +\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above] {$\frac{2\pi}{3}$}; +\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\frac{11\pi}{12}$}; +\draw (0.1,1) -- (0,1) node [left] {$1$}; +\draw (0.1,-1) -- (0,-1) node [left] {$-1$}; +\draw [domain = {-pi/12}:{11*pi/12},samples = 100] plot (\x,{sin(2*\x/pi*180+30)}); +\end{tikzpicture}\\ +(2) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-1,0) -- (15,0) node [below] {$x$}; +\draw [->] (0,-3) -- (0,3) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\pi$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (3*pi,0.1) -- (3*pi,0) node [below] {$\frac{3\pi}{2}$}; +\draw (4*pi,0.1) -- (4*pi,0) node [below] {$4\pi$}; +\draw (0.1,2) -- (0,2) node [left] {$2$}; +\draw (0.1,-2) -- (0,-2) node [left] {$-2$}; +\draw [domain =0:4*pi,samples = 100] plot (\x,{2*sin(0.5*\x/pi*180)}); +\end{tikzpicture}\\ +(3) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-1,0) -- (4,0) node [below] {$x$}; +\draw [->] (0,-1) -- (0,1) node [left] {$y$}; +\draw (0,0) node [below right] {$O$}; +\draw (0.25*pi,0.1) -- (0.25*pi,0) node [below] {$\frac{\pi}{4}$}; +\draw (pi,0.1) -- (pi,0) node [below] {$\pi$}; +\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\frac{\pi}{2}$}; +\draw (0.75*pi,0.1) -- (0.75*pi,0) node [above] {$\frac{3\pi}{4}$}; +\draw (0.1,0.5) -- (0,0.5) node [left] {$\frac{1}{2}$}; +\draw (0.1,-0.5) -- (0,-0.5) node [left] {$-\frac{1}{2}$}; +\draw [domain =0:pi,samples = 100] plot (\x,{0.5*sin(2*\x/pi*180)}); +\end{tikzpicture}\\ +(4) \begin{tikzpicture}[>=latex, scale = 0.7] +\draw [->] (-1.5,0) -- (3.5,0) node [below] {$x$}; +\draw [->] (0,-5.5) -- (0,5.5) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw ({-pi/3},0.1) -- ({-pi/3},0) node [below left] {$-\frac{\pi}{3}$}; +\draw ({-pi/12},0.1) -- ({-pi/12},0) node [above left] {$-\frac{\pi}{12}$}; +\draw ({pi/6},0.1) -- ({pi/6},0) node [below right] {$\frac{\pi}{6}$}; +\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\frac{5\pi}{12}$}; +\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above right] {$\frac{2\pi}{3}$}; +\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\frac{11\pi}{12}$}; +\draw (0.1,5) -- (0,5) node [left] {$5$}; +\draw (0.1,-5) -- (0,-5) node [below left] {$-5$}; +\draw [domain = {-4*pi/12}:{2*pi/3},samples = 100] plot (\x,{5*sin(2*\x/pi*180-60)}); +\end{tikzpicture} -021965 -20230616 2025届高一09班 0.814 0.786 -021966 -20230616 2025届高一11班 0.923 +021695 +$4\pi$;$4$. -021967 -20230616 2025届高一11班 1.000 -021968 -20230616 2025届高一11班 0.897 +021696 +$f(x)=4\sin(x+\dfrac{\pi}{6})$ -021969 -20230616 2025届高一11班 0.231 -021970 -20230616 2025届高一11班 1.000 +021697 +(1) $f(x)=\dfrac{\sqrt{3}}{2}\sin(3x+\pi)+\dfrac{\sqrt{3}}{2};$\\ +(2) $[-\dfrac{\pi}{2}+\dfrac{2k\pi}{3},-\dfrac{\pi}{6}+\dfrac{2k\pi}{3}],k \in \bf{Z}$;\\ +(3) 函数最大值为$\sqrt{3}$,此时$x$值为${x|x=-\dfrac{\pi}{6}+\dfrac{2k\pi}{3},k \in \bf{Z}}$ -021971 -20230616 2025届高一11班 0.974 -021972 -20230616 2025届高一11班 0.795 +021698 +$x=\pi+2k\pi,k \in \bf{Z}$ -021973 -20230616 2025届高一11班 0.987 -021974 -20230616 2025届高一11班 0.974 +021699 +纵;伸长; $3$. -021975 -20230616 2025届高一11班 0.936 -021976 -20230616 2025届高一11班 0.936 +021700 +缩短; $\dfrac{1}{2}$; 缩短; $\dfrac{1}{3}$. -021966 -20230616 2025届高一12班 0.900 -021967 -20230616 2025届高一12班 0.983 +021701 +$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{3})$ -021968 -20230616 2025届高一12班 1.000 -021969 -20230616 2025届高一12班 0.600 +021702 +$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{6})$ -021970 -20230616 2025届高一12班 1.000 -021971 -20230616 2025届高一12班 0.850 +021703 +$f(x)=2\sin(\dfrac{1}{3}x+\dfrac{\pi}{6})$ -021972 -20230616 2025届高一12班 0.775 -021973 -20230616 2025届高一12班 0.963 +021704 +$x=\dfrac{\pi}{3}+2k\pi,k \in \bf{Z}$; $(-\dfrac{2\pi}{3}+2k\pi,0),k \in \bf{Z}$. -021974 -20230616 2025届高一12班 0.963 -021975 -20230616 2025届高一12班 0.912 +021705 +C -021976 -20230616 2025届高一12班 0.850 -021966 -20230616 2025届高一01班 0.923 +021706 +左; $\dfrac{\pi}{8}$. -021967 -20230616 2025届高一01班 0.923 -021968 -20230616 2025届高一01班 0.872 +021707 +$f(x)=\sin(2x+\dfrac{\pi}{2})$, +$g(x)=\sin x$. -021969 -20230616 2025届高一01班 0.385 -021970 -20230616 2025届高一01班 1.000 +021708 +(1) $\sqrt{2}$; +(2) $g(x)=2\cos(\dfrac{1}{2}x-\dfrac{\pi}{3}) $, 单调递减区间为$[\dfrac{2\pi}{3}+4k\pi,\dfrac{8\pi}{3}+4k\pi],k \in \bf{Z}$. -021971 -20230616 2025届高一01班 0.923 -021972 -20230616 2025届高一01班 0.692 +021709 +(1) $2\pi$; (2) $1$; (3) $\dfrac{\pi}{2}$. -021973 -20230616 2025届高一01班 1.000 -021974 -20230616 2025届高一01班 0.795 +021710 +(1) $[0,\dfrac{\pi}{2})$, $(\dfrac{3\pi}{2},2\pi]$; \\ +(2) $[0,\dfrac{\pi}{2})$, $(\dfrac{\pi}{2},\pi]$. -021975 -20230616 2025届高一01班 0.808 -021976 -20230616 2025届高一01班 0.436 +021711 +(1) 奇函数; (2) 偶函数. -021966 -20230616 2025届高一04班 0.926 -021967 -20230616 2025届高一04班 0.951 +021712 +$[-5,+\infty)$ -021968 -20230616 2025届高一04班 0.941 -021969 -20230616 2025届高一04班 0.882 +021713 +(1) $<$; (2) $>$; (3) $>$; (4)$<$. -021970 -20230616 2025届高一04班 0.971 -021971 -20230616 2025届高一04班 0.706 +021714 +\textcircled{3} -021972 -20230616 2025届高一04班 0.618 -021973 -20230616 2025届高一04班 0.956 +021715 +最小值为$-\dfrac{\sqrt{3}}{3}$，此时$x=-\dfrac{\pi}{3}$. -021974 -20230616 2025届高一04班 0.618 -021975 -20230616 2025届高一04班 0.765 +021716 +(1) $ \{x|x \neq \dfrac{k\pi}{2},k \in \bf{Z}\} $;\\ +(2) 单调增区间为$(-\dfrac{\pi}{2}+\dfrac{k\pi}{2},\dfrac{k\pi}{2}), k \in \bf{Z}$. -021976 -20230616 2025届高一04班 0.647 -021966 -20230616 2025届高一05班 0.971 +021717 +$\{x|x\neq \dfrac{\pi}{4}-\dfrac{1}{2}+\dfrac{k\pi}{2},k \in \bf{Z} \}$ -021967 -20230616 2025届高一05班 0.990 -021968 -20230616 2025届高一05班 0.971 +021718 +$(-\dfrac{\pi}{4}+\dfrac{k\pi}{3},\dfrac{\pi}{12}+\dfrac{k\pi}{3}), k \in \bf{Z}$ -021969 -20230616 2025届高一05班 0.971 -021970 -20230616 2025届高一05班 1.000 +021719 +B -021971 -20230616 2025届高一05班 0.912 -021972 -20230616 2025届高一05班 0.500 +021720 +定义域为$ \{x|x \neq \dfrac{7\pi}{5}+2k\pi,k \in \bf{Z}\} $;\\ +严格增区间为$(-\dfrac{3\pi}{5}+2k\pi,\dfrac{7\pi}{5}+2k\pi), k \in \bf{Z}$. -021973 -20230616 2025届高一05班 0.971 -021974 -20230616 2025届高一05班 0.868 +021721 +函数零点为$x=\dfrac{2k\pi}{5}+2k\pi,k \in \bf{Z}$. -021975 -20230616 2025届高一05班 0.750 -021976 -20230616 2025届高一05班 0.603 +021722 +(1) 假命题; (2) 假命题; (3) 假命题; (4) 真命题. -021966 -20230616 2025届高一06班 0.843 -021967 -20230616 2025届高一06班 0.962 +021723 +$[-4,2+4\sqrt{3}]$ -021968 -20230616 2025届高一06班 0.743 -021969 -20230616 2025届高一06班 0.286 +021724 +最大张角的正切值为$\dfrac{\sqrt{2}}{4}$, 此时学生距离时钟$\sqrt{0.18}$米. -021970 -20230616 2025届高一06班 0.943 -021971 -20230616 2025届高一06班 0.657 +021726 +A -021972 -20230616 2025届高一06班 0.629 -021973 -20230616 2025届高一06班 0.986 +021727 +C -021974 -20230616 2025届高一06班 0.643 -021975 -20230616 2025届高一06班 0.829 +021728 +B -021976 -20230616 2025届高一06班 0.486 -021966 -20230616 2025届高一08班 0.970 +021729 +单位圆 -021967 -20230616 2025届高一08班 0.798 -021968 -20230616 2025届高一08班 0.849 +021730 +B -021969 -20230616 2025届高一08班 0.091 -021970 -20230616 2025届高一08班 1.000 +021731 +$\overrightarrow{CD}$ -021971 -20230616 2025届高一08班 0.909 -021972 -20230616 2025届高一08班 0.682 +021732 +$\overrightarrow{AC}$ -021973 -20230616 2025届高一08班 1.000 -021974 -20230616 2025届高一08班 0.909 +021733 +(1) 假命题; (2) 真命题; (3) 假命题; (4) 假命题. -021975 -20230616 2025届高一08班 0.591 -021976 -20230616 2025届高一08班 0.970 +021734 +(1) $\overrightarrow{DB}$; $\overrightarrow{FE}$.\\ +(2) $\overrightarrow{ED}$; $\overrightarrow{CF}$; $\overrightarrow{FA}$.\\ +(3) $\overrightarrow{EF}$; $\overrightarrow{AD}$; $\overrightarrow{DA}$; $\overrightarrow{DB}$; $\overrightarrow{BD}$; $\overrightarrow{AB}$; $\overrightarrow{BA}$. -021966 -20230616 2025届高一09班 0.986 -021967 -20230616 2025届高一09班 0.907 +021735 +$40$ -021968 -20230616 2025届高一09班 0.833 -021969 -20230616 2025届高一09班 0.333 +021736 +$40$ -021970 -20230616 2025届高一09班 1.000 -021971 -20230616 2025届高一09班 0.778 +021737 +$2$ -021972 -20230616 2025届高一09班 0.694 -021973 -20230616 2025届高一09班 0.986 +021739 +$-3\overrightarrow {a}+6 \overrightarrow {b}$ -021974 -20230616 2025届高一09班 0.806 -021975 -20230616 2025届高一09班 0.569 +021740 +$7 \overrightarrow {a}-2 \overrightarrow {b}- \overrightarrow {c}$ -021976 -20230616 2025届高一09班 0.889 -021977 -20230616 2025届高一11班 0.949 1.000 0.795 +021741 +(1) 假命题; (2) 真命题; (3) 假命题; (4) 真命题. -021978 -20230616 2025届高一11班 0.949 -021979 -20230616 2025届高一11班 0.923 +021742 +(1) $\overrightarrow {AB}=\dfrac{1}{2}\overrightarrow {a}-\dfrac{1}{2}\overrightarrow {b}$;\\ +(2) $\overrightarrow {BC}=\dfrac{1}{2}\overrightarrow {a}+\dfrac{1}{2}\overrightarrow {b}$. -021980 -20230616 2025届高一11班 0.897 -021981 -20230616 2025届高一11班 0.974 +021743 +$\lambda=\dfrac{1}{3}$ -021982 -20230616 2025届高一11班 1.000 -021983 -20230616 2025届高一11班 0.885 +021744 +$x=2$; $y=1$. -021984 -20230616 2025届高一11班 0.949 -021985 -20230616 2025届高一11班 0.923 +021745 +(2) $m=1$或$-1$. -021986 -20230616 2025届高一11班 0.808 -021977 -20230616 2025届高一12班 0.974 0.921 0.895 +021746 +$\overrightarrow{DC}=\dfrac{1}{2}\overrightarrow{a}$;\\ $\overrightarrow{DC}=-\dfrac{1}{2}\overrightarrow{a}+\overrightarrow{b}$;\\ +$\overrightarrow{MN}=-\dfrac{1}{4}\overrightarrow{a}-\overrightarrow{b}$. -021978 -20230616 2025届高一12班 0.974 -021979 -20230616 2025届高一12班 0.974 +021747 +$\overrightarrow{0}$ -021980 -20230616 2025届高一12班 0.842 -021981 -20230616 2025届高一12班 1.000 +021748 +$\dfrac{2}{3}\overrightarrow{a}+\dfrac{1}{3}\overrightarrow{b}$ -021982 -20230616 2025届高一12班 1.000 -021983 -20230616 2025届高一12班 0.934 +021749 +A -021984 -20230616 2025届高一12班 0.921 -021985 -20230616 2025届高一12班 0.868 +021750 +B -021986 -20230616 2025届高一12班 0.868 -021977 -20230616 2025届高一01班 0.897 0.795 0.846 +021751 +C -021978 -20230616 2025届高一01班 0.949 -021979 -20230616 2025届高一01班 0.897 +021752 +$\sqrt{3}$ -021980 -20230616 2025届高一01班 0.667 -021981 -20230616 2025届高一01班 0.846 +021753 +$-\dfrac{3\sqrt{3}}{2}$ -021982 -20230616 2025届高一01班 0.923 -021983 -20230616 2025届高一01班 0.872 +021754 +等边三角形 -021984 -20230616 2025届高一01班 0.795 -021985 -20230616 2025届高一01班 0.833 +021755 +$\dfrac{\pi}{4}$ -021986 -20230616 2025届高一01班 0.628 -021977 -20230616 2025届高一04班 0.921 0.947 0.868 +021756 +$\dfrac{2\pi}{3}$ -021978 -20230616 2025届高一04班 1.000 -021979 -20230616 2025届高一04班 0.711 +021757 +$-10\sqrt{2}$ -021980 -20230616 2025届高一04班 0.500 -021981 -20230616 2025届高一04班 0.816 +021758 +$\dfrac{4}{3}$ -021982 -20230616 2025届高一04班 0.974 -021983 -20230616 2025届高一04班 0.921 +021759 +$-\dfrac{2}{3}\overrightarrow {a}$ -021984 -20230616 2025届高一04班 0.763 -021985 -20230616 2025届高一04班 0.618 +021760 +B -021986 -20230616 2025届高一04班 0.526 -021977 -20230616 2025届高一05班 0.949 0.949 0.821 +021761 +B -021978 -20230616 2025届高一05班 1.000 -021979 -20230616 2025届高一05班 0.897 +021762 +A -021980 -20230616 2025届高一05班 0.538 -021981 -20230616 2025届高一05班 0.923 +021763 +$7$ -021982 -20230616 2025届高一05班 1.000 -021983 -20230616 2025届高一05班 0.897 +021764 +$2$ -021984 -20230616 2025届高一05班 0.846 -021985 -20230616 2025届高一05班 0.615 +021765 +C -021986 -20230616 2025届高一05班 0.615 -021977 -20230616 2025届高一06班 0.975 0.725 0.850 +021766 +外心; 重心; 垂心. -021978 -20230616 2025届高一06班 0.900 -021979 -20230616 2025届高一06班 0.875 +021767 +$\dfrac{\pi}{3}$ -021980 -20230616 2025届高一06班 0.550 -021981 -20230616 2025届高一06班 0.925 +021768 +$-25$ -021982 -20230616 2025届高一06班 0.950 -021983 -20230616 2025届高一06班 0.775 +021769 +$\lambda=\dfrac{7}{12}$ -021984 -20230616 2025届高一06班 0.775 -021985 -20230616 2025届高一06班 0.713 +021770 +$AB=8$ -021986 -20230616 2025届高一06班 0.338 -021977 -20230616 2025届高一08班 0.972 0.889 0.861 +021771 +$t=\dfrac{1}{3}$ -021978 -20230616 2025届高一08班 1.000 -021979 -20230616 2025届高一08班 0.556 +021772 +(1) $(\overrightarrow {a}-\overrightarrow {b}) \cdot \overrightarrow {c}=\overrightarrow {a} \cdot \overrightarrow {c}- \overrightarrow {b} \cdot \overrightarrow {c}=1*1*(-\dfrac{1}{2})-1*1*(-\dfrac{1}{2})=0;\\$ +(2) $k<0$或$k>2$. -021980 -20230616 2025届高一08班 0.528 -021981 -20230616 2025届高一08班 0.917 +021773 +$[2,5]$ -021982 -20230616 2025届高一08班 0.972 -021983 -20230616 2025届高一08班 0.792 +021774 +$\arccos \dfrac{4}{5}$ -021984 -20230616 2025届高一08班 0.889 -021985 -20230616 2025届高一08班 0.778 +021775 +$\overrightarrow{OP}=\dfrac{3}{11}\overrightarrow {a}+\dfrac{2}{11}\overrightarrow {b}$ -021986 -20230616 2025届高一08班 0.556 -021977 -20230616 2025届高一09班 0.909 0.939 0.849 +021776 +(1) $(-1,0)$; (2) $(2,\dfrac{1}{2})$; (3) $(2,0)$或 $(-2,0)$; (4) $(\dfrac{3\sqrt{2}}{2},-\dfrac{3\sqrt{2}}{2})$. -021978 -20230616 2025届高一09班 1.000 -021979 -20230616 2025届高一09班 0.788 +021777 +(1) 10; (2) $(-\dfrac{4}{5},\dfrac{3}{5})$. -021980 -20230616 2025届高一09班 0.515 -021981 -20230616 2025届高一09班 0.939 +021778 +$x=4$, $y=1$. -021982 -20230616 2025届高一09班 0.970 -021983 -20230616 2025届高一09班 0.803 +021779 +$(\dfrac{3}{5},-\dfrac{4}{5})$ -021984 -20230616 2025届高一09班 0.818 -021985 -20230616 2025届高一09班 0.545 +021780 +$(4,-8)$ -021986 -20230616 2025届高一09班 0.636 -021987 -20230616 2025届高一11班 0.992 +021781 +$(1,2)$ -021988 -20230616 2025届高一11班 1.000 -021989 -20230616 2025届高一11班 0.974 +021782 +C -021990 -20230616 2025届高一11班 0.872 -021991 -20230616 2025届高一11班 0.923 +021783 +A -021992 -20230616 2025届高一11班 0.962 -021993 -20230616 2025届高一11班 0.910 0.833 +021784 +B -021994 -20230616 2025届高一11班 0.872 -021995 -20230616 2025届高一11班 0.923 +021786 +$\lambda=\mu$ 且$\lambda$和$\mu$非零. -021996 -20230616 2025届高一11班 0.846 -021997 -20230616 2025届高一11班 0.872 +021787 +(1) 当$t=\dfrac{3}{2}$时,点$P$在$x$轴上; 当$t=\dfrac{1}{3}$时,点$P$在$y$轴上;当$-\dfrac{2}{3}