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 00c773ed..11629a5f 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 = "14911" +problems = "40070" def generate_number_set(string,dict): string = re.sub(r"[\n\s]","",string) diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index 354ed23c..cbf54d2a 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,547 +1,1223 @@ ans -13512 -$2$ +021441 +错误, 正确, 错误, 错误 -13513 -$x=\mu$ -13514 -可能异面, 可能相交 +021442 +D -13515 -$\dfrac{y^2}{15}+\dfrac{x^2}{16}=1$, $x\ne 0$ -13516 -$[1,15]$ +021443 +C -13517 -$-\dfrac 13$ -13518 -$\dfrac 43$ +021444 +A -13519 -$(-\infty,-1]\cup [3,+\infty)$ -13520 +021445 +C + + +021446 +D + + +021447 +$-390^\circ$ + + +021448 +$304^\circ$, $-56^\circ$ + + +021449 +$-144^\circ$ + + +021450 +二, 四 + + +021451 +(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$ + + +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} + + +021453 +$-1290^{\circ}$;第二象限 + + +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) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. + + +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) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$. + + +021456 +C + + +021457 +B + + +021458 +$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$ + + +021459 +(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$ + + +021460 $\sqrt{3}$ -13521 -$\pi$ -13522 -A +021461 +(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ -13523 -D -13524 -B +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. -13525 -(1) $\dfrac{5}{12}\text{h}$; (2) 能, $v$的取值范围为$(\dfrac{9\sqrt{3}}2,\dfrac{\sqrt{559}}3]$ -13526 -(1) 证明略; (2) $\dfrac{a_1}{a_2}\le \dfrac{a_1+a_3+\cdots+a_{2n-1}}{a_2+a_4+\cdots+a_{2n}}$, 当且仅当$n=1$或$d=0$时成立等号; (3) $2023^2$ +021463 +$\frac{1}{2}$ -13527 -$\{(0,1),(2,5)\}$ -13528 -$x>1$且$y>1$ +021464 +(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. -13529 -$\sqrt{2}$ -13530 -$(-\infty,-8]\cup [2,+\infty)$ +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) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. -13531 -$[-2,2]$ -13532 -$\dfrac 13$ +021466 +(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. -13533 -$\dfrac{4\pi}{3}$ -13534 -$20$ +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. -13535 -\textcircled{3}\textcircled{4} -13536 -\textcircled{1}\textcircled{3}\textcircled{4} +021468 +$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ -13537 -B -13538 -C +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} -13539 -D -13540 -(1) 甲与乙的平均数分别为$7$和$7$; (2) 甲与乙的方差分别为$3$和$1.2$; (3) 两人射击水平相当, 甲的发挥更稳定 +021470 +$2\sqrt{5}$ -13541 -(1) $\dfrac 12$; (2) $\dfrac{4\sqrt{5}}5$ +021471 +$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ -13542 -$3.5$ -13543 -$\dfrac{20}{11}$ +021472 +$ \left( -2,\frac{2}{3} \right)$ -13544 -$a=\pm 1$ -13545 -$-17$ +021473 +$<$ -13546 -$0.7$ -13547 -$5$ +021474 +5 -13548 -$6\sqrt{3}$ -13549 -$0.6$ +021475 +2 -13550 -$2\pi^2+16\pi$ -13551 -$\dfrac 83$ +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, $\cos \alpha=-1$, $\tan \alpha = 0$. -13552 -C -13553 -C +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}$, $\tan \alpha=\frac{4}{3}$. -13554 -B -13555 -(1) $f(x)=\begin{cases}2^x-1+\log_2 (x+1), & x\ge 0, \\ 1-2^{-x}-\log_2(-x+1), & x<0;\end{cases}$ (2) $f(x)=-2^{x-2}+1-\log_2(x-1)$, $16.635$, 有$99.9\%$的把握认为患该疾病群体与为患该疾病群体的卫生习惯有差异; (2) 证明略, $R$的估计值为$6$ -13571 -(1) $y=2x$; (2) $(-\infty,-1)$ +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}$, $\tan \alpha=3$. -13572 -$-\dfrac 12$ -13573 -$2\pi$ +021487 +$\sin k\pi =0$;\\$\cos k\pi=\left\{ + \begin{array}{lc} + $1$, & k=2n \\ + $ -1$ , &k=2n-1\\ + \end{array} +\right.$ ($n \in \mathbf{Z}$). -13574 -$\dfrac{\sqrt{6}}2a^2$ -13575 -$3x-y-2=0$ +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) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. -13576 -$-\dfrac{3}{25}\overrightarrow{b}$ -13577 -$-2$ +021489 +第二象限 -13578 -$\dfrac{2\sqrt{5}}5$ -13579 -$[\dfrac 54,\dfrac{3\sqrt{17}}4]$ +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) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ -13580 -$77$ -13581 -$4$ +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}$. -13582 -A -13583 -B +021492 +$-\dfrac{3}{8}$ -13584 -D -13585 -(1) $0.89$; (2) $0.0014$ +021493 +$-\dfrac{1}{20}$ -13586 -(1) $x^2-\dfrac{y^2}{3}=1$; (2) 证明略 -13587 -$\{1,2\}$ +021494 +$\dfrac{7\sqrt{2}}{4}$ -13588 -$2$ -13589 -$6$ +021495 +$\dfrac{3\sqrt{5}}{5}$ -13590 -$3$ -13591 -$5$ +021496 +$11$ -13592 -$-\sqrt{2}$ -13593 -$\dfrac 16$ +021497 +$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ -13594 -$-28$ -13595 -$0.14$ +021498 +$\sin ^2 \alpha$ -13596 -$2$ -13597 -$\ln 2$ - -13598 -$\dfrac{\sqrt{13}}2$ - -13599 -A - -13600 -C - -13601 -C - -13602 -B - -13603 -(1) $\dfrac\pi 6$; (2) $6+6\sqrt{3}$ - -13604 -(1) 证明略; (2) $\dfrac{\sqrt{6}}8$ - -13605 -(1) $X\sim \begin{pmatrix} 0 & 20 & 100\\ 0.2 & 0.32 & 0.48\end{pmatrix}$; (2) 应选择先回答B类问题 - -13606 -(1) $\dfrac{x^2}{25}+\dfrac{y^2}{9}=1$; (2) $2\sqrt{2}+\sqrt{17}$; (3) 定值为$34$ - -13607 -(1) $y=x$; (2) 在$[0,+\infty)$上是严格增函数; (3) 证明略 - -13608 +021499 $1$ -13609 -$[\dfrac 12,1]$ -13610 -$2\sqrt{3}$ - -13611 -$x\le \dfrac{a+b}{2}$, 等号成立当且仅当$a=b$ +021502 +$-\dfrac{12}{5}$ -13612 -$2x-y+1=0$ +021503 +$-\dfrac{\sqrt{3}}{2}$ -13613 -$\dfrac{3\pi}{4}$ -13614 -$115$ +021504 +$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ -13615 + +021505 +$-\dfrac{\sqrt{11}}{3}$ + + +021506 +$\dfrac{\pi}{3}$ + + +021507 +$\left[ 0,\pi \right )$ + + +021508 +$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$ + + +021509 +$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$ + + +021510 +$\cot \alpha$ + + +021511 $-1$ -13616 -如$x^2+(y-2)^2=1$等(答案不唯一) -13617 -$(0,-4)$ - -13618 -$72$ - -13619 -$\dfrac 78$ - -13620 -B - -13621 -A - -13622 -C - -13623 -C - -13624 -(1) $\dfrac 13$; (2) 证明略 - -13625 -(1) $a_n=3n-1$; (2) $S_n=\dfrac{21}{4}-\dfrac{6n+7}{4\cdot 3^{n-1}}$ - -13626 -(1) $V=x(3-2x)^2$, $x\in (0,\dfrac 32)$; (2) 当$x=\dfrac 12$时, $V$取到最大值$2$ - -13627 -(1) 最小正周期为$\pi$, 取值范围为$[-1,2]$; (2) $\sqrt{3}$ - -13628 -(1) $2$; (2) 双曲线方程为$x^2-\dfrac{y^2}{3}=1$, 过顶点$(2,0)$与$(-1,0)$ +021512 +$-1$ -13629 -$4$或$-6$ +021513 +$ \sin 2-\cos 2$ -13630 -$(\dfrac\pi 6,\dfrac{5\pi}6)$ -13631 -$44$ - -13632 -$41$ - -13633 -$1$ - -13634 -$24$ - -13635 -$\dfrac{7\sqrt{3}}3\pi$ - -13636 -$20$ - -13637 -$2.5$ - -13638 -$76$元 - -13639 -$p_1$,$p_4$ - -13640 -$\dfrac 34$ - -13641 -D - -13642 -B - -13643 -C - -13644 -B - -13645 -证明略 - -13646 -(1) $\dfrac\pi 3$; (2) $(6,12]$ - -13647 -(1) $0.6$; (2) $x\sim \begin{pmatrix}0 & 10 & 20 & 30\\0.16 & 0.44 & 0.34 & 0.06\end{pmatrix}$, $E[X]=13$ - -13648 -(1) $\dfrac{x^2}3+y^2=1$; (2) $\sqrt{6}$; (3) $1$ - -13649 -(1) 在$(-1,1)$上是严格增函数, 在$(1,+\infty)$上是严格减函数; (2) $(-\infty,0]$; (3) 证明略 - -13650 -$\{(0,0),(1,0),(-1,0)\}$ - -13651 -$7$ - -13652 -$-2$ - -13653 +021514 $0$ -13654 -$\dfrac{6\pi}{5}$ -13655 -$0.75$ +021515 +$0$ -13656 -$(-6,2)$ -13657 -$\dfrac{2\sqrt{3}}3$ +021516 +$-\dfrac{\sqrt{1-a^2}}{a}$ -13658 -$\dfrac{16}3$ -13659 -$\dfrac\pi 6$ +021517 +$-\dfrac{2+\sqrt{3}}{3}$ -13660 -\textcircled{1}\textcircled{2}\textcircled{4} -13661 -$12120$ +021518 +(1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$. -13662 -B -13663 -B +021519 +(1) $-\dfrac{2}{3}$; \\ +(2) $\dfrac{2}{3}$; \\ +(3) $-\dfrac{\sqrt{5}}{3}$;\\ +(4) $\dfrac{\sqrt{5}}{2}$. -13664 -D -13665 -D +021520 +(1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ; +(3) $-\tan \dfrac{\pi}{9}$; (4) $\cot \dfrac{7\pi}{15}$. -13666 -(1) $1$; (2) $\arcsin\dfrac{\sqrt{3}}4$ -13667 -(1) $\sqrt{7}$; (2) $-1-\dfrac{\sqrt{3}}2$ +021521 +$\dfrac{2}{5}$ -13668 -(1) $(x-2)^2+y^2=\dfrac{12}7$; (2) $\dfrac{3\sqrt{2}}2$或$\dfrac{\sqrt{2}}2$ -13669 -(1) $\dfrac 25$; (2) $X\sim \begin{pmatrix} 0 & 1 & 2 \\ \dfrac{6}{25} & \dfrac{13}{25} & \dfrac{6}{25}\end{pmatrix}$; (3) 不认为人数有变化, 理由略 +021522 +$(3,4)$ -13670 -(1) $y=x-1$; (2) $(-\infty,\dfrac{3}{2}]$; (3) $(-\infty,\dfrac{\sqrt{2}}2)$ -13671 -$1$ +021523 +$0$ -13672 -$3$ -13673 -$\dfrac 12$ +021524 +$\sin \alpha$ -13674 -$(0,2)$ -13675 -$2$ +021525 +$-\dfrac{1}{5}$ -13676 -$0.57$ -13677 -$\dfrac 72+\sqrt{6}$ +021526 +(1) $\dfrac{\sqrt{6}}{6}-\sqrt{3}$;\\ +(2) $-\dfrac{\sqrt{6}}{3}$;\\ +(3) $1$ -13678 -$\dfrac\pi 3$或$\dfrac{2\pi}3$ -13679 -$\sqrt{5}$ +021527 +(1) $\dfrac{6 \pi}{5}$; (2) $\dfrac{4 \pi}{5}$; (3) $\dfrac{13 \pi}{10}$; (4) $\dfrac{17 \pi}{10}$. -13680 -$\dfrac{7\sqrt{3}}3$ -13681 -$\dfrac 83$ +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, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=\sqrt{3}$. -13682 -$\dfrac 32$ -13683 -A +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$x=k \pi - \dfrac{3\pi}{8} ,\ k \in \mathbf{Z}\}$; -13684 + +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 +$\dfrac{2\sqrt{6}-1}{6}$ + + +021540 C -13685 + +021541 A -13686 + +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 + + +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 +$-\dfrac{63}{65}$ + + +031288 +$[7,10]$ + + +031289 +$(-\infty,-2)\cup(-2,3]$ + + +031290 +$2$ + + +031291 +$7$ + + +031292 +$a\ge3$ + + +031293 +$-9$或$3$ + + +031294 +$\dfrac{1}{27}$ + + +031295 +$[-3,3]$ + + +031296 +$45$ + + +031297 +$(1,\dfrac 32]$ + + +031298 +$[0,1]$ + + +031299 +$\dfrac{\sqrt{6}}{4}$ + + +031300 +D + + +031301 B -13687 -(1) 证明略; (2) $\dfrac\pi 6$ -13688 -(1) 证明略; (2) $(\dfrac 94,\dfrac{15}4)$ +031302 +A -13689 -(1) $l=\dfrac{1}{\sin \theta}+\dfrac{1}{\cos\theta}+\dfrac{1}{\sin\theta\cdot \cos\theta}$, $\theta\in (\dfrac\pi 6,\dfrac\pi 3)$; (2) $2+2\sqrt{2}$, 此时$\theta=\dfrac\pi 4$ -13690 -(1) $\dfrac{\sqrt{2}}2$; (2) $t=\dfrac{\sqrt{6}}3b$ +031303 +A + + +031304 +$(1)a_n=-3n+19,b_n=4^{3-n}\\ +(2)1\le n \le 28,S_n>T_n;n=29,S_n=T_n;n \ge 30,S_nT_n;n=29,S_n=T_n;n \\ge 30,S_n