diff --git a/工具/文本文件/metadata.txt b/工具/文本文件/metadata.txt index ea1b1d2d..f1c51a61 100644 --- a/工具/文本文件/metadata.txt +++ b/工具/文本文件/metadata.txt @@ -1,63 +1,2907 @@ ans -17465 -$\{-1,1\}$ -17466 -$\dfrac{\sqrt{2}}{2}$ +021441 +错误, 正确, 错误, 错误 -17467 -$(-\infty,-3]\cup (1,+\infty)$ -17468 -$-\dfrac{1}{8}$ - -17469 -$\pi$ - -17470 -$x=4$ - -17471 -$28$ - -17472 -$8.5$ - -17473 -$(-3,+\infty)$ - -17474 -$95.5$ - -17475 -$(-4,0)cup \{2\sqrt{2}-2\}$ - -17476 -$1518.5$ - -17477 -A - -17478 +021442 D -17479 + +021443 +C + + +021444 +A + + +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 -17480 + +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 +$\sqrt{3}$ + + +021461 +(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$ + + +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. + + +021463 +$\frac{1}{2}$ + + +021464 +(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$. + + +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) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$. + + +021466 +(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$. + + +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. + + +021468 +$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$ + + +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} + + +021470 +$2\sqrt{5}$ + + +021471 +$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ + + +021472 +$ \left( -2,\frac{2}{3} \right)$ + + +021473 +$<$ + + +021474 +5 + + +021475 +2 + + +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, $\cos \alpha=-1$, $\tan \alpha = 0$. + + +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}$, $\tan \alpha=\frac{4}{3}$. + + +021478 +$-\frac{\sqrt{3}}{4}$ + + +021479 +(1) 第四象限； (2) 第一、四象限；(3)第一、三象限；(4)第一、三象限. + + +021480 +$A=\left\{ -2,-0,4 \right\}$ + + +021481 +(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ +(2) $[0,3)$ + + +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} + + +021483 +(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\ +(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$ + + +021484 +$-\frac{2\sqrt{5}}{5}$;$2$ + + +021485 +\textcircled{2} \textcircled{4} + + +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}$, $\tan \alpha=3$. + + +021487 +$\sin k\pi =0$;\\$\cos k\pi=\left\{ + \begin{array}{lc} + $1$, & k=2n \\ + $ -1$ , &k=2n-1\\ + \end{array} +\right.$ ($n \in \mathbf{Z}$). + + +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) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. + + +021489 +第二象限 + + +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) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ + + +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}$. + + +021492 +$-\dfrac{3}{8}$ + + +021493 +$-\dfrac{1}{20}$ + + +021494 +$\dfrac{7\sqrt{2}}{4}$ + + +021495 +$\dfrac{3\sqrt{5}}{5}$ + + +021496 +$11$ + + +021497 +$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ + + +021498 +$\sin ^2 \alpha$ + + +021499 +$1$ + + +021502 +$-\dfrac{12}{5}$ + + +021503 +$-\dfrac{\sqrt{3}}{2}$ + + +021504 +$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ + + +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 +$-1$ + + +021512 +$-1$ + + +021513 +$ \sin 2-\cos 2$ + + +021514 +$0$ + + +021515 +$0$ + + +021516 +$-\dfrac{\sqrt{1-a^2}}{a}$ + + +021517 +$-\dfrac{2+\sqrt{3}}{3}$ + + +021518 +(1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$. + + +021519 +(1) $-\dfrac{2}{3}$; \\ +(2) $\dfrac{2}{3}$; \\ +(3) $-\dfrac{\sqrt{5}}{3}$;\\ +(4) $\dfrac{\sqrt{5}}{2}$. + + +021520 +(1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ; +(3) $-\tan \dfrac{\pi}{9}$; (4) $\cot \dfrac{7\pi}{15}$. + + +021521 +$\dfrac{2}{5}$ + + +021522 +$(3,4)$ + + +021523 +$0$ + + +021524 +$\sin \alpha$ + + +021525 +$-\dfrac{1}{5}$ + + +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 +$\dfrac{\pi}{2}$ + + +021545 +$-\dfrac{2+\sqrt{15}}{6}$ + + +021546 +$-\dfrac{\sqrt{2}}{2}$ + + +021547 +$\sin 2\beta$ + + +021548 +$0$ + + +021549 +$2-\sqrt{3}$ + + +021550 +$\dfrac{16}{65}$ + + +021551 +$-\dfrac{7}{25}$ + + +021552 +$-\dfrac{4\sqrt{14}+3\sqrt{2}}{20}$ + + +021553 +$(\dfrac{4\sqrt{3}+3}{2},\dfrac{3\sqrt{3}-4}{2})$ + + +021554 +$-\dfrac{33}{65}$或$\dfrac{63}{65}$ + + +021555 B -17481 -(1) $a_n=n$, $b_n=2^{n-1}$; (2) 证明略 -17482 -(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\sqrt{3}}{3}$ +021556 +C -17483 -(1) $y=27\times (\dfrac{4}{3})^x$, $x\ge 0$; (2) $9$分钟 -17484 -(1) $6$; (2) $-4$; (3) $(2,0)$或$(-\dfrac{2}{7},-\dfrac{12}{7})$ +021557 +$-\dfrac{56}{65}$ + + +021558 +$-3$ + + +021559 +$\dfrac{3}{4}$ + + +021560 +$\dfrac{-6+5\sqrt{3}}{3}$ + + +021561 +$\tan \alpha$ + + +021562 +$\sqrt{3}$ + + +021563 +$-\dfrac{\sqrt{3}}{3}$ + + +021564 +A + + +021565 +$-\dfrac{17}{31}$ + + +021566 +$\dfrac{\pi}{4}$ + + +021567 +(1) $\dfrac{1}{3}$; +(2) $\dfrac{1}{7}$ + + +021568 +$-\dfrac{1}{5}$ + + +021569 +当$CD = 1.4$米时，$\tan \angle ACB$最大 + + +021570 +(1) $2 \sin (\alpha+\dfrac{\pi}{6})$; +(2) $\sqrt{2} \sin (\alpha+\dfrac{7\pi}{4})$. + + +021571 +$6\cos(\alpha+\dfrac{\pi}{3})$ + + +021572 +$2k \pi-\dfrac{\pi}{3}(k\in \mathbf{Z} )$ + + +021573 +B + + +021574 +$\dfrac{1}{3}$ + + +021575 +$\dfrac{\pi}{12}$或$\dfrac{5\pi}{12}$ + + +021576 +$5$ + + +021577 +$\dfrac{13}{3}$ + + +021578 +$-\dfrac{p}{1+q}$ + + +021579 +$\dfrac{3}{5}$ + + +021580 +$\dfrac{24}{7}$ + + +021581 +$-\dfrac{24}{25}$ + + +021582 +$-\dfrac{15}{17}$ + + +021583 +$\sin 2 \varphi=\dfrac{4\sqrt{2}}{9}$; +$\cos 2 \varphi=-\dfrac{7}{9}$; +$\tan 2 \varphi=-\dfrac{4\sqrt{2}}{7}$. + + +021584 +$\dfrac{24}{25}$; $\dfrac{7}{25}$; $\dfrac{24}{7}$ + + +021585 +(1) $-\dfrac{\sqrt{3}}{3}$;\\ +(2) $\dfrac{3}{4}$. + + +021586 +$\dfrac{7}{24}$ + + +021587 +$-\dfrac{2\sqrt{10}}{5}$ + + +021588 +$1$ + + +021590 +$1$或$\dfrac{7}{25}$ + + +021591 +$-\dfrac{\sqrt{2-2a}}{2}$ + + +021592 +第三象限 + + +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， +$\sin \dfrac{\theta}{2}=-\dfrac{\sqrt{3}}{3}$, +$\cos \dfrac{\theta}{2}=\dfrac{\sqrt{6}}{3}$, +$\tan \dfrac{\theta}{2}=-\dfrac{\sqrt{2}}{2}$. + + +021594 +$\dfrac{3}{5}$;$\dfrac{4}{5}$ + + +021596 +$\dfrac{2}{3}$ + + +021597 +$\cos \alpha-\sin \alpha$ + + +021598 +$\sin \dfrac{ \alpha}{2}$ + + +021599 +(1) $\tan \dfrac{\theta}{2}$; (2) $\sin \alpha$. + + +021600 +$\dfrac{\sqrt{6}}{2}$ + + +021601 +$30^{\circ}$或$90^{\circ}$ + + +021602 +$\sqrt{6}$ + + +021603 +$55$ + + +021604 +$\dfrac{\pi}{3}$或$\dfrac{2\pi}{3}$ + + +021605 +$1: \sqrt{3}: 2$ + + +021606 +$2$ + + +021607 +$\dfrac{5}{8}$ + + +021608 +等腰 + + +021609 +$\dfrac{3\sqrt{2}}{2}$ + + +021610 +$\sqrt{3}$ + + +021611 +$\dfrac{7\pi}{12}$ + + +021612 +$\dfrac{2\pi}{3}$ + + +021613 +(1) $\left( 0,9 \right)$; \\ +(2) $\{9\} \cup \left[18,+ \infty \right)$;\\ +(3) $\left( 9,18 \right)$. + + +021614 +$\dfrac{3\sqrt{7}}{8}$ + + +021615 +$\sqrt{17}$或$\sqrt{65}$ + + +021616 +$\dfrac{\pi}{4}$ + + +021617 +\textcircled{1}；\textcircled{2} + + +021618 +$a>3$ + + +021619 +$a=\sqrt{21}$和$\sin B=\dfrac{5\sqrt{7}}{14}$ + + +021620 +$\dfrac{2\pi}{3}$ + + +021621 +$c=\sqrt{6}+\sqrt{2}$;$C=75^\circ$. + + +021622 +$\dfrac{\sqrt{19}}{2}$ + + +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. + + +021624 +$\dfrac{\sqrt{5}}{5}$ + + +021625 +$\dfrac{2\sqrt{5}}{5}$或$-\dfrac{2\sqrt{5}}{25}$ + + +021626 +$\dfrac{\sqrt{5}}{5}$或$\dfrac{11\sqrt{5}}{25}$ + + +021627 +$\left ( 2,2\sqrt{2} \right )$ + + +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. + + +021629 +$a=\sqrt{13}$;$R=\dfrac{\sqrt{39}}{3}$. + + +021630 +$6\sqrt{19}$ + + +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) $x=k\pi- \arctan \dfrac{1}{2},k \in \mathbf{Z}$. + + +021632 +$300\sqrt{3}$ + + +021633 +证明略 + + +021634 +$\theta=\dfrac{\pi}{12}$;塔高为$1.5$千米. + + +021635 +$64.81$米 + + +021636 +(1) $3.9$千米;(2) $4.0$千米. + + +021637 +$2.4$千米 + + +021638 +$\dfrac{\pi}{2}$ + + +021639 +B + + +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} + + +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$\left \{x|\dfrac{\pi}{2}+2k\pi \leq x \leq \dfrac{3\pi}{2}+2k\pi,k \in \mathbf{Z} \right \}$. + + +021642 +$\left \{x|\dfrac{\pi}{6} \leq x \leq \dfrac{5\pi}{6},k \in \mathbf{Z} \right \}$ + + +021643 +$2\pi$ + + +021644 +C + + +021645 +C + + +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. + + +021647 +(1) $8\pi$; +(2) $\pi$;(3) $\pi$;(4) $2\pi$. + + +021648 +$3$ + + +021649 +A + + +021650 +C + + +021651 +(1) 假;(1) 假;(3) 真. + + +021652 +D + + +021653 +(1) $\pi$; (2) $\pi$; (3) $\dfrac{\pi}{2}$; (4) $\dfrac{\pi}{|a|}$. + + +021654 +$4\sin(\dfrac{\pi x}{2})-2$ + + +021655 +B + + +021656 +A + + +021657 +(1) $f(3)=-1$; $f(5)=1$; $f(7)=-1$;\\ +(2) $T=4$. + + +021658 +$\left [2,4\right] $ + + +021659 +$\left [-2,2\right] $ + + +021660 +$ [-\dfrac{3}{2},3] $ + + +021661 +$ (-\dfrac{\sqrt{3}}{2},1] $ + + +021662 +$3$; $\left \{x|x=-\dfrac{\pi}{2}+2k\pi,k \in \bf{Z} \right\}$ + + +021663 +$-3$; $\left \{x|x=-\dfrac{\pi}{12}+k\pi,k \in \bf{Z} \right\}$ + + +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$-\sqrt{13}$. + + +021665 +D + + +021666 +C + + +021667 +当$\alpha=\dfrac{\pi}{2}-\theta$时，竹竿的影子最长，最长为$\dfrac{\sin(\alpha+\theta)}{\sin \theta}*l$. + + +021668 +$[-1,1]$ + + +021669 +$\{x|x\neq 2k\pi,k \in \bf{Z}\}$;$(-\infty,0]$ + + +021670 +$k=3$或$-3$;$b=-1$ + + +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$-1$. + + +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} + + +021695 +$4\pi$;$4$. + + +021696 +$f(x)=4\sin(x+\dfrac{\pi}{6})$ + + +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${x|x=-\dfrac{\pi}{6}+\dfrac{2k\pi}{3},k \in \bf{Z}}$ + + +021698 +$x=\pi+2k\pi,k \in \bf{Z}$ + + +021699 +纵;伸长; $3$} + + +021700 +缩短; $\dfrac{1}{2}$; 缩短; $\dfrac{1}{3}$. + + +021701 +$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{3})$ + + +021702 +$f(x)=\sin(\dfrac{1}{2}x-\dfrac{\pi}{6})$ + + +021703 +$f(x)=2\sin(\dfrac{1}{3}x+\dfrac{\pi}{6})$ + + +021704 +$x=\dfrac{\pi}{3}+2k\pi,k \in \bf{Z}$; $(-\dfrac{2\pi}{3}+2k\pi,0),k \in \bf{Z}$. + + +021705 +C + + +021706 +左; $\dfrac{\pi}{8}$. + + +021707 +$f(x)=\sin(2x+\dfrac{\pi}{2})$, +$g(x)=\sin x$. + + +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}$. + + +021709 +(1) $2\pi$; (2) $1$; (3) $\dfrac{\pi}{2}$. + + +021710 +(1) $[0,\dfrac{\pi}{2})$, $(\dfrac{3\pi}{2},2\pi]$; \\ +(2) $[0,\dfrac{\pi}{2})$, $(\dfrac{\pi}{2},\pi]$. + + +021711 +(1) 奇函数; (2) 偶函数. + + +021712 +$[-5,+\infty)$ + + +021713 +(1) $<$; (2) $>$; (3) $>$; (4)$<$. + + +021714 +\textcircled{3} + + +021715 +最小值为$-\dfrac{\sqrt{3}}{3}$，此时$x=-\dfrac{\pi}{3}$. + + +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}$. + + +021717 +$\{x|x\neq \dfrac{\pi}{4}-\dfrac{1}{2}+\dfrac{k\pi}{2},k \in \bf{Z} \}$ + + +021718 +$(-\dfrac{\pi}{4}+\dfrac{k\pi}{3},\dfrac{\pi}{12}+\dfrac{k\pi}{3}), k \in \bf{Z}$ + + +021719 +B + + +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}$. + + +021721 +函数零点为$x=\dfrac{2k\pi}{5}+2k\pi,k \in \bf{Z}$. + + +021722 +(1) 假命题; (2) 假命题; (3) 假命题; (4) 真命题. + + +021723 +$[-4,2+4\sqrt{3}]$ + + +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. + + +021726 +A + + +021727 +C + + +021728 +B + + +021729 +单位圆 + + +021730 +B + + +021731 +$\overrightarrow{CD}$ + + +021732 +$\overrightarrow{AC}$ + + +021733 +(1) 假命题; (2) 真命题; (3) 假命题; (4) 假命题. + + +021734 +(1) $\overrightarrow{DB}$; $\overrightarrow{FE}$.\\ +(2) $\overrightarrow{ED}$; $\overrightarrow{CF}$; $\overrightarrow{FA}$.\\ +(3) $\overrightarrow{EF}$; $\overrightarrow{AD}$; $\overrightarrow{DA}$; $\overrightarrow{DB}$; $\overrightarrow{BD}$; $\overrightarrow{AB}$; $\overrightarrow{BA}$. + + +021735 +$40$ + + +021736 +$40$ + + +021737 +$2$ + + +021739 +$-3\overrightarrow {a}+6 \overrightarrow {b}$ + + +021740 +$7 \overrightarrow {a}-2 \overrightarrow {b}- \overrightarrow {c}$ + + +021741 +(1) 假命题; (2) 真命题; (3) 假命题; (4) 真命题. + + +021742 +(1) $\overrightarrow {AB}=\dfrac{1}{2}\overrightarrow {a}-\dfrac{1}{2}\overrightarrow {b}$;\\ +(2) $\overrightarrow {BC}=\dfrac{1}{2}\overrightarrow {a}+\dfrac{1}{2}\overrightarrow {b}$. + + +021743 +$\lambda=\dfrac{1}{3}$ + + +021744 +$x=2$; $y=1$. + + +021745 +(2) $m=1$或$-1$. + + +021746 +$\overrightarrow{DC}=\dfrac{1}{2}\overrightarrow{a}$;\\ $\overrightarrow{DC}=-\dfrac{1}{2}\overrightarrow{a}+\overrightarrow{b}$;\\ +$\overrightarrow{MN}=-\dfrac{1}{4}\overrightarrow{a}-\overrightarrow{b}$. + + +021747 +$\overrightarrow{0}$ + + +021748 +$\dfrac{2}{3}\overrightarrow{a}+\dfrac{1}{3}\overrightarrow{b}$ + + +021749 +A + + +021750 +B + + +021751 +C + + +021752 +$\sqrt{3}$ + + +021753 +$-\dfrac{3\sqrt{3}}{2}$ + + +021754 +等边三角形 + + +021755 +$\dfrac{\pi}{4}$ + + +021756 +$\dfrac{2\pi}{3}$ + + +021757 +$-10\sqrt{2}$ + + +021758 +$\dfrac{4}{3}$ + + +021759 +$-\dfrac{2}{3}\overrightarrow {a}$ + + +021760 +B + + +021761 +B + + +021762 +A + + +021763 +$7$ + + +021764 +$2$ + + +021765 +C + + +021766 +外心; 重心; 垂心. + + +021767 +$\dfrac{\pi}{3}$ + + +021768 +$-25$ + + +021769 +$\lambda=\dfrac{7}{12}$ + + +021770 +$AB=8$ + + +021771 +$t=\dfrac{1}{3}$ + + +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$k>2$. + + +021773 +$[2,5]$ + + +021774 +$\arccos \dfrac{4}{5}$ + + +021775 +$\overrightarrow{OP}=\dfrac{3}{11}\overrightarrow {a}+\dfrac{2}{11}\overrightarrow {b}$ + + +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 +$\{x|2k\pi+\dfrac{\pi}4=latex, scale = 0.7]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (-pi,0.1) -- (-pi,0) node [below left] {$-\\pi$};\n\\draw (-0.5*pi,0.1) -- (-0.5*pi,0) node [below] {$-\\frac{\\pi}{2}$};\n\\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\\frac{\\pi}{2}$};\n\\draw (pi,0.1) -- (pi,0) node [below] {$\\pi$};\n\\draw (0.1,1) -- (0,1) node [left] {$1$};\n\\draw (0.1,-1) -- (0,-1) node [left] {$-1$};\n\\draw [domain = -pi:pi,samples = 100] plot (\\x,{sin(\\x/pi*180)+1});\n\\end{tikzpicture}\\\\\n(2) \\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (0,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (pi/2,0.1) -- (pi/2,0) node [below] {$\\frac{\\pi}{2}$};\n\\draw (pi,0.1) -- (pi,0) node [below] {$\\pi$};\n\\draw (1.5*pi,0.1) -- (1.5*pi,0) node [below] {$\\frac{3\\pi}{2}$};\n\\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\\pi$};\n\\draw (0.1,1) -- (0,1) node [left] {$1$};\n\\draw (0.1,-1) -- (0,-1) node [left] {$-1$};\n\\draw [domain = 0:2*pi,samples = 100] plot (\\x,{-cos(\\x/pi*180)});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [ @@ -494698,7 +494698,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) 定义域为$\\left \\{x|x \\neq-\\dfrac{\\pi}{2}+2k\\pi,k \\in \\mathbf{Z} \\right \\}$;\\\\\n(2) 定义域为$\\left \\{x|\\dfrac{\\pi}{2}+2k\\pi \\leq x \\leq \\dfrac{3\\pi}{2}+2k\\pi,k \\in \\mathbf{Z} \\right \\}$.", "solution": "", "duration": -1, "usages": [ @@ -494727,7 +494727,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\left \\{x|\\dfrac{\\pi}{6} \\leq x \\leq \\dfrac{5\\pi}{6},k \\in \\mathbf{Z} \\right \\}$", "solution": "", "duration": -1, "usages": [ @@ -494756,7 +494756,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2\\pi$", "solution": "", "duration": -1, "usages": [ @@ -494785,7 +494785,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -494814,7 +494814,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -494843,7 +494843,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 当$a \\in (-\\infty，-\\dfrac{\\sqrt{2}}{2})\\cup (1,+\\infty)$ 时，方程实数解个数为$0$个；\\\\\n当$a \\in [-\\dfrac{\\sqrt{2}}{2},0)\\cup \\{1\\}$ 时，方程实数解个数为$1$个；\\\\\n当$a \\in [0,1)$时，方程实数解个数为$2$个.\\\\\n(2) 当$a \\in (-\\infty，-1)\\cup (1,+\\infty)$ 时，方程实数解个数为$0$个；\\\\\n当$a \\in (0,1]$时，方程实数解个数为$1$个;\\\\\n当$a \\in \\{0,-1\\}$时，方程实数解个数为$2$个;\\\\\n当$a \\in (-1,0)$时，方程实数解个数为$3$个.", "solution": "", "duration": -1, "usages": [ @@ -494872,7 +494872,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $8\\pi$;\n(2) $\\pi$;(3) $\\pi$;(4) $2\\pi$.", "solution": "", "duration": -1, "usages": [ @@ -494901,7 +494901,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$", "solution": "", "duration": -1, "usages": [ @@ -494930,7 +494930,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -494959,7 +494959,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -494988,7 +494988,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 假;(1) 假;(3) 真.", "solution": "", "duration": -1, "usages": [ @@ -495017,7 +495017,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -495046,7 +495046,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\pi$; (2) $\\pi$; (3) $\\dfrac{\\pi}{2}$; (4) $\\dfrac{\\pi}{|a|}$.", "solution": "", "duration": -1, "usages": [ @@ -495075,7 +495075,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$4\\sin(\\dfrac{\\pi x}{2})-2$", "solution": "", "duration": -1, "usages": [ @@ -495104,7 +495104,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -495133,7 +495133,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [ @@ -495162,7 +495162,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $f(3)=-1$; $f(5)=1$; $f(7)=-1$;\\\\\n(2) $T=4$.", "solution": "", "duration": -1, "usages": [ @@ -495191,7 +495191,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\left [2,4\\right] $", "solution": "", "duration": -1, "usages": [ @@ -495220,7 +495220,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\left [-2,2\\right] $", "solution": "", "duration": -1, "usages": [ @@ -495249,7 +495249,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$ [-\\dfrac{3}{2},3] $", "solution": "", "duration": -1, "usages": [ @@ -495278,7 +495278,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$ (-\\dfrac{\\sqrt{3}}{2},1] $", "solution": "", "duration": -1, "usages": [ @@ -495307,7 +495307,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$3$; $\\left \\{x|x=-\\dfrac{\\pi}{2}+2k\\pi,k \\in \\bf{Z} \\right\\}$", "solution": "", "duration": -1, "usages": [ @@ -495336,7 +495336,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-3$; $\\left \\{x|x=-\\dfrac{\\pi}{12}+k\\pi,k \\in \\bf{Z} \\right\\}$", "solution": "", "duration": -1, "usages": [ @@ -495365,7 +495365,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "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$\\sqrt{13}$;\\\\\n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$-\\sqrt{13}$.", "solution": "", "duration": -1, "usages": [ @@ -495394,7 +495394,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [ @@ -495423,7 +495423,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -495452,7 +495452,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "当$\\alpha=\\dfrac{\\pi}{2}-\\theta$时，竹竿的影子最长，最长为$\\dfrac{\\sin(\\alpha+\\theta)}{\\sin \\theta}*l$.", "solution": "", "duration": -1, "usages": [ @@ -495481,7 +495481,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[-1,1]$", "solution": "", "duration": -1, "usages": [ @@ -495510,7 +495510,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\{x|x\\neq 2k\\pi,k \\in \\bf{Z}\\}$;$(-\\infty,0]$", "solution": "", "duration": -1, "usages": [ @@ -495539,7 +495539,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$k=3$或$-3$;$b=-1$", "solution": "", "duration": -1, "usages": [ @@ -495568,7 +495568,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "当$x=0$时，函数$y$取到最大值，最大值为$0$;\\\\\n当$x=\\dfrac{\\pi}{4}$时，函数$y$取到最小值，最小值为$-1$.", "solution": "", "duration": -1, "usages": [ @@ -495597,7 +495597,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$f(a)=\\begin{cases}\na^2+2a+2, & a\\leq -1,\\\\\n1, & -1=latex, scale = 0.7]\n\\draw [->] (-4,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-1.5) -- (0,2) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw ({-pi/12},0.1) -- ({-pi/12},0) node [below left] {$-\\frac{\\pi}{12}$};\n\\draw ({pi/6},0.1) -- ({pi/6},0) node [below] {$\\frac{\\pi}{6}$};\n\\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\\frac{5\\pi}{12}$};\n\\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above] {$\\frac{2\\pi}{3}$};\n\\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\\frac{11\\pi}{12}$};\n\\draw (0.1,1) -- (0,1) node [left] {$1$};\n\\draw (0.1,-1) -- (0,-1) node [left] {$-1$};\n\\draw [domain = {-pi/12}:{11*pi/12},samples = 100] plot (\\x,{sin(2*\\x/pi*180+30)});\n\\end{tikzpicture}\\\\\n(2) \\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-1,0) -- (15,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw (2*pi,0.1) -- (2*pi,0) node [below] {$2\\pi$};\n\\draw (pi,0.1) -- (pi,0) node [below] {$\\pi$};\n\\draw (3*pi,0.1) -- (3*pi,0) node [below] {$\\frac{3\\pi}{2}$};\n\\draw (4*pi,0.1) -- (4*pi,0) node [below] {$4\\pi$};\n\\draw (0.1,2) -- (0,2) node [left] {$2$};\n\\draw (0.1,-2) -- (0,-2) node [left] {$-2$};\n\\draw [domain =0:4*pi,samples = 100] plot (\\x,{2*sin(0.5*\\x/pi*180)});\n\\end{tikzpicture}\\\\\n(3) \\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-1,0) -- (4,0) node [below] {$x$};\n\\draw [->] (0,-1) -- (0,1) node [left] {$y$};\n\\draw (0,0) node [below right] {$O$};\n\\draw (0.25*pi,0.1) -- (0.25*pi,0) node [below] {$\\frac{\\pi}{4}$};\n\\draw (pi,0.1) -- (pi,0) node [below] {$\\pi$};\n\\draw (0.5*pi,0.1) -- (0.5*pi,0) node [below] {$\\frac{\\pi}{2}$};\n\\draw (0.75*pi,0.1) -- (0.75*pi,0) node [above] {$\\frac{3\\pi}{4}$};\n\\draw (0.1,0.5) -- (0,0.5) node [left] {$\\frac{1}{2}$};\n\\draw (0.1,-0.5) -- (0,-0.5) node [left] {$-\\frac{1}{2}$};\n\\draw [domain =0:pi,samples = 100] plot (\\x,{0.5*sin(2*\\x/pi*180)});\n\\end{tikzpicture}\\\\\n(4) \\begin{tikzpicture}[>=latex, scale = 0.7]\n\\draw [->] (-1.5,0) -- (3.5,0) node [below] {$x$};\n\\draw [->] (0,-5.5) -- (0,5.5) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw ({-pi/3},0.1) -- ({-pi/3},0) node [below left] {$-\\frac{\\pi}{3}$};\n\\draw ({-pi/12},0.1) -- ({-pi/12},0) node [above left] {$-\\frac{\\pi}{12}$};\n\\draw ({pi/6},0.1) -- ({pi/6},0) node [below right] {$\\frac{\\pi}{6}$};\n\\draw ({5*pi/12},0.1) -- ({5*pi/12},0) node [below] {$\\frac{5\\pi}{12}$};\n\\draw ({2*pi/3},0.1) -- ({2*pi/3},0) node [above right] {$\\frac{2\\pi}{3}$};\n\\draw ({11*pi/12},0.1) -- ({11*pi/12},0) node [below right] {$\\frac{11\\pi}{12}$};\n\\draw (0.1,5) -- (0,5) node [left] {$5$};\n\\draw (0.1,-5) -- (0,-5) node [below left] {$-5$};\n\\draw [domain = {-4*pi/12}:{2*pi/3},samples = 100] plot (\\x,{5*sin(2*\\x/pi*180-60)});\n\\end{tikzpicture}", "solution": "", "duration": -1, "usages": [ @@ -496264,7 +496264,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$4\\pi$;$4$.", "solution": "", "duration": -1, "usages": [ @@ -496293,7 +496293,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$f(x)=4\\sin(x+\\dfrac{\\pi}{6})$", "solution": "", "duration": -1, "usages": [ @@ -496322,7 +496322,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $f(x)=\\dfrac{\\sqrt{3}}{2}\\sin(3x+\\pi)+\\dfrac{\\sqrt{3}}{2};$\\\\\n(2) $[-\\dfrac{\\pi}{2}+\\dfrac{2k\\pi}{3},-\\dfrac{\\pi}{6}+\\dfrac{2k\\pi}{3}],k \\in \\bf{Z}$;\\\\\n(3) 函数最大值为$\\sqrt{3}$,此时$x$值为${x|x=-\\dfrac{\\pi}{6}+\\dfrac{2k\\pi}{3},k \\in \\bf{Z}}$", "solution": "", "duration": -1, "usages": [ @@ -496351,7 +496351,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$x=\\pi+2k\\pi,k \\in \\bf{Z}$", "solution": "", "duration": -1, "usages": [ @@ -496380,7 +496380,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "纵;伸长; $3$}", "solution": "", "duration": -1, "usages": [ @@ -496409,7 +496409,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "缩短; $\\dfrac{1}{2}$; 缩短; $\\dfrac{1}{3}$.", "solution": "", "duration": -1, "usages": [ @@ -496438,7 +496438,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$f(x)=\\sin(\\dfrac{1}{2}x-\\dfrac{\\pi}{3})$", "solution": "", "duration": -1, "usages": [ @@ -496467,7 +496467,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$f(x)=\\sin(\\dfrac{1}{2}x-\\dfrac{\\pi}{6})$", "solution": "", "duration": -1, "usages": [ @@ -496496,7 +496496,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$f(x)=2\\sin(\\dfrac{1}{3}x+\\dfrac{\\pi}{6})$", "solution": "", "duration": -1, "usages": [ @@ -496525,7 +496525,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$x=\\dfrac{\\pi}{3}+2k\\pi,k \\in \\bf{Z}$; $(-\\dfrac{2\\pi}{3}+2k\\pi,0),k \\in \\bf{Z}$.", "solution": "", "duration": -1, "usages": [ @@ -496554,7 +496554,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [ @@ -496583,7 +496583,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "左; $\\dfrac{\\pi}{8}$.", "solution": "", "duration": -1, "usages": [ @@ -496612,7 +496612,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$f(x)=\\sin(2x+\\dfrac{\\pi}{2})$,\n$g(x)=\\sin x$.", "solution": "", "duration": -1, "usages": [ @@ -496641,7 +496641,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\sqrt{2}$;\n(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}$.", "solution": "", "duration": -1, "usages": [ @@ -496670,7 +496670,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $2\\pi$; (2) $1$; (3) $\\dfrac{\\pi}{2}$.", "solution": "", "duration": -1, "usages": [ @@ -496699,7 +496699,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $[0,\\dfrac{\\pi}{2})$, $(\\dfrac{3\\pi}{2},2\\pi]$; \\\\\n(2) $[0,\\dfrac{\\pi}{2})$, $(\\dfrac{\\pi}{2},\\pi]$.", "solution": "", "duration": -1, "usages": [ @@ -496728,7 +496728,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 奇函数; (2) 偶函数.", "solution": "", "duration": -1, "usages": [ @@ -496757,7 +496757,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[-5,+\\infty)$", "solution": "", "duration": -1, "usages": [ @@ -496786,7 +496786,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) $<$; (2) $>$; (3) $>$; (4)$<$.", "solution": "", "duration": -1, "usages": [ @@ -496815,7 +496815,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}", "solution": "", "duration": -1, "usages": [ @@ -496844,7 +496844,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "最小值为$-\\dfrac{\\sqrt{3}}{3}$，此时$x=-\\dfrac{\\pi}{3}$.", "solution": "", "duration": -1, "usages": [ @@ -496873,7 +496873,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $ \\{x|x \\neq \\dfrac{k\\pi}{2},k \\in \\bf{Z}\\} $;\\\\\n(2) 单调增区间为$(-\\dfrac{\\pi}{2}+\\dfrac{k\\pi}{2},\\dfrac{k\\pi}{2}), k \\in \\bf{Z}$.", "solution": "", "duration": -1, "usages": [ @@ -496902,7 +496902,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\{x|x\\neq \\dfrac{\\pi}{4}-\\dfrac{1}{2}+\\dfrac{k\\pi}{2},k \\in \\bf{Z} \\}$", "solution": "", "duration": -1, "usages": [ @@ -496931,7 +496931,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\dfrac{\\pi}{4}+\\dfrac{k\\pi}{3},\\dfrac{\\pi}{12}+\\dfrac{k\\pi}{3}), k \\in \\bf{Z}$", "solution": "", "duration": -1, "usages": [ @@ -496960,7 +496960,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -496989,7 +496989,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "定义域为$ \\{x|x \\neq \\dfrac{7\\pi}{5}+2k\\pi,k \\in \\bf{Z}\\} $;\\\\\n严格增区间为$(-\\dfrac{3\\pi}{5}+2k\\pi,\\dfrac{7\\pi}{5}+2k\\pi), k \\in \\bf{Z}$.", "solution": "", "duration": -1, "usages": [ @@ -497018,7 +497018,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "函数零点为$x=\\dfrac{2k\\pi}{5}+2k\\pi,k \\in \\bf{Z}$.", "solution": "", "duration": -1, "usages": [ @@ -497047,7 +497047,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) 假命题; (2) 假命题; (3) 假命题; (4) 真命题.", "solution": "", "duration": -1, "usages": [ @@ -497076,7 +497076,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$[-4,2+4\\sqrt{3}]$", "solution": "", "duration": -1, "usages": [ @@ -497105,7 +497105,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "最大张角的正切值为$\\dfrac{\\sqrt{2}}{4}$, 此时学生距离时钟$\\sqrt{0.18}$米.", "solution": "", "duration": -1, "usages": [ @@ -497154,7 +497154,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -497174,7 +497174,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -497194,7 +497194,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -497214,7 +497214,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "单位圆", "solution": "", "duration": -1, "usages": [], @@ -497234,7 +497234,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [ @@ -497263,7 +497263,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\overrightarrow{CD}$", "solution": "", "duration": -1, "usages": [ @@ -497292,7 +497292,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "$\\overrightarrow{AC}$", "solution": "", "duration": -1, "usages": [ @@ -497321,7 +497321,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) 假命题; (2) 真命题; (3) 假命题; (4) 假命题.", "solution": "", "duration": -1, "usages": [ @@ -497350,7 +497350,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\overrightarrow{DB}$; $\\overrightarrow{FE}$.\\\\\n(2) $\\overrightarrow{ED}$; $\\overrightarrow{CF}$; $\\overrightarrow{FA}$.\\\\\n(3) $\\overrightarrow{EF}$; $\\overrightarrow{AD}$; $\\overrightarrow{DA}$; $\\overrightarrow{DB}$; $\\overrightarrow{BD}$; $\\overrightarrow{AB}$; $\\overrightarrow{BA}$.", "solution": "", "duration": -1, "usages": [ @@ -497379,7 +497379,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$40$", "solution": "", "duration": -1, "usages": [ @@ -497408,7 +497408,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$40$", "solution": "", "duration": -1, "usages": [ @@ -497437,7 +497437,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [ @@ -497495,7 +497495,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-3\\overrightarrow {a}+6 \\overrightarrow {b}$", "solution": "", "duration": -1, "usages": [ @@ -497524,7 +497524,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$7 \\overrightarrow {a}-2 \\overrightarrow {b}- \\overrightarrow {c}$", "solution": "", "duration": -1, "usages": [ @@ -497553,7 +497553,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "(1) 假命题; (2) 真命题; (3) 假命题; (4) 真命题.", "solution": "", "duration": -1, "usages": [ @@ -497582,7 +497582,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $\\overrightarrow {AB}=\\dfrac{1}{2}\\overrightarrow {a}-\\dfrac{1}{2}\\overrightarrow {b}$;\\\\\n(2) $\\overrightarrow {BC}=\\dfrac{1}{2}\\overrightarrow {a}+\\dfrac{1}{2}\\overrightarrow {b}$.", "solution": "", "duration": -1, "usages": [ @@ -497611,7 +497611,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\lambda=\\dfrac{1}{3}$", "solution": "", "duration": -1, "usages": [ @@ -497640,7 +497640,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$x=2$; $y=1$.", "solution": "", "duration": -1, "usages": [ @@ -497669,7 +497669,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(2) $m=1$或$-1$.", "solution": "", "duration": -1, "usages": [ @@ -497698,7 +497698,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\overrightarrow{DC}=\\dfrac{1}{2}\\overrightarrow{a}$;\\\\ $\\overrightarrow{DC}=-\\dfrac{1}{2}\\overrightarrow{a}+\\overrightarrow{b}$;\\\\\n$\\overrightarrow{MN}=-\\dfrac{1}{4}\\overrightarrow{a}-\\overrightarrow{b}$.", "solution": "", "duration": -1, "usages": [ @@ -497727,7 +497727,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\overrightarrow{0}$", "solution": "", "duration": -1, "usages": [ @@ -497756,7 +497756,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{2}{3}\\overrightarrow{a}+\\dfrac{1}{3}\\overrightarrow{b}$", "solution": "", "duration": -1, "usages": [ @@ -497798,7 +497798,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -497818,7 +497818,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -497838,7 +497838,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -497858,7 +497858,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{3}$", "solution": "", "duration": -1, "usages": [], @@ -497878,7 +497878,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{3\\sqrt{3}}{2}$", "solution": "", "duration": -1, "usages": [], @@ -497898,7 +497898,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "等边三角形", "solution": "", "duration": -1, "usages": [], @@ -497918,7 +497918,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{\\pi}{4}$", "solution": "", "duration": -1, "usages": [], @@ -497938,7 +497938,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{2\\pi}{3}$", "solution": "", "duration": -1, "usages": [], @@ -497958,7 +497958,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-10\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -497978,7 +497978,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{4}{3}$", "solution": "", "duration": -1, "usages": [], @@ -497998,7 +497998,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-\\dfrac{2}{3}\\overrightarrow {a}$", "solution": "", "duration": -1, "usages": [], @@ -498018,7 +498018,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -498038,7 +498038,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -498058,7 +498058,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -498078,7 +498078,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$7$", "solution": "", "duration": -1, "usages": [], @@ -498098,7 +498098,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -498118,7 +498118,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -498138,7 +498138,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "外心; 重心; 垂心.", "solution": "", "duration": -1, "usages": [], @@ -498158,7 +498158,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\dfrac{\\pi}{3}$", "solution": "", "duration": -1, "usages": [], @@ -498178,7 +498178,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-25$", "solution": "", "duration": -1, "usages": [], @@ -498198,7 +498198,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\lambda=\\dfrac{7}{12}$", "solution": "", "duration": -1, "usages": [], @@ -498218,7 +498218,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$AB=8$", "solution": "", "duration": -1, "usages": [], @@ -498238,7 +498238,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$t=\\dfrac{1}{3}$", "solution": "", "duration": -1, "usages": [], @@ -498258,7 +498258,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $(\\overrightarrow {a}-\\overrightarrow {b}) \\cdot \\overrightarrow {c}=\\overrightarrow {a} \\cdot \\overrightarrow {c}- \\overrightarrow {b} \\cdot \\overrightarrow {c}=1*1*(-\\dfrac{1}{2})-1*1*(-\\dfrac{1}{2})=0;\\\\$\n(2) $k<0$或$k>2$.", "solution": "", "duration": -1, "usages": [], @@ -498278,7 +498278,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$[2,5]$", "solution": "", "duration": -1, "usages": [], @@ -498298,7 +498298,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$\\arccos \\dfrac{4}{5}$", "solution": "", "duration": -1, "usages": [], @@ -498318,7 +498318,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\overrightarrow{OP}=\\dfrac{3}{11}\\overrightarrow {a}+\\dfrac{2}{11}\\overrightarrow {b}$", "solution": "", "duration": -1, "usages": [], @@ -554070,7 +554070,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "二", "solution": "", "duration": -1, "usages": [], @@ -554090,7 +554090,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -554110,7 +554110,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2$", "solution": "", "duration": -1, "usages": [], @@ -554130,7 +554130,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -554150,7 +554150,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [], @@ -554170,7 +554170,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\sqrt{2}\\pi$", "solution": "", "duration": -1, "usages": [], @@ -554190,7 +554190,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[\\dfrac 12,1)$", "solution": "", "duration": -1, "usages": [], @@ -554210,7 +554210,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[0,\\dfrac 23\\pi]$", "solution": "", "duration": -1, "usages": [], @@ -554230,7 +554230,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "左，$\\dfrac{\\pi}6$", "solution": "", "duration": -1, "usages": [], @@ -554250,7 +554250,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[2k\\pi-\\dfrac{\\pi}3,2k\\pi+\\dfrac 23 \\pi],k \\in \\mathbb{Z}$", "solution": "", "duration": -1, "usages": [], @@ -554270,7 +554270,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [], @@ -554290,7 +554290,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -554310,7 +554310,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -554330,7 +554330,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -554350,7 +554350,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2},\\textcircled{3},\\textcircled{6}", "solution": "", "duration": -1, "usages": [], @@ -554370,7 +554370,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{2},\\textcircled{3}", "solution": "", "duration": -1, "usages": [], @@ -554390,7 +554390,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1},\\textcircled{2},\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -554410,7 +554410,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1},\\textcircled{2}", "solution": "", "duration": -1, "usages": [], @@ -554430,7 +554430,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{1},\\textcircled{2},\\textcircled{4}", "solution": "", "duration": -1, "usages": [], @@ -554450,7 +554450,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$(\\sqrt{3},2\\sqrt{7}]$", "solution": "", "duration": -1, "usages": [], @@ -554470,7 +554470,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) \\textcircled{1} $\\varphi=k\\pi,k \\in \\mathbb{Z}$时为奇函数；\\\\\n\\textcircled{2} $\\varphi=k\\pi+\\dfrac{\\pi}2,k \\in \\mathbb{Z}$时为偶函数；\\\\\n\\textcircled{3} $\\varphi \\neq \\dfrac{k\\pi}2,k \\in \\mathbb{Z}$时为非奇非偶函数.\\\\\n(2)非奇非偶函数", "solution": "", "duration": -1, "usages": [], @@ -554490,7 +554490,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1)$k=\\sqrt{2}$或$k \\in [-1,1)$时，一解；$k \\in [1,\\sqrt{2})$时，两解；$k \\in (-\\infty，-1)\\cup (\\sqrt{2},+\\infty)$时，无解.\n\\\\\n(2)$k=\\dfrac 54$或$k \\in [-1,1)$时，一解；$k \\in [1,\\dfrac 54)$时，两解；$k \\in (-\\infty，-1)\\cup (\\dfrac 54,+\\infty)$时，无解.", "solution": "", "duration": -1, "usages": [], @@ -554510,7 +554510,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1)不符合；\\\\\n(2)$\\theta=\\dfrac{\\pi}8$时，$S$取最小值，最小值为$12\\sqrt{2}-12$", "solution": "", "duration": -1, "usages": [], @@ -554530,7 +554530,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1)$-\\dfrac 12$\\\\\n(2)\\\\\n(3)$\\{x|x=k\\pi+2\\arcsin{\\dfrac 16}$或$x=k\\pi-\\dfrac{\\pi}3,k \\in \\mathbb{Z}\\}$", "solution": "", "duration": -1, "usages": [], @@ -554550,7 +554550,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1)$f(x)=2\\sin(2x+\\dfrac{\\pi}3)$\\\\\n(2)单调增区间为$[k\\pi-\\dfrac{5\\pi}{12},k\\pi+\\dfrac{\\pi}{12}]$,最小值为2，此时$x=k\\pi-\\dfrac{5\\pi}{12}$\\\\\n(3)$0