2278 lines
37 KiB
Plaintext
2278 lines
37 KiB
Plaintext
ans
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021441
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错误, 正确, 错误, 错误
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021442
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D
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021443
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C
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021444
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A
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021445
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C
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021446
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D
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021447
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$-390^\circ$
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021448
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$304^\circ$, $-56^\circ$
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021449
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$-144^\circ$
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021450
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二, 四
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021451
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(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$
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021452
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\begin{tikzpicture}[>=latex]
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\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle;
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\draw (30:2) -- (0,0) -- (60:2);
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\draw [->] (-2,0) -- (2,0) node [below] {$x$};
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\draw [->] (0,-2) -- (0,2) node [left] {$y$};
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\draw (0,0) node [below left] {$O$};
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\end{tikzpicture}
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021453
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$-1290^{\circ}$;第二象限
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021454
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(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
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021455
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(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
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(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.
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021456
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C
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021457
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B
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021458
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$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$
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021459
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(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$
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021460
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$\sqrt{3}$
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021461
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(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$
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021462
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(1)$16\pi+\frac{2\pi}{3}$,二;\\
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(2)$-18\pi+\frac{4\pi}{3}$,三;\\
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(3)$-2\pi+\frac{7\pi}{5}$,三;\\
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(4)$-2\pi+\frac{3\pi}{4}$,二.
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021463
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$\frac{1}{2}$
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021464
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(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\
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(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$.
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021465
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(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
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(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
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(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\
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(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$.
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021466
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(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
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(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$.
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021467
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(1) 第四象限；第四象限；\\
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(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.
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021468
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$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$
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021469
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\begin{tabular}{|c|c|c|c|c|c|}
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\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\
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\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\
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\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\
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\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\
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\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\
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\hline
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\end{tabular}
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021470
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$2\sqrt{5}$
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021471
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$\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$
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021472
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$ \left( -2,\frac{2}{3} \right)$
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021473
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$<$
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021474
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5
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021475
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2
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021476
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当$t=\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha =- \frac{\sqrt{15}}{3}$;\\
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当$t=-\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha = \frac{\sqrt{15}}{3}$;\\
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当$t=0$时, $\cos \alpha=-1$, $\tan \alpha = 0$.
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021477
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当$\alpha$在第二象限时，$ \sin \alpha =\frac{4}{5}$, $\tan \alpha=-\frac{4}{3}$;\\
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当$\alpha$在第三象限时，$ \sin \alpha =-\frac{4}{5}$, $\tan \alpha=\frac{4}{3}$.
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021478
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$-\frac{\sqrt{3}}{4}$
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021479
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(1) 第四象限； (2) 第一、四象限；(3)第一、三象限；(4)第一、三象限.
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021480
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$A=\left\{ -2,-0,4 \right\}$
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021481
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(1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
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(2) $[0,3)$
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021482
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\begin{center}
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\begin{tabular}{|c|c|c|c|c|c|}
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\hline$\alpha$&$\dfrac{\pi}{3}$&$\dfrac{7 \pi}{4}$&$\dfrac{2021 \pi}{2}$&$-\dfrac{\pi}{6}$&$-\dfrac{22 \pi}{3}$\\
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\hline$\sin \alpha$& $\frac{\sqrt{3}}{2}$ &$-\frac{\sqrt{2}}{2}$ & $1$&$-\frac{1}{2}$ &$\frac{\sqrt{3}}{2}$ \\
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\hline$\cos \alpha$&$\frac{1}{2}$ &$\frac{\sqrt{2}}{2}$ & $0$&$\frac{\sqrt{3}}{2}$ &$-\frac{1}{2}$ \\
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\hline$\tan \alpha$&$\sqrt{3}$ &$-1$ & 不存在 &$-\frac{\sqrt{3}}{3}$ &$-\sqrt{3}$\\
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\hline$\cot \alpha$&$\frac{\sqrt{3}}{3}$ &$-1$ & $ 0$&$-\sqrt{3}$ &$-\frac{\sqrt{3}}{3}$ \\
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\hline
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\end{tabular}
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\end{center}
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021483
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(1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\
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(2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$
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021484
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$-\frac{2\sqrt{5}}{5}$;$2$
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021485
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\textcircled{2} \textcircled{4}
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021486
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当$\alpha$在第一象限时，$ \sin \alpha =\frac{3\sqrt{10}}{10}$, $\cos \alpha =\frac{\sqrt{10}}{10}$,$\tan \alpha=3$;\\
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当$\alpha$在第三象限时，$ \sin \alpha =-\frac{3\sqrt{10}}{10}$,$\cos \alpha =-\frac{\sqrt{10}}{10}$, $\tan \alpha=3$.
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021487
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$\sin k\pi =0$;\\$\cos k\pi=\left\{
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\begin{array}{lc}
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$1$, & k=2n \\
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$ -1$ , &k=2n-1\\
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\end{array}
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\right.$ ($n \in \mathbf{Z}$).
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021488
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(1) $\{\theta | 2k \pi+\dfrac{\pi}{3}<\theta<2k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$;\\
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(2) $\{\theta | k \pi-\dfrac{\pi}{2}<\theta \le k \pi-\dfrac{\pi}{6},\ k \in \mathbf{Z} \}$;\\
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(3) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$.
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021489
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第二象限
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021490
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(1) 当$\dfrac{\alpha}{2}$在第二象限时，点$P$在第四象限；\\
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当$\dfrac{\alpha}{2}$在第四象限时，点$P$在第二象限.\\
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(2) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$
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021491
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当$m=0$时，$ \cos (\alpha+1905^{\circ})=-1$,$\tan (\alpha-615^{\circ})=0$;\\
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当$m=\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=-\frac{\sqrt{15}}{3}$;\\
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当$m=-\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=\frac{\sqrt{15}}{3}$.
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021492
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$-\dfrac{3}{8}$
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021493
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$-\dfrac{1}{20}$
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021494
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$\dfrac{7\sqrt{2}}{4}$
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021495
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$\dfrac{3\sqrt{5}}{5}$
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021496
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$11$
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021497
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$5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$
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021498
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$\sin ^2 \alpha$
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021499
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$1$
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021502
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$-\dfrac{12}{5}$
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021503
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$-\dfrac{\sqrt{3}}{2}$
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021504
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$\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$
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021505
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$-\dfrac{\sqrt{11}}{3}$
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021506
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$\dfrac{\pi}{3}$
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021507
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$\left[ 0,\pi \right )$
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021508
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$-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$
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021509
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$69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$
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021510
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$\cot \alpha$
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021511
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$-1$
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021512
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$-1$
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021513
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$ \sin 2-\cos 2$
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021514
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$0$
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021515
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$0$
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021516
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$-\dfrac{\sqrt{1-a^2}}{a}$
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021517
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$-\dfrac{2+\sqrt{3}}{3}$
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021518
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(1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$.
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021519
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(1) $-\dfrac{2}{3}$; \\
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(2) $\dfrac{2}{3}$; \\
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(3) $-\dfrac{\sqrt{5}}{3}$;\\
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(4) $\dfrac{\sqrt{5}}{2}$.
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021520
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(1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ;
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(3) $-\tan \dfrac{\pi}{9}$; (4) $\cot \dfrac{7\pi}{15}$.
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021521
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$\dfrac{2}{5}$
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021522
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$(3,4)$
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021523
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$0$
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021524
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$\sin \alpha$
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021525
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$-\dfrac{1}{5}$
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021526
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(1) $\dfrac{\sqrt{6}}{6}-\sqrt{3}$;\\
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(2) $-\dfrac{\sqrt{6}}{3}$;\\
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(3) $1$
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021527
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(1) $\dfrac{6 \pi}{5}$; (2) $\dfrac{4 \pi}{5}$; (3) $\dfrac{13 \pi}{10}$; (4) $\dfrac{17 \pi}{10}$.
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021528
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(1) 当$\alpha$在第一象限时, $\sin (2 \pi-\alpha)=-\dfrac{\sqrt{3}}{2}$;
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当$\alpha$在第三象限时, $\sin (2 \pi-\alpha)=\dfrac{\sqrt{3}}{2}$.\\
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(2) 当$\alpha$在第一象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=-\sqrt{3}$;
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当$\alpha$在第四象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=\sqrt{3}$.
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021529
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(1) $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\
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(2) $\{x | x=2k \pi \pm \dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\
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(3) $\{x | x=k \pi + \dfrac{5\pi}{6},\ k \in \mathbf{Z}\}$;\\
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(4) $\{x | x=2k \pi + \dfrac{5\pi}{6}$ 或$x=2k \pi + \dfrac{3\pi}{2} ,\ k \in \mathbf{Z}\}$;\\
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第二种写法： $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{6}+\dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\
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(5) $\{x | x=k \pi - \arctan \dfrac{\sqrt{3}}{2}+ \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\
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(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}\}$;\\
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(7) $\{x | x=k \pi - \dfrac{5\pi}{8}$ 或$x=k \pi - \dfrac{3\pi}{8} ,\ k \in \mathbf{Z}\}$;
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021530
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(1) $\{ \dfrac{\pi}{12},\dfrac{17\pi}{12} \}$;\\
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(2) $\{ \dfrac{5\pi}{6} \}$;\\
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(3) $\{ \dfrac{\pi}{12},\dfrac{5\pi}{12} \}$;\\
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(4) $\{ \dfrac{5\pi}{6} \}$.
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021531
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(1) $\{x | x= \dfrac{2k \pi}{5} ,\ k \in \mathbf{Z}\}$;\\
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(2) $\{x | x= \dfrac{2k \pi}{3} +\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\
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(3) $\{x | x= 2k \pi$ 或$x=k \pi +(-1)^k \cdot \dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\
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(4) $\{x | x= k \pi+\dfrac{ \pi}{3}$ 或$x=k \pi -\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$.
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021532
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$\dfrac{3+4\sqrt{3}}{10}$
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021533
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$-1$
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021534
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$-\dfrac{33}{50}$
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021535
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(1) $\dfrac{\sqrt{6}-\sqrt{2}}{4}$;
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(2) $\dfrac{\sqrt{6}+\sqrt{2}}{4}$;
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(3) $0$.
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021536
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(1) $\sqrt{3} \sin \alpha$;
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(2) $\cos(\alpha-2\beta)$.
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021537
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$\dfrac{140}{221}$
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021538
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$\dfrac{2\sqrt{6}-1}{6}$
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021539
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证明略
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021540
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C
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021541
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A
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021542
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$\dfrac{3\sqrt{10}+6\sqrt{2}+2\sqrt{14}-\sqrt{70}}{24}$
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021543
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$\dfrac{8\sqrt{3}-21}{20}$
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021544
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$\dfrac{\pi}{2}$
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021545
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$-\dfrac{2+\sqrt{15}}{6}$
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021546
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$-\dfrac{\sqrt{2}}{2}$
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021547
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$\sin 2\beta$
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021548
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$0$
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021549
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$2-\sqrt{3}$
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021550
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$\dfrac{16}{65}$
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021551
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$-\dfrac{7}{25}$
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021552
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$-\dfrac{4\sqrt{14}+3\sqrt{2}}{20}$
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021553
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$(\dfrac{4\sqrt{3}+3}{2},\dfrac{3\sqrt{3}-4}{2})$
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021554
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$-\dfrac{33}{65}$或$\dfrac{63}{65}$
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021555
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B
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021556
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C
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021557
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$-\dfrac{56}{65}$
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021558
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$-3$
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021559
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$\dfrac{3}{4}$
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021560
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$\dfrac{-6+5\sqrt{3}}{3}$
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021561
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$\tan \alpha$
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021562
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$\sqrt{3}$
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021563
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$-\dfrac{\sqrt{3}}{3}$
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021564
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A
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021565
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$-\dfrac{17}{31}$
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021566
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$\dfrac{\pi}{4}$
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021567
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(1) $\dfrac{1}{3}$;
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(2) $\dfrac{1}{7}$
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021568
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$-\dfrac{1}{5}$
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021569
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当$CD = 1.4$米时，$\tan \angle ACB$最大
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021570
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(1) $2 \sin (\alpha+\dfrac{\pi}{6})$;
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(2) $\sqrt{2} \sin (\alpha+\dfrac{7\pi}{4})$.
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021571
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$6\cos(\alpha+\dfrac{\pi}{3})$
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021572
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$2k \pi-\dfrac{\pi}{3}(k\in \mathbf{Z} )$
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021573
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B
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021574
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$\dfrac{1}{3}$
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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
|
||
|
||
$f(a)=\begin{cases}
|
||
a^2+2a+2, & a\leq -1,\\
|
||
1, & -1<a<1,\\
|
||
a^2-2a+2, & a\geq 1.
|
||
\end{cases}$
|
||
|
||
021673
|
||
|
||
(1) 偶函数； (2) 不是奇函数也不是偶函数； (3) 奇函数； (4) 偶函数.
|
||
|
||
021674
|
||
(1) 真命题； (2) 真命题； (3) 假命题； (4) 真命题.
|
||
|
||
021675
|
||
B
|
||
|
||
021676
|
||
$f(x)=\cos4x$
|
||
|
||
021677
|
||
$-7$
|
||
|
||
021678
|
||
(1) 不是奇函数也不是偶函数；(2) 偶函数；(3) 偶函数.
|
||
|
||
021679
|
||
(1) 假命题；(2) 假命题；(3) 真命题； (4) 真命题.
|
||
|
||
021680
|
||
不存在这样的$\theta$,使得函数$f(x)=1+\sin (x+\theta)+\sqrt{3} \cos (x+\theta)$为奇函数.
|
||
|
||
021681
|
||
$0<\beta<\alpha<\dfrac{\pi}{2}$
|
||
|
||
|
||
021682
|
||
(1) 假命题； (2) 真命题；(3) 假命题； (4)真命题.
|
||
|
||
021683
|
||
$[-\dfrac{3\pi}{2},-\dfrac{\pi}{2}]$
|
||
|
||
021684
|
||
$[-\dfrac{\pi}{4}+k\pi,\dfrac{\pi}{4}+k\pi],k \in \bf{Z}$
|
||
|
||
021685
|
||
(1) $[\dfrac{3\pi}{2},2\pi]$;
|
||
(2) $[\pi,\dfrac{3\pi}{2}]$.
|
||
|
||
021686
|
||
|
||
(1) $[\dfrac{5\pi}{4}+2k\pi,\dfrac{9\pi}{4}+2k\pi],k \in \bf{Z}$;\\
|
||
(2) $[-\dfrac{7\pi}{6}+2k\pi,-\dfrac{\pi}{6}+2k\pi],k \in \bf{Z}$.
|
||
|
||
021687
|
||
|
||
$[\dfrac{\pi}{6}+\dfrac{k\pi}{2},\dfrac{5\pi}{12}+\dfrac{k\pi}{2}],k \in \bf{Z}$
|
||
|
||
021688
|
||
$[k\pi,k\pi+\dfrac{\pi}{2}],k \in \bf{Z}$
|
||
|
||
021690
|
||
$4\pi$; $3$; $\dfrac{\pi}{3}$; $\dfrac{1}{4\pi}$.
|
||
|
||
021691
|
||
$\pi$; $[-\dfrac{4}{3},\dfrac{4}{3}].$
|
||
|
||
021692
|
||
$b-|a|$
|
||
|
||
021693
|
||
$y=3\sin(7x+\dfrac{\pi}{6})$
|
||
|
||
021694
|
||
|
||
(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 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
|
||
$\{x|2k\pi+\dfrac{\pi}4<x<2k\pi+\dfrac 34 \pi, k\in \mathbb{Z} \}$
|
||
|
||
040397
|
||
$\{x|2k\pi+\dfrac{\pi}4 \leq x \leq 2k\pi+\dfrac 54 \pi, k\in \mathbb{Z} \}$
|
||
|
||
040398
|
||
$[k\pi+\dfrac{\pi}{4},k\pi+\dfrac 34 \pi],k \in \mathbb{Z}$
|
||
|
||
040399
|
||
$[4k\pi-\dfrac 83 \pi,4k\pi-\dfrac 23 \pi],k \in \mathbb{Z}$
|
||
|
||
040400
|
||
$[2k\pi-\dfrac {\pi}3 ,2k\pi+\dfrac {\pi}6],k \in \mathbb{Z}$
|
||
|
||
040401
|
||
$\{x|x=k\pi-\dfrac 38\pi,k \in \mathbb{Z}\}$
|
||
|
||
040402
|
||
$(-\dfrac 14,2]$
|
||
|
||
040403
|
||
$[-1,2]$
|
||
|
||
040404
|
||
$3,\dfrac{\pi}3$
|
||
|
||
040405
|
||
$y=3\cos(2x+\dfrac{\pi}3)$
|
||
|
||
040406
|
||
$\dfrac 12\sin(2x-\dfrac{\pi}2)+1$
|
||
|
||
040407
|
||
$[\dfrac{197}2 \pi,\dfrac{201}2 \pi)$
|
||
|
||
040408
|
||
$(0,\dfrac 32]$
|
||
|
||
040409
|
||
$[0,\sqrt{2}+\dfrac 32]$
|
||
|
||
040410
|
||
(1)$f(x)=2\sin(\dfrac{\pi}4x+\dfrac{\pi}4)$\\
|
||
(2)$x=-\dfrac 23$时，取最大值为$\sqrt{6}$;$x=-4$时，取最小值为$-2\sqrt{2}$
|
||
|
||
040411
|
||
$199$个
|
||
|
||
040412
|
||
(1)$T=\pi$\\
|
||
(2)非奇非偶函数\\
|
||
(3)增区间为$[k\pi-\dfrac{\pi}3,k\pi+\dfrac{\pi}6],k\in \mathbb{Z}$,减区间为$[k\pi+\dfrac{\pi}{6},k\pi+\dfrac 23\pi],k\in \mathbb{Z}$\\
|
||
(4)$y_{min}=1,x=\dfrac{\pi}2;y_{max}=\dfrac 52,x=\dfrac{\pi}6$
|
||
|
||
040413
|
||
$-1-\sqrt{2}<a<1+\sqrt{2}$
|
||
|
||
040414
|
||
$2$
|
||
|
||
040415
|
||
$[2k-1,2k],k \in \mathbb{Z}$
|
||
|
||
040416
|
||
$\dfrac{\pi}2$
|
||
|
||
040417
|
||
$[0,\dfrac 38 \pi]$和$[\dfrac 78 \pi, \pi]$
|
||
|
||
040418
|
||
$\pm \dfrac{\pi}2$
|
||
|
||
040419
|
||
$y=\sin(4x)$
|
||
|
||
040420
|
||
(1)$\dfrac{\pi}6$\\
|
||
(2)$\sqrt{3}$
|
||
|
||
040421
|
||
(1)最小正周期为$\pi$，单调减区间为$[k\pi+\dfrac{\pi}{12},k\pi+\dfrac 7{12}\pi],k \in \mathbb{Z}$\\
|
||
(2)$y_{\max}=\sqrt{3},x=\dfrac{\pi}6$时取; $y_{\min}=-2,x=\dfrac 7{12}\pi$时取
|
||
|
||
040527
|
||
二
|
||
|
||
040528
|
||
$1$
|
||
|
||
040529
|
||
$2$
|
||
|
||
040530
|
||
$1$
|
||
|
||
040531
|
||
$6$
|
||
|
||
040532
|
||
$\sqrt{2}\pi$
|
||
|
||
040533
|
||
$[\dfrac 12,1)$
|
||
|
||
040534
|
||
$[0,\dfrac 23\pi]$
|
||
|
||
040535
|
||
左，$\dfrac{\pi}6$
|
||
|
||
040536
|
||
$[2k\pi-\dfrac{\pi}3,2k\pi+\dfrac 23 \pi],k \in \mathbb{Z}$
|
||
|
||
040537
|
||
$-1$
|
||
|
||
040538
|
||
B
|
||
|
||
040539
|
||
A
|
||
|
||
040540
|
||
B
|
||
|
||
040541
|
||
\textcircled{2},\textcircled{3},\textcircled{6}
|
||
|
||
040542
|
||
\textcircled{2},\textcircled{3}
|
||
|
||
040543
|
||
\textcircled{1},\textcircled{2},\textcircled{4}
|
||
|
||
040544
|
||
\textcircled{1},\textcircled{2}
|
||
|
||
040545
|
||
\textcircled{1},\textcircled{2},\textcircled{4}
|
||
|
||
040546
|
||
$(\sqrt{3},2\sqrt{7}]$
|
||
|
||
040547
|
||
(1) \textcircled{1} $\varphi=k\pi,k \in \mathbb{Z}$时为奇函数；\\
|
||
\textcircled{2} $\varphi=k\pi+\dfrac{\pi}2,k \in \mathbb{Z}$时为偶函数；\\
|
||
\textcircled{3} $\varphi \neq \dfrac{k\pi}2,k \in \mathbb{Z}$时为非奇非偶函数.\\
|
||
(2)非奇非偶函数
|
||
|
||
040548
|
||
(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.
|
||
\\
|
||
(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.
|
||
|
||
040549
|
||
(1)不符合；\\
|
||
(2)$\theta=\dfrac{\pi}8$时，$S$取最小值，最小值为$12\sqrt{2}-12$
|
||
|
||
040550
|
||
(1)$-\dfrac 12$\\
|
||
(2)\\
|
||
(3)$\{x|x=k\pi+2\arcsin{\dfrac 16}$或$x=k\pi-\dfrac{\pi}3,k \in \mathbb{Z}\}$
|
||
|
||
040551
|
||
(1)$f(x)=2\sin(2x+\dfrac{\pi}3)$\\
|
||
(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$x=k\pi-\dfrac{5\pi}{12}$\\
|
||
(3)$0<a\leq \dfrac 4{199\pi}$
|
||
|
||
040667
|
||
$\overrightarrow{0}$
|
||
|
||
040668
|
||
$4$
|
||
|
||
040669
|
||
$\dfrac 92$
|
||
|
||
040670
|
||
$\dfrac 12,\dfrac{\pi}4+k\pi,k \in \mathbb{Z}$
|
||
|
||
040671
|
||
填$(1,2)$内的任意数均可
|
||
|
||
040672
|
||
$-\dfrac 23 \sqrt{3}\overrightarrow{a}$
|
||
|
||
040673
|
||
$[2k\pi-\dfrac{5\pi}6,2k\pi+\dfrac{\pi}6], k \in \mathbb{Z}$
|
||
|
||
040674
|
||
$-\sqrt{2}$
|
||
|
||
040675
|
||
$\{x|-\dfrac{\pi}6+2k\pi<x<\dfrac{\pi}6+2k\pi,k \in \mathbb{Z}\}$
|
||
|
||
040676
|
||
$4$
|
||
|
||
040677
|
||
$[\dfrac{\pi}3,\dfrac{11\pi}3)$
|
||
|
||
040678
|
||
B
|
||
|
||
040679
|
||
A
|
||
|
||
040680
|
||
D
|
||
|
||
040681
|
||
ABD
|
||
|
||
040682
|
||
ACD
|
||
|
||
040683
|
||
(1)$\dfrac 23 \pi$;(2)$6\sqrt{3}$
|
||
|
||
040684
|
||
(1)$\dfrac{\pi}4$;(2)$1$;\\
|
||
(3)面积最大值为$4+4\sqrt{2}$,周长的取值范围是$(8,4+4\sqrt{4+2\sqrt{2}})$
|
||
|
||
040685
|
||
(1)最大值为$2$，此时$x=\dfrac{\pi}6+k\pi,k\in\mathbb{Z}$;\\
|
||
(2)$[k\pi-\dfrac{\pi}3,k\pi+\dfrac{\pi}6],,k\in\mathbb{Z}$;\\
|
||
(3)$y_1=1,y_2=-1,y_1+y_2+y_3+\cdots+y_{2025}=1$
|
||
|
||
040686
|
||
(1)$S=$;\\
|
||
(2)$[\sqrt{2}-1,2-\sqrt{2}]$
|
||
|
||
040687
|
||
$\{x|\dfrac{5\pi}{6}+2k\pi<x<\dfrac{13\pi}{6}+2k\pi,k\in\mathbb{Z}\}$
|
||
|
||
040688
|
||
$[1,\sqrt{2}]$
|
||
|
||
040689
|
||
$\sqrt{3}$
|
||
|
||
040690
|
||
$-\dfrac 12 \overrightarrow{a}-\dfrac 12 \overrightarrow{b}$
|
||
|
||
040691
|
||
2,-1
|
||
|
||
040692
|
||
$[-\dfrac{5\pi}8+k\pi,-\dfrac{\pi}8+k\pi],k\in \mathbb{Z}$
|
||
|
||
040693
|
||
$\dfrac 43$
|
||
|
||
040694
|
||
$y=-\sin(2x)$
|
||
|
||
040695
|
||
$(\dfrac{\pi}{12},0),(\dfrac{5\pi}{12},0)$
|
||
|
||
040696
|
||
$-2$
|
||
|
||
040697
|
||
$-\dfrac 32$
|
||
|
||
040698
|
||
$41$
|
||
|
||
040699
|
||
B
|
||
|
||
040700
|
||
D
|
||
|
||
040701
|
||
C
|
||
|
||
040702
|
||
B
|
||
|
||
040703
|
||
$\dfrac{\overrightarrow {a}+\overrightarrow {b}+\overrightarrow {c}}3$
|
||
|
||
040704
|
||
$\dfrac 23$
|
||
|
||
040705
|
||
略
|
||
|
||
040706
|
||
(1)$f(\dfrac 12)=\sqrt{2},f(\dfrac 14)=2^{\dfrac 14},f(0)=1$\\
|
||
(2)$f(x)=2^{|x|}$\\
|
||
(3)周期为2\\
|
||
(4)$f(x)=2^{|x-2k|},x \in [2k-1,2k+1],k \in \mathbb{Z}$
|
||
|
||
040707
|
||
充分非必要
|
||
|
||
040708
|
||
$1,\sqrt{7}$
|
||
|
||
040709
|
||
$\dfrac{2\pi}3$
|
||
|
||
040710
|
||
$\pi$
|
||
|
||
040711
|
||
$[2k\pi,2k\pi+\dfrac{\pi}2],k \in \mathbb{Z}$
|
||
|
||
040712
|
||
$\{x|x \neq \dfrac{\pi}4+k\pi,k \in \mathbb{Z}\}$
|
||
|
||
040713
|
||
$[\dfrac{5\pi}6,\dfrac{11\pi}6)$
|
||
|
||
040714
|
||
$-19$
|
||
|
||
040715
|
||
(1)$\omega=2$,严格减区间为$[k\pi+\dfrac{5\pi}{12},k\pi+\dfrac{11\pi}{12}],k \in \mathbb{Z}$\\
|
||
(2)$(2,\dfrac{4\sqrt{21}}{3}]$
|
||
|
||
040716
|
||
$(-1,-1)$
|
||
|
||
040717
|
||
$(-1,8),(1,2)$
|
||
|
||
040718
|
||
$4$
|
||
|
||
040719
|
||
$(10,-5)$
|
||
|
||
040720
|
||
$-3,3$
|
||
|
||
040721
|
||
$1,2,-3$
|
||
|
||
040722
|
||
$(2,4),(0,-4),(-2,0)$
|
||
|
||
040723
|
||
$\pm 1$
|
||
|
||
040724
|
||
$-2$
|
||
|
||
040725
|
||
22
|
||
|
||
040726
|
||
B
|
||
|
||
040727
|
||
$-\dfrac{72}{25}$
|
||
|
||
040728
|
||
$14$
|
||
|
||
040729
|
||
$(-\dfrac 79,\dfrac 73)$
|
||
|
||
040730
|
||
A
|
||
|
||
040731
|
||
B
|
||
|
||
040732
|
||
C
|
||
|
||
040733
|
||
$[-37,-13]$
|
||
|
||
040734
|
||
$\dfrac 23$
|
||
|
||
040735
|
||
(1)$\pi-\arccos{\dfrac{\sqrt{21}}{14}}$\\
|
||
(2)$k \in (-2,0) \cup (0,+\infty)$
|
||
|
||
040736
|
||
(1)$\overrightarrow{OC}=(\dfrac{1+t}2,-\dfrac{\sqrt{3}}{2} \cdot (1+t)),\overrightarrow{OD}=(\dfrac{2t+1}{2t+2},-\dfrac{\sqrt{3}}{2} \cdot \dfrac{1}{1+t})$\\
|
||
(2)$\dfrac{\pi}3$
|
||
|
||
040737
|
||
(1)$\sqrt{5}$\\(2)$k=-2\pm\sqrt{3}$\\(3)$\theta=\arctan{2}$或$\theta=\pi-\arctan{2}$
|
||
|
||
040283
|
||
$S=T$
|
||
|
||
040336
|
||
$-\dfrac {24}{25}$
|
||
|
||
040337
|
||
$\dfrac{\sqrt{3}}2$
|
||
|
||
040338
|
||
$2$
|
||
|
||
040339
|
||
$2\sin(\alpha+\dfrac 23 \pi)$
|
||
|
||
040340
|
||
$-\dfrac 12$
|
||
|
||
040341
|
||
$-4$
|
||
|
||
040342
|
||
$\{\dfrac {23}{12}\pi,\dfrac{7}{12}\pi\}$
|
||
|
||
040343
|
||
$3$
|
||
|
||
040344
|
||
$-\dfrac 12$
|
||
|
||
040345
|
||
B
|
||
|
||
040346
|
||
C
|
||
|
||
040347
|
||
A
|
||
|
||
040348
|
||
(1)$\dfrac 13$\\
|
||
(2)$\dfrac{\pi}4$
|
||
|
||
040349
|
||
(1)$2k$;\\
|
||
(2)$10k$;\\
|
||
(3)$\dfrac2{25}\sqrt{5}$
|
||
|
||
040350
|
||
$-\dfrac 13$
|
||
|
||
040351
|
||
$x=2k\pi+\dfrac{\pi}2,k \in \mathbb{Z}$
|
||
|
||
040352
|
||
$\pi$
|
||
|
||
040353
|
||
$-\dfrac 45$
|
||
|
||
040354
|
||
$\{x|k\pi \leq x < k\pi+\dfrac{\pi}2,k \in \mathbb{Z}\}$
|
||
|
||
040355
|
||
$-2$
|
||
|
||
040356
|
||
$\{0,\pi,-\dfrac{\pi}3,\dfrac{\pi}3,\dfrac 53 \pi\}$
|
||
|
||
040357
|
||
$(1,+\infty)$
|
||
|
||
040358
|
||
$[2^{-\dfrac 14},4]$
|
||
|
||
040359
|
||
$[0,\dfrac 23\pi]$
|
||
|
||
040360
|
||
$\dfrac {\pi}6$
|
||
|
||
040361
|
||
$16$
|
||
|
||
040362
|
||
D
|
||
|
||
040363
|
||
B
|
||
|
||
040364
|
||
(1)$\omega =2$，定义域为$\{x|x\neq \dfrac{k\pi}2+\dfrac{\pi}8,k \in \mathbb{Z}\}$\\
|
||
(2)$\dfrac 43$
|
||
|
||
040365
|
||
(1)$500\sqrt{7}$\\
|
||
(2)55706元
|
||
|
||
040366
|
||
(1)$x \leq \log_2 3$\\
|
||
(2)$k \in [\dfrac{225}{271},\dfrac{19}9)$
|
||
|
||
040367
|
||
(1)$m=2$\\
|
||
(2)在$(-2,2)$上严格减\\
|
||
(3)$\dfrac {13}4$
|
||
|
||
015269
|
||
$(0,+\infty)$
|
||
|
||
015270
|
||
$\dfrac{2\pi}{3}$
|
||
|
||
015271
|
||
$-3$
|
||
|
||
015272
|
||
$\dfrac{\pi}{6}$
|
||
|
||
015273
|
||
$3$
|
||
|
||
015274
|
||
$[2k\pi,2k\pi+\pi]$, $k\in \mathbf{Z}$
|
||
|
||
015275
|
||
$f(x)=-1-2x$
|
||
|
||
015276
|
||
$[3,4]$
|
||
|
||
015277
|
||
$1$
|
||
|
||
015278
|
||
\textcircled{1}
|
||
|
||
015279
|
||
$(0,\dfrac{\pi}{4})\cup (\dfrac{3\pi}{4},\pi)$
|
||
|
||
015280
|
||
$[4,+\infty)$
|
||
|
||
015281
|
||
D
|
||
|
||
015282
|
||
A
|
||
|
||
015283
|
||
D
|
||
|
||
015284
|
||
C
|
||
|
||
015285
|
||
$[1,3)$
|
||
|
||
015286
|
||
(1) $\dfrac{3}{5}$; (2) $\dfrac{49}{32}$
|
||
|
||
015287
|
||
(1) $\sqrt{7}$; (2) $\dfrac{9\sqrt{3}}{4}$
|
||
|
||
015288
|
||
(1) $y=3\sin(\dfrac{\pi}{6}x+\dfrac{\pi}{6})+8$, $x\in [0,24]$; (2) 可以进港的时间段为0点至6点, 以及12点至16点; 在0点进港开始卸货, 5点暂时驶离港口, 11点返回港口继续卸货, 16点完成卸货任务
|
||
|