1224 lines
16 KiB
Plaintext
1224 lines
16 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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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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040018
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(1) $\dfrac{\pi}{4}$; (2) $\dfrac{\pi}{6}$; (3) $\dfrac{\pi}{10}$; (4) $\dfrac{\pi}{3}$; (5) $\dfrac{5\pi}{12}$; (6) $\dfrac{\pi}{15}$
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040019
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(1) $60^{\circ}$; (2) $36^{\circ}$; (3) $45^{\circ}$; (4) $75^{\circ}$; (5) $40^{\circ}$; (6) $54^{\circ}$
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040020
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(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) $\dfrac{k\pi}{2}+\dfrac{\pi}{6}$
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040021
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(1) $k \times 360^{\circ}+60^{\circ}$;\\
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(2) $k \times 360^{\circ}+330^{\circ}$; \\
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(3) $k \times 360^{\circ}-210^{\circ}$; \\
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(4) $k \times 180^{\circ}-45^{\circ}$; \\
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(5) $k \times 90^{\circ}+50^{\circ}$
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040022
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(1) $330^{\circ}$; (2) $240^{\circ}$; (3) $210^{\circ}$; (4) $300^{\circ}$
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040023
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(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
|
|
$(4,\dfrac{14}{3}]$
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|
|
|
|
|
040031
|
|
$2n-1$
|
|
|
|
|
|
040032
|
|
$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$
|
|
|
|
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|
040033
|
|
$200$
|
|
|
|
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|
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
|
|
$\dfrac{19}{28}\sqrt{7}$
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|
|
|
|
|
040058
|
|
$\dfrac{79}{156}$
|
|
|
|
|
|
040059
|
|
$2$
|
|
|
|
|
|
040060
|
|
$-\dfrac{\sqrt{1-m^2}}{m}$
|
|
|
|
|
|
040061
|
|
$-\dfrac{1}{5}, \dfrac{1}{5}$
|
|
|
|
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|
040062
|
|
$-\dfrac{1}{3}, 3$
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|
|
|
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|
040063
|
|
$\dfrac{1}{2}, -2$
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|
|
|
|
|
040064
|
|
$\dfrac{\sqrt{6}}{3}$
|
|
|
|
|
|
040065
|
|
$\dfrac{1}{3}, -\dfrac{9}{4}$
|
|
|
|
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|
040066
|
|
$\dfrac{1}{3}, \dfrac{7}{9}$
|
|
|
|
|
|
040067
|
|
$\pm\dfrac{\sqrt{2}}{3}$
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|
|
|
|
|
040068
|
|
$\dfrac{1}{4}, \dfrac{2}{5}$
|
|
|
|
|
|
040069
|
|
$\dfrac{1-\sqrt{17}}{4}$
|
|
|
|
|
|
040070
|
|
(1) 三； (2) 三
|
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|
|
|
|
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
|
|
$-\dfrac{10}{9}$
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|
|
|
|
|
040075
|
|
$a_n=\dfrac{1}{3n-2}$
|
|
|
|
|
|
040076
|
|
$a_n=\dfrac{1}{n}$
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|
|
|
|
|
040077
|
|
$(n-\dfrac{4}{5})5^n$
|
|
|
|
|
|
040078
|
|
$2^{n+1}-3$
|
|
|
|
|
|
040079
|
|
$1078$
|
|
|
|
|
|
040080
|
|
$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$
|
|
|
|
|
|
040081
|
|
(1) 略； (2) $n^2$
|
|
|
|
|
|
040082
|
|
(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$
|
|
|
|
|
|
040083
|
|
$\dfrac{\sqrt{3}}{2}$
|
|
|
|
|
|
040084
|
|
$0$
|
|
|
|
|
|
040085
|
|
$\{0,-2\pi\}$
|
|
|
|
|
|
040086
|
|
$-\dfrac{\pi}6,\dfrac 56\pi$
|
|
|
|
|
|
040087
|
|
$\cot \alpha$
|
|
|
|
|
|
040088
|
|
$7+4\sqrt{3}$
|
|
|
|
|
|
040089
|
|
$\dfrac{\sqrt{2}-\sqrt{6}}{4}$
|
|
|
|
|
|
040090
|
|
$\dfrac{\sqrt{3}+\sqrt{35}}{12}$
|
|
|
|
|
|
040091
|
|
$\dfrac 12$
|
|
|
|
|
|
040092
|
|
$5$
|
|
|
|
|
|
040093
|
|
$-\dfrac 12$
|
|
|
|
|
|
040094
|
|
$\dfrac{\pi}{12}$
|
|
|
|
|
|
040095
|
|
$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$
|
|
|
|
|
|
040096
|
|
$\dfrac 43 \pi$
|
|
|
|
|
|
040097
|
|
\textcircled{4}
|
|
|
|
|
|
040098
|
|
C
|
|
|
|
|
|
040099
|
|
$\dfrac{-2\sqrt{2}-\sqrt{3}}6$
|
|
|
|
|
|
040100
|
|
$-\dfrac 7{25}$
|
|
|
|
|
|
040101
|
|
$-\dfrac {\pi}3$
|
|
|
|
|
|
040102
|
|
$(-\dfrac {12}{13}, \dfrac{5}{13})$
|
|
|
|
|
|
040103
|
|
$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$
|
|
|
|
|
|
040104
|
|
略
|
|
|
|
|
|
040105
|
|
$\dfrac {171} {221}, -\dfrac {21} {221}$
|
|
|
|
|
|
040106
|
|
$\{-\pi\}$
|
|
|
|
|
|
040107
|
|
$\dfrac{8\sqrt{2}-3}{15}$
|
|
|
|
|
|
040108
|
|
$\sin \theta$
|
|
|
|
|
|
040109
|
|
$-\dfrac{56}{65}$
|
|
|
|
|
|
040110
|
|
$\dfrac {\pi}4$
|
|
|
|
|
|
040111
|
|
略
|
|
|
|
|
|
040112
|
|
略
|
|
|
|
|
|
040131
|
|
$-\dfrac{25}{12}$
|
|
|
|
|
|
040132
|
|
$\dfrac 52$
|
|
|
|
|
|
040133
|
|
$-\dfrac{\pi}4$
|
|
|
|
|
|
040134
|
|
$-\dfrac 12$
|
|
|
|
|
|
040135
|
|
$\dfrac 6{19}$
|
|
|
|
|
|
040136
|
|
$-\dfrac {\sqrt{3}}3$
|
|
|
|
|
|
040137
|
|
$\dfrac 3{22}$
|
|
|
|
|
|
040138
|
|
$4$
|
|
|
|
|
|
040139
|
|
$-\dfrac{63}{65}$
|
|
|
|
|
|
031288
|
|
$[7,10]$
|
|
|
|
|
|
031289
|
|
$(-\infty,-2)\cup(-2,3]$
|
|
|
|
|
|
031290
|
|
$2$
|
|
|
|
|
|
031291
|
|
$7$
|
|
|
|
|
|
031292
|
|
$a\ge3$
|
|
|
|
|
|
031293
|
|
$-9$或$3$
|
|
|
|
|
|
031294
|
|
$\dfrac{1}{27}$
|
|
|
|
|
|
031295
|
|
$[-3,3]$
|
|
|
|
|
|
031296
|
|
$45$
|
|
|
|
|
|
031297
|
|
$(1,\dfrac 32]$
|
|
|
|
|
|
031298
|
|
$[0,1]$
|
|
|
|
|
|
031299
|
|
$\dfrac{\sqrt{6}}{4}$
|
|
|
|
|
|
031300
|
|
D
|
|
|
|
|
|
031301
|
|
B
|
|
|
|
|
|
031302
|
|
A
|
|
|
|
|
|
031303
|
|
A
|
|
|
|
|
|
031304
|
|
$(1)a_n=-3n+19,b_n=4^{3-n}\\
|
|
(2)1\le n \le 28,S_n>T_n;n=29,S_n=T_n;n \ge 30,S_n<T_n $
|
|
|
|
|
|
031305
|
|
$(1)[-1,3];(2)a \ge 2$
|
|
|
|
|
|
031307
|
|
$(1)a_n=m^n;(2)m=\dfrac 13;(3)T_n=\dfrac {2n-3}4 \cdot 3^{n+1}+ \dfrac 94$
|
|
|
|
|
|
031308
|
|
$(1)(-\infty,2];(2)[2\sqrt{3},\dfrac{91}{20}];(3)a=-12,b=\dfrac{17}2$
|
|
|
|
|
|
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
|
|
$-\dfrac{484}{729}$
|
|
|
|
|
|
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
|
|
|
|
|
|
|
|
|