419 lines
5.9 KiB
Plaintext
419 lines
5.9 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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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) $-10+4\pi$
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040024
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$18$
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040025
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$3$,$-2$
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040026
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(1) $1037$; (2) $-4k+53$; (3) $500$
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040027
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$-2n+10$
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040028
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15
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040029
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$7$
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040030
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$(4,\dfrac{14}{3}]$
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040031
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$2n-1$
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040032
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$(3,\dfrac{35}{9})$或$(\dfrac{35}{9},3)$
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040033
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$200$
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040034
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略
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040035
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$a_n=\begin{cases}1, & n=1,\\ 2n, & n=2k, \\ 2n-2, & n=2k+1\end{cases}$($k\in \mathbf{N}$, $k\ge 1$)
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040036
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$6n-3$
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040057
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$\dfrac{19}{28}\sqrt{7}$
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040058
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$\dfrac{79}{156}$
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040059
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$2$
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040060
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$-\dfrac{\sqrt{1-m^2}}{m}$
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040061
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$-\dfrac{1}{5}, \dfrac{1}{5}$
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040062
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$-\dfrac{1}{3}, 3$
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040063
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$\dfrac{1}{2}, -2$
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040064
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$\dfrac{\sqrt{6}}{3}$
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040065
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$\dfrac{1}{3}, -\dfrac{9}{4}$
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040066
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$\dfrac{1}{3}, \dfrac{7}{9}$
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040067
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$\pm\dfrac{\sqrt{2}}{3}$
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040068
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$\dfrac{1}{4}, \dfrac{2}{5}$
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040069
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$\dfrac{1-\sqrt{17}}{4}$
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040070
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(1) 三； (2) 三
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040071
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(1) $[-\dfrac{1}{2},\dfrac{1}{2})\cup\{1\}$; (2) $[-\dfrac{\pi}{3},\dfrac{\pi}{3})$; (3) $\{-\dfrac{1}{2}\}$
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040072
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(1) $-\tan \alpha-\cot \alpha$; (2) $-\dfrac{\sqrt{2}}{\sin \alpha}$; (3) $-1$; (4) $0$
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040073
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略
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040074
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$-\dfrac{10}{9}$
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040075
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$a_n=\dfrac{1}{3n-2}$
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040076
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$a_n=\dfrac{1}{n}$
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040077
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$(n-\dfrac{4}{5})5^n$
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040078
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$2^{n+1}-3$
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040079
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$1078$
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040080
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$S_n=\begin{cases}\dfrac{n^2}{2}+n-\dfrac 23+\dfrac 23\cdot 2^n, & n\text{为偶数},\\ \dfrac{n^2}{2}-\dfrac 76+\dfrac 23\cdot 2^{n+1}, & n\text{为奇数} \end{cases}$
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040081
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(1) 略； (2) $n^2$
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040082
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(1) 不存在； (2) 存在, 如$c_n=2^{n-1}$
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040083
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$\dfrac{\sqrt{3}}{2}$
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040084
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$0$
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040085
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$\{0,-2\pi\}$
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040086
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$-\dfrac{\pi}6,\dfrac 56\pi$
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040087
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$\cot \alpha$
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040088
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$7+4\sqrt{3}$
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040089
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$\dfrac{\sqrt{2}-\sqrt{6}}{4}$
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040090
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$\dfrac{\sqrt{3}+\sqrt{35}}{12}$
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040091
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$\dfrac 12$
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040092
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$5$
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040093
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$-\dfrac 12$
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040094
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$\dfrac{\pi}{12}$
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040095
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$\{x|x=\pm\frac 23 \pi+2k\pi,k \in \mathbf{Z}\}$
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040096
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$\dfrac 43 \pi$
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040097
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$\textcircled{4}$
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040098
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C
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040099
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$\dfrac{-2\sqrt{2}-\sqrt{3}}6$
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040100
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$-\dfrac 7{25}$
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040101
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$-\dfrac {\pi}3$
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040102
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$(-\dfrac {12}{13}, \dfrac{5}{13})$
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040103
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$(\dfrac {5-12\sqrt{3}}{2}, \dfrac{12-5\sqrt{3}}{2})$
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040104
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略
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