ans

021441
错误, 正确, 错误, 错误


021442
D


021443
C


021444
A


021445
C


021446
D


021447
$-390^\circ$


021448
$304^\circ$, $-56^\circ$


021449
$-144^\circ$


021450
二, 四


021451
(1) $\{\alpha|\alpha=60^\circ+k\cdot 360^\circ, \ k\in \mathbf{Z}\}$, $-300^\circ$, $60^\circ$, $420^\circ$; (2) $\{\alpha|\alpha = -21^\circ+k\cdot 360^\circ, \ k \in \mathbf{Z}\}$, $-21^\circ$, $339^\circ$, $699^\circ$


021452
\begin{tikzpicture}[>=latex]
\fill [pattern = north east lines] (30:2) arc (30:60:2) -- (0,0) -- cycle;
\draw (30:2) -- (0,0) -- (60:2);
\draw [->] (-2,0) -- (2,0) node [below] {$x$};
\draw [->] (0,-2) -- (0,2) node [left] {$y$};
\draw (0,0) node [below left] {$O$};
\end{tikzpicture}


021453
$-1290^{\circ}$;第二象限


021454
(1) $ \{\alpha|\alpha=45^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
(2) $\{\alpha|\alpha=135^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
(3) $\{\alpha|\alpha=45^{\circ}+k\cdot 90^{\circ}, \ k \in \mathbf{Z}\}$;\\
(4) $\{\alpha|180^{\circ}+k\cdot 360^{\circ}<\alpha<270^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.


021455
(1) $ \{\beta|\beta=\alpha+180^{\circ}+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
(2) $\{\beta|\beta=\alpha+90^{\circ}+k\cdot 180^{\circ}, \ k \in \mathbf{Z}\}$;\\
(3) $\{\beta|\beta=-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$;\\
(4) $\{\beta|\beta=90^{\circ}-\alpha+k\cdot 360^{\circ}, \ k \in \mathbf{Z}\}$.


021456
C


021457
B


021458
$\dfrac{\pi}{12}$; $\dfrac{7\pi}{12}$; $\dfrac{5\pi}{4}$; $300^{\circ}$; $324^{\circ}$; $315^{\circ}$; $(\dfrac{270}{\pi})^{\circ}$


021459
(1)$\frac{50\pi+180}{9}$;(2)$\frac{250\pi}{9}$


021460
$\sqrt{3}$


021461
(1)$\frac{\pi}{3}$;(2)$\frac{2\pi}{3}$


021462
(1)$16\pi+\frac{2\pi}{3}$,二;\\
(2)$-18\pi+\frac{4\pi}{3}$,三;\\
(3)$-2\pi+\frac{7\pi}{5}$,三;\\
(4)$-2\pi+\frac{3\pi}{4}$,二.


021463
$\frac{1}{2}$


021464
(1) $\{\alpha|-\frac{\pi}{2}+2k\pi<\alpha<2k\pi,\ k \in \mathbf{Z}\}$;\\
(2) $\{\alpha|\alpha=\frac{k\pi}{2},\ k \in \mathbf{Z}\}$.


021465
(1) $\beta=\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
(2) $\beta=-\alpha+2k\pi,\ k \in \mathbf{Z}$;\\
(3) $\beta=-\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$;\\
(4) $\beta=\alpha+\pi+2k\pi,\ k \in \mathbf{Z}$.


021466
(1) $\{\alpha|-\frac{\pi}{4}+2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\
(2) $\{\alpha|\frac{\pi}{6}+k\pi \le \alpha \le \frac{5\pi}{6}+k\pi,\ k \in \mathbf{Z}\}$.


021467
(1) 第四象限；第四象限；\\
(2) 第二象限或者第四象限；第一象限或第二象限或者$y$轴正半轴.


021468
$A\cap B=\{\alpha | 2k \pi+\dfrac{5\pi}{6}<\alpha<2k \pi+\dfrac{7\pi}{6},\ k \in \mathbf{Z} \}$


021469
\begin{tabular}{|c|c|c|c|c|c|}
\hline &$P(-5,12)$&$P(0,-6)$&$P(6,0)$&$P(-9,-12)$&$P(1,-\sqrt{3})$\\
\hline$\sin \alpha$&$\dfrac{12}{13}$ &$-1$ & $0$&$-\dfrac{4}{5}$ &$-\dfrac{\sqrt{3}}2$ \\
\hline$\cos \alpha$&$-\dfrac{5}{13}$ &$0$ & $1$&$-\dfrac{3}{5}$ &$\dfrac 12$ \\
\hline$\tan \alpha$&$-\dfrac{12}{5}$ &不存在 & $0$&$\dfrac{4}{3}$ &$-\sqrt{3}$ \\
\hline$\cot \alpha$&$-\dfrac{5}{12}$ &$0$ & 不存在 &$\dfrac {3}{4}$ &$-\dfrac{\sqrt{3}}3$ \\
\hline
\end{tabular}


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