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} 021470 $2\sqrt{5}$ 021471 $\frac{2\sqrt{13}}{13}$;$-\frac{2}{3}$ 021472 $ \left( -2,\frac{2}{3} \right)$ 021473 $<$ 021474 5 021475 2 021476 当$t=\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha =- \frac{\sqrt{15}}{3}$;\\ 当$t=-\sqrt{5}$时, $\cos \alpha=- \frac{\sqrt{6}}{4}$, $\tan \alpha = \frac{\sqrt{15}}{3}$;\\ 当$t=0$时, $\cos \alpha=-1$, $\tan \alpha = 0$. 021477 当$\alpha$在第二象限时，$ \sin \alpha =\frac{4}{5}$, $\tan \alpha=-\frac{4}{3}$;\\ 当$\alpha$在第三象限时，$ \sin \alpha =-\frac{4}{5}$, $\tan \alpha=\frac{4}{3}$. 021478 $-\frac{\sqrt{3}}{4}$ 021479 (1) 第四象限； (2) 第一、四象限；(3)第一、三象限；(4)第一、三象限. 021480 $A=\left\{ -2,-0,4 \right\}$ 021481 (1) $\{\alpha|2k\pi \le \alpha \le \frac{\pi}{2}+2k\pi,\ k \in \mathbf{Z}\}$;\\ (2) $[0,3)$ 021482 \begin{center} \begin{tabular}{|c|c|c|c|c|c|} \hline$\alpha$&$\dfrac{\pi}{3}$&$\dfrac{7 \pi}{4}$&$\dfrac{2021 \pi}{2}$&$-\dfrac{\pi}{6}$&$-\dfrac{22 \pi}{3}$\\ \hline$\sin \alpha$& $\frac{\sqrt{3}}{2}$ &$-\frac{\sqrt{2}}{2}$ & $1$&$-\frac{1}{2}$ &$\frac{\sqrt{3}}{2}$ \\ \hline$\cos \alpha$&$\frac{1}{2}$ &$\frac{\sqrt{2}}{2}$ & $0$&$\frac{\sqrt{3}}{2}$ &$-\frac{1}{2}$ \\ \hline$\tan \alpha$&$\sqrt{3}$ &$-1$ & 不存在 &$-\frac{\sqrt{3}}{3}$ &$-\sqrt{3}$\\ \hline$\cot \alpha$&$\frac{\sqrt{3}}{3}$ &$-1$ & $ 0$&$-\sqrt{3}$ &$-\frac{\sqrt{3}}{3}$ \\ \hline \end{tabular} \end{center} 021483 (1) $\{x|x=\frac{4\pi}{3}+2k \pi$或$ x=\frac{5\pi}{3}+2k \pi,\ k \in \mathbf{Z} \}$;\\ (2) $\{-\frac{2\pi}{3},-\frac{\pi}{3},\frac{4\pi}{3} ,\frac{5\pi}{3},\frac{10\pi}{3},\frac{11\pi}{3} \}$ 021484 $-\frac{2\sqrt{5}}{5}$;$2$ 021485 \textcircled{2} \textcircled{4} 021486 当$\alpha$在第一象限时，$ \sin \alpha =\frac{3\sqrt{10}}{10}$, $\cos \alpha =\frac{\sqrt{10}}{10}$,$\tan \alpha=3$;\\ 当$\alpha$在第三象限时，$ \sin \alpha =-\frac{3\sqrt{10}}{10}$,$\cos \alpha =-\frac{\sqrt{10}}{10}$, $\tan \alpha=3$. 021487 $\sin k\pi =0$;\\$\cos k\pi=\left\{ \begin{array}{lc} $1$, & k=2n \\ $ -1$ , &k=2n-1\\ \end{array} \right.$ ($n \in \mathbf{Z}$). 021488 (1) $\{\theta | 2k \pi+\dfrac{\pi}{3}<\theta<2k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$;\\ (2) $\{\theta | k \pi-\dfrac{\pi}{2}<\theta \le k \pi-\dfrac{\pi}{6},\ k \in \mathbf{Z} \}$;\\ (3) $\{\theta | k \pi+\dfrac{\pi}{3} \le \theta \le k \pi+\dfrac{2\pi}{3},\ k \in \mathbf{Z} \}$. 021489 第二象限 021490 (1) 当$\dfrac{\alpha}{2}$在第二象限时，点$P$在第四象限；\\ 当$\dfrac{\alpha}{2}$在第四象限时，点$P$在第二象限.\\ (2) $\sin (\cos \alpha) \cdot \cos (\sin \alpha)<0$ 021491 当$m=0$时，$ \cos (\alpha+1905^{\circ})=-1$,$\tan (\alpha-615^{\circ})=0$;\\ 当$m=\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=-\frac{\sqrt{15}}{3}$;\\ 当$m=-\sqrt{5}$时，$ \cos (\alpha+1905^{\circ}) =-\frac{\sqrt{6}}{4}$,$\tan (\alpha-615^{\circ})=\frac{\sqrt{15}}{3}$. 021492 $-\dfrac{3}{8}$ 021493 $-\dfrac{1}{20}$ 021494 $\dfrac{7\sqrt{2}}{4}$ 021495 $\dfrac{3\sqrt{5}}{5}$ 021496 $11$ 021497 $5$;$-\dfrac{12}{5}$;$\dfrac{4}{9}$ 021498 $\sin ^2 \alpha$ 021499 $1$ 021502 $-\dfrac{12}{5}$ 021503 $-\dfrac{\sqrt{3}}{2}$ 021504 $\dfrac{\sqrt{7}}{2}$;$\dfrac{\sqrt{7}}{4}$ 021505 $-\dfrac{\sqrt{11}}{3}$ 021506 $\dfrac{\pi}{3}$ 021507 $\left[ 0,\pi \right )$ 021508 $-\dfrac{\sqrt{3}}{2}$;$-\dfrac{\sqrt{2}}{2}$;$-\sqrt{3}$;$-\sqrt{3}$ 021509 $69^{\circ}$;$72^{\circ}$;$\dfrac{\pi}{9}$;$\dfrac{7 \pi}{15}$ 021510 $\cot \alpha$ 021511 $-1$ 021512 $-1$ 021513 $ \sin 2-\cos 2$ 021514 $0$ 021515 $0$ 021516 $-\dfrac{\sqrt{1-a^2}}{a}$ 021517 $-\dfrac{2+\sqrt{3}}{3}$ 021518 (1) $\dfrac{\sqrt{3}}{2}$;(2) $\dfrac{1}{4}$. 021519 (1) $-\dfrac{2}{3}$; \\ (2) $\dfrac{2}{3}$; \\ (3) $-\dfrac{\sqrt{5}}{3}$;\\ (4) $\dfrac{\sqrt{5}}{2}$. 021520 (1) $\sin 69^{\circ}$ ; (2) $-\cos 8^{\circ}$ ; (3) $-\tan \dfrac{\pi}{9}$; (4) $\cot \dfrac{7\pi}{15}$. 021521 $\dfrac{2}{5}$ 021522 $(3,4)$ 021523 $0$ 021524 $\sin \alpha$ 021525 $-\dfrac{1}{5}$ 021526 (1) $\dfrac{\sqrt{6}}{6}-\sqrt{3}$;\\ (2) $-\dfrac{\sqrt{6}}{3}$;\\ (3) $1$ 021527 (1) $\dfrac{6 \pi}{5}$; (2) $\dfrac{4 \pi}{5}$; (3) $\dfrac{13 \pi}{10}$; (4) $\dfrac{17 \pi}{10}$. 021528 (1) 当$\alpha$在第一象限时, $\sin (2 \pi-\alpha)=-\dfrac{\sqrt{3}}{2}$; 当$\alpha$在第三象限时, $\sin (2 \pi-\alpha)=\dfrac{\sqrt{3}}{2}$.\\ (2) 当$\alpha$在第一象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=-\sqrt{3}$; 当$\alpha$在第四象限时, $\dfrac{1}{\tan [\dfrac{(2 k+1) \pi}{2}+\alpha]}=\sqrt{3}$. 021529 (1) $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\ (2) $\{x | x=2k \pi \pm \dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\ (3) $\{x | x=k \pi + \dfrac{5\pi}{6},\ k \in \mathbf{Z}\}$;\\ (4) $\{x | x=2k \pi + \dfrac{5\pi}{6}$ 或$x=2k \pi + \dfrac{3\pi}{2} ,\ k \in \mathbf{Z}\}$;\\ 第二种写法： $\{x | x=k \pi+ (-1)^k \cdot \dfrac{\pi}{6}+\dfrac{2\pi}{3},\ k \in \mathbf{Z}\}$;\\ (5) $\{x | x=k \pi - \arctan \dfrac{\sqrt{3}}{2}+ \dfrac{\pi}{4},\ k \in \mathbf{Z}\}$;\\ (6) $\{x | x=\dfrac{2k \pi}{5} + \dfrac{7\pi}{60}$ 或$ x=\dfrac{2k \pi}{5} - \dfrac{13\pi}{60} ,\ k \in \mathbf{Z}\}$;\\ (7) $\{x | x=k \pi - \dfrac{5\pi}{8}$ 或$x=k \pi - \dfrac{3\pi}{8} ,\ k \in \mathbf{Z}\}$; 021530 (1) $\{ \dfrac{\pi}{12},\dfrac{17\pi}{12} \}$;\\ (2) $\{ \dfrac{5\pi}{6} \}$;\\ (3) $\{ \dfrac{\pi}{12},\dfrac{5\pi}{12} \}$;\\ (4) $\{ \dfrac{5\pi}{6} \}$. 021531 (1) $\{x | x= \dfrac{2k \pi}{5} ,\ k \in \mathbf{Z}\}$;\\ (2) $\{x | x= \dfrac{2k \pi}{3} +\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\ (3) $\{x | x= 2k \pi$ 或$x=k \pi +(-1)^k \cdot \dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$;\\ (4) $\{x | x= k \pi+\dfrac{ \pi}{3}$ 或$x=k \pi -\dfrac{ \pi}{6},\ k \in \mathbf{Z}\}$. 021532 $\dfrac{3+4\sqrt{3}}{10}$ 021533 $-1$ 021534 $-\dfrac{33}{50}$ 021535 (1) $\dfrac{\sqrt{6}-\sqrt{2}}{4}$; (2) $\dfrac{\sqrt{6}+\sqrt{2}}{4}$; (3) $0$. 021536 (1) $\sqrt{3} \sin \alpha$; (2) $\cos(\alpha-2\beta)$. 021537 $\dfrac{140}{221}$ 021538 $\dfrac{2\sqrt{6}-1}{6}$ 021540 C 021541 A 021542 $\dfrac{3\sqrt{10}+6\sqrt{2}+2\sqrt{14}-\sqrt{70}}{24}$ 021543 $\dfrac{8\sqrt{3}-21}{20}$ 021544 $\dfrac{\pi}{2}$ 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 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