¶Ô¿Úµ¥ÕÐÊýѧ֪ʶÊáÀíÆª£¨Ò»ÂÖ£©´ð°¸£¨ÉÏ£© ÏÂÔØ±¾ÎÄ

7.???22?,?4??3??5,???;

2?9x8.(1)f(x)?10?3x(2)?0,104?

£¬¶¨ÒåÓò£¨0,3£©

???27???210?xlg?lg(0.01?5)?x(lg2?lg3)?lg0.01?lg

32?2?lg10?lg2?x??7.388

lg2?lg3ËùÒÔÖÁÉÙÒª¾­¹ý8´Î²ÅÄÜʹ²úÆ·´ïµ½Êг¡ÒªÇó. £¨Èý£©ÑÝÁ··´À¡

1.A 2.90Íò¶Ö 3.300Ö» ¿ÎºóÍØÕ¹ÑµÁ· ½â´ðÌâ 1.1.27£®

2. 46Сʱ.¹ý³Ì£º1Сʱºó£¬Ï¸°û×ÜÊýΪ£º

¿ÎºóÍØÕ¹ÑµÁ· Ò»¡¢Ñ¡ÔñÌâ

1.B 2.B 3.A 4.B ¶þ¡¢Ìî¿ÕÌâ

5.£¼,£¾ £»6.?1,???£»

?3?7. ?,1? 8.?2,???£» ?5?Èý¡¢½â´ðÌâ

113?100??100?2??100£» 2222Сʱºó£¬Ï¸°û×ÜÊýΪ£º

?1?9.?5,???£»??,3?

?3?10. ??5,?2?13139??100???100?2??100£» 222243Сʱºó£¬Ï¸°û×ÜÊýΪ£º

?7,??? 11.?1,5?

µÚÁù½Ú Ö¸Êýº¯Êý¡¢¶ÔÊýº¯ÊýµÄʵ¼ÊÓ¦ÓÃ

[±äʽѵÁ·]

1. y?1?(1?6%)?0.94£¬µ±x=8ʱy?0.94?0.6 2.ÖÁÉÙ¹ýÂËx´Î²ÅÄÜʹ²úÆ·´ïµ½Êг¡ÒªÇó,Ôò¸ù¾ÝÌâÒâµÃ£º

xx8191927??100???100?2??100£» 242484Сʱºó£¬Ï¸°û×ÜÊýΪ£º

12712781??100???100?2??100£» 282816?3?¿É¼ûϸ°û×ÜÊýyÓëʱ¼äxµÄ¹ØÏµÎª£ºy?100???

?2?3.y?a?1?r?£»11176.8. 4.7.18%£»26296Ôª.

5.8231.9Íò£»y?8050??1?0.56%?

xxx122%?(1?)x?0.1%?()x?0.05?

332lg()x?lg0.05(Á½±ßͬʱȡÒÔ10 Ϊµ×µÄ¶ÔÊý) 3µÚÎåÕ Èý½Çº¯Êý

µÚÒ»½Ú ½ÇµÄ¸ÅÄîµÄÍÆ¹ãºÍÈý½Çº¯ÊýµÄ¶¨Òå

¡¾¿Îǰ×ÔÖ÷ÊáÀí¡¿

£¨Ò»£©ÖªÊ¶»Ø¹Ë 1. Õý½Ç£»¸º½Ç£»Áã½Ç 2. {¦Â|¦Â=¦Á+k¡¤360¡ã£¬k?Z} 3. ³¤¶ÈµÈÓÚ°ë¾¶³¤µÄ»¡Ëù¶ÔµÄÔ²ÐĽÇ

yx1y4.?r2 5. 22222xx?yx?y6. ¦Á(½Ç¶È) »¡¶È 0¡ã 30¡ã 45¡ã 60¡ã 90¡ã 180¡ã 270¡ã 360¡ã0 ¦Ð6123233 ¦Ð422221 ¦Ð332 ¦Ð21 ¦Ð 3¦Ð2 2¦Ð sin¦Á 0 0 -1 0 cos¦Á 1 120 -1 0 1 tan¦Á 0 3²»´æÔÚ 0 ²»´æÔÚ 0 (¶þ)»ù´¡¹ý¹Ø ¦Ð1£®Èý 2.{x|x=2k¦Ð+,k?Z} 34?4?3¦Ð3.; 4.420¡ã , ? 4335£®3?1433;?;? 6. ¶þ»òËÄ 7. 5445¡¾¿ÎÌõäÀý̽¾¿¡¿

£¨Ò»£©µäÀý¾«Îö [±äʽѵÁ·Ò»] ½â(1)420¡ã=360¡ã+60¡ã,Óë60¡ã½ÇÖÕ±ßÏàͬ,ÊǵÚÒ»ÏóÏÞ½Ç.

17

(2) ?5¦Ð19¦Ð19¦Ð,Óë½ÇÖÕ±ßÏàͬ,ΪµÚËÄÏóÏÞ½Ç. ??2¦Ð?121212111l?r?(¦Ð?2)?1?¦Ð?1,Ñ¡B 222[±äʽѵÁ·Èý] 25 5[±äʽѵÁ·ËÄ] sin???[±äʽѵÁ·¶þ] ½â: S?[±äʽѵÁ·Èý]

½â: r?(?4k)2?(3k)2?5k(k?0)

½â:

sin(???)cos(???)sin?cos?= 23tan(???)cos(????)sin2?3(?cos?)cos2?2sin??cos??2?(¶þ)¾­µä¿¼Ìâ 1.?3k4k2?? 5k5k5=?sin?cos?1=? 2sin?cos?sin?329 2.? 15514 5. 2£»2 4[±äʽѵÁ·Îå] Ö¤Ã÷: ×ó±ß

(Èý)ÑÝÁ··´À¡

1.B 2.-1 3.¶þ 4.-1 ,

6.Èñ½ÇÈý½ÇÐÎ ¿ÎºóÍØÕ¹ÑµÁ· Ò»¡¢Ñ¡ÔñÌâ:

1.D 2.B 3.D 4.D 5.C 6.B ¶þ¡¢Ìî¿ÕÌâ 7.240; 8.10.?sin2?cos2??sin2?1== 22cos?cos?cos2?sin?tan?1ÓÒ±ß==cos?=

sin?cos?sin?cos?cos2?=1?tan2??1?×ó±ß=ÓÒ±ß,ԭʽ³ÉÁ¢. (¶þ)¾­µä¿¼Ìâ 1.

1 2.A 3.A 4.(1) -2 (2)3 24; 3352,0; ; 9.215(Èý)ÑÝÁ··´À¡

1£®C; 2.B; 3.B; 4.cos?; 5.?6.1;

2265 11.?; 12.?,-1 525Èý¡¢½â´ðÌâ:

13£®½â:sin5760=sin(3600+2160)=sin2160<0

474 7.;?

355cos14¦Ð4¦Ð4¦Ð?cos(2¦Ð?)?cos?0 55519¦Ð5¦Ð5¦Ðtan(?)??tan(2¦Ð?)??tan?0

777¿ÎºóÍØÕ¹ÑµÁ·

Ò»¡¢Ñ¡ÔñÌâ

1.B 2.C 3.D 4.D 5.C 6.A ¶þ¡¢Ìî¿ÕÌâ 7.?14£®×ÔÐгµ5ÃëÄÚת¹ý8Ȧ,Ôòת¹ýµÄ»¡¶ÈÊýΪ |¦Á|=2¦Ð?8?16¦Ð,

¶ÔÓ¦µÄ»¡³¤Îªl?|?|?r?16¦Ð?0.35?17.58(Ã×) ´ð:×ÔÐгµ5ÃëÄÚ×ß¹ýÁËÔ¼17.58Ã×.

µÚ¶þ½Ú ͬ½ÇÈý½Çº¯ÊýµÄ»ù±¾¹ØÏµÊ½¼°ÓÕµ¼¹«Ê½ ¡¾¿Îǰ×ÔÖ÷ÊáÀí¡¿ £¨Ò»£©ÖªÊ¶»Ø¹Ë

1.1 tan¦Á 2.-sin¦Á -cos¦Á - tan¦Á -cos¦Á sin¦Á (¶þ)»ù´¡¹ý¹Ø 1.C 2.C 3.

1672; 8.; 9.-1; 10.? 2135Èý¡¢½â´ðÌâ 11.½â:

??¦Ð3?5¦Ð????¦Ð?cos?????cos?¦Ð????????cos??????

3?6????6???612.½â: °´ÌâÒâ,sin??cos???8k1, sin?cos?? 689k2, 16 sin2??cos2??2sin?cos??42333,?,, 4.? 222393 225192 . ?k , k??341613.ÓÉÌâÒâÖª£¬tan???2£¬

1?5.1£¬?cos100? 6.0 7.¡¾¿ÎÌõäÀý̽¾¿¡¿ £¨Ò»£©µäÀý¾«Îö [±äʽѵÁ·Ò»] ½â(1)ÒòΪtan??22¡àԭʽ=

sin??5cos?tan??53???

?2cos??sin??2?tan?4

µÚÈý½Ú ÕýÏÒº¯ÊýºÍÓàÏÒº¯ÊýµÄͼÏóºÍÐÔÖÊ

¡¾¿Îǰ×ÔÖ÷ÊáÀí¡¿ £¨Ò»£©ÖªÊ¶»Ø¹Ë 1.¶¨ÒåÓò£ºR R

ÖµÓò£º[-1,1] [-1,1] ÖÜÆÚÐÔ£º2¦Ð 2¦Ð

ÆæÅ¼ÐÔ£ºÆæº¯Êý żº¯Êý 2.A -A

4,Éèsin??4m,cos??3m, 32

sin??cos??1,µÃ25m=1, ÓÖÒòΪ¦ÁÔÚµÚÈýÏóÏÞ,ËùÒÔ

143m<0,µÃm??sin???,cos???

555[±äʽѵÁ·¶þ]

4sin??2cos?4tan??2=10, =10

5cos??3sin?5?3tan?µÃtan???2

½â:

2¦Ð?3¦Ð??¦Ð?

3.(0,0)¡¢?,1?¡¢(¦Ð,0)¡¢?,?1?¡¢??2??2?

18

?2¦Ð,0?£»(0,1)¡¢??(¶þ)»ù´¡¹ý¹Ø

¦Ð??3¦Ð?,0?¡¢(¦Ð,-1)¡¢?,0?¡¢?2¦Ð,1?£»

?2??2?(¶þ)¾­µä¿¼Ìâ 1.

¦Ð 2.C 3.A 4.B 41.D 2.D 3.B 4.B 5. k¦Ð?3¦Ð¦Ð,k?Z, 3,k¦Ð?,k?Z, -1 44

(Èý)ÑÝÁ··´À¡ 1.ͼÂÔ,T=2¦Ð;

2.(1) 6¦Ð, (2) ¦Ð; 3.C; 4. C ;

6.

7¦Ð11¦Ð5¦Ð¦Ð7¦Ð11¦Ð£»?,?,?, ,6666665.(1)13, -3; (2) 2,

1 27.D

¡¾¿ÎÌõäÀý̽¾¿¡¿ £¨Ò»£©µäÀý¾«Îö [±äʽѵÁ·Ò»] ½â:ͼÂÔ.ËùÇó¼õÇø¼äΪ[[±äʽѵÁ·¶þ] ½â:x?[,

6.(1)2¦Ð, (2) 7.?0,1?

?5?5? ; (3) ??2k??,,k?Z 6667¦Ð,2¦Ð] 6¦Ð2¦Ð], 63¦Ð¦Ð,]ÄÚ, ymax?2, 63¿ÎºóÍØÕ¹ÑµÁ· Ò»¡¢Ñ¡ÔñÌâ

1.C 2.C 3.C 4.C 5.B 6.B ¶þ¡¢Ìî¿ÕÌâ

7.R, [-2,2], ¦Ð; 8.3, -1; 9. [,3] 10.1?a?2 Èý¡¢½â´ðÌâ

11£®½â:x?{x|x?2k¦Ð?ÓÉy?2cosxµÄͼÏó¿ÉÖª,ÔÚ[?¶ø2cos(?)?3, 2cos34¦Ð6¦Ð?1,ËùÒÔymin?1 33¦Ð3,k?Z}; ymax?.; 22[±äʽѵÁ·Èý]

½â: (1) ÓÉy?sin?µÄͼÏó¿ÉÖª,ÔÚ¦ÈÈñ½Çʱ,Âú×ãÌõ¼þµÄ¦ÈÖ»

??5???k?,?k??,k?Z 12.(1)µ¥µ÷ÔöÇø¼ä£º??12?12?(2)??¦Ð¦Ð3?,ËùÇó¦È? 323(2) ÓÉy?sin?µÄͼÏó¿ÉÖª,ÔÚ??(0£¬¦Ð)ÄÚº¯Êý,Âú×ãÌõ¼þ

ÓÐÒ»¸ö,ÓÉsinµÄ¦ÈÖ»Óжþ¸ö,ÓÉsin»ò??????2? ?x?,???2x??36333¦Ð3¦Ð¦Ð3?,sin(¦Ð?)?, ,ËùÇó??323232¦Ð 3¦Ð»ò3(3)ÓÉy?sinxµÄÖÜÆÚÐÔ,ËùÇó??2k¦Ð???2k¦Ð?2¦Ð,(k?Z) 3[±äʽѵÁ·ËÄ]

?3?? ??¼´x??ʱ£¬ymin??3233??5??µ±2x??¼´x?ʱ£¬ymax?1

1232¦Ð3¦Ð13.f(0)?3sin? (2) ??4,y?3sin(4x?)

626?33¦Ð¦Ð1(3) f()?, ?3sin(4x?), sin(2??)?,

222662¦Ð¦Ð¦Ð7¦Ð¦Ð5¦Ð??(0,), ????ËùÒÔ??»ò??.

266666?µ±2x?13¦Ð¦Ð??2¦Ð 6611µÃT=4¦Ð,ËùÒÔ??,ÓÖA=2, y?2sin(x??)

22¦Ð1¦Ð¦Ð(,?2)Ï൱ÓÚÎåµã·¨×÷ͼÖеĵڶþµã,Ôò????,µÃ62625¦Ð15¦Ð£¬ËùÒÔy?2sin(x?) ??12212½â:

×î¸ßµãÓë×îµÍµãºá×ø±êÖ®²îΪ[±äʽѵÁ·Îå]

½â: f(x)?sin2x?2sin2x=sin2x?2?

µÚËÄ½Ú Á½½ÇºÍ²îÓë¶þ±¶½Ç

£¨Ò»£©ÖªÊ¶»Ø¹Ë

1.ºÍ½Ç¡¢²î½Ç¹«Ê½ sin(¦Á+¦Â)= sin¦Ácos¦Â+ cos¦Ásin¦Â£» sin(¦Á-¦Â)= sin¦Ácos¦Â- cos¦Ásin¦Â£» cos(¦Á+¦Â)= cos¦Ácos¦Â-sin¦Ásin¦Â£» cos(¦Á-¦Â)= cos¦Ácos¦Â+sin¦Ásin¦Â£»

tan??????tan??????tan??tan?;

1?tan?tan?tan??tan?.

1?tan?tan?1?cos2x 2¦Ð?sin2x?cos2x?1?2sin(2x?)?1

4(1)T=¦Ð

¦Ð3¦Ð5¦Ð,¼´x?k¦Ð?,(k?Z)ʱ, (2)µ±2x??2k¦Ð?428ymin??2?1,

2.±¶½Ç¹«Ê½

sin2¦Á= 2sin¦Ácos¦Â£»

cos2¦Á= cos2¦Á-sin2¦Á =1-2 sin2¦Á =2 cos2¦Á-1£»

tan2??

2tan?.

1?tan2? 19

3.½µÃݹ«Ê½ sin2¦Á=

1?cos2?cos2£»cos2¦Á=2??12. 4.¸¨Öú½Ç¹«Ê½ asin¦Á+ bcos¦Á=a2?b2sin(???)£»tan??ba. £¨¶þ£©»ù´¡¹ý¹Ø 1.sinx sin?2 22

2.32 272 3. 9 4.?2 5. -sin4-cos4 6.?1665 ¡¾¿ÎÌõäÀý̽¾¿¡¿ [±äʽѵÁ·Ò»] 1.??????56???2,?0???6?3 ,?sin(??6)?13 ?cos??cos????????????123?56???6?? ?262.¡ßcosA=51213>0£¬¡àAΪÈñ½Ç ¡àsinA=13

ÓÖ¡ßsinA>sinB,¡àA>B ¡àcosB=45 ¡àBҲΪÈñ½Ç

sinC=sin[¦Ð?(A?B)]?sin(A?B)?124536313?5?13?5?65[±äʽѵÁ·¶þ]

sin10¡ãsin30¡ãsin50¡ãsin70¡ã=12cos20?cos40?cos80?=116 [±äʽѵÁ·Èý]

¡ßsin¦È+cos¦È=3?12£¬sin¦Ècos¦È=m2 ¡àsin?cos?sin?cos?1?cot??1?tan?=? 1?cos?sin?1?sin?cos?=sin2?cos2sin??cos???cos??sin?

=

sin2??cos2?sin??cos??sin??cos??3?12

[±äʽѵÁ·ËÄ]

?sin??35,?ΪÈñ½Ç£¬?cos??45 ?tan??1727,?ΪÈñ½Ç£¬?cos??10,sin?210 ÓÖ??,?ΪÈñ½Ç£¬?0??????£¬ ?cos??????22£¬ ??????4 £¨¶þ£©¾­µä¿¼Ìâ

1.D 2.3?178 3.C

£¨Èý£©ÑÝÁ··´À¡ 1£®153?834 2.32 3.?132 4.?4 5.B 6.C 7.(1)T??;(2)ymax?12 ¿ÎºóÍØÕ¹ÑµÁ· Ò»¡¢Ñ¡ÔñÌâ

1.C 2.B 3.D 4.A 5.A 6.C 7.A 8.B

¶þ¡¢Ìî¿ÕÌâ

9£®

54 10.116 11.?2cosx 12.?12

13.6365 14.2

Èý¡¢½â´ðÌâ

15£®(1)sinx?cosx??75 ;(2)95 16.ÓÉÌâÒ⣬֪cos???45£¬¡àcos2??725

ÓÖ¡ß450????540?£¬¡àsin??35

¡àsin??2¦Ð?3?????43?3??10 17.£¨1£©sin???55£¬??(?¦Ð2,0) ¡àcos??255 ¡àtan???12 ?1?1 ¡àtan(???)?23??1 1?(?12)(?13)¡ß?¦Ð2???0,?¦Ð2???0¡à?¦Ð?????0¡à?????¦Ð4£¨2£©¡ß?????¦Ð4 ¡à???¦Ð4??

¡à2sin(¦Ð4??)?cos(¦Ð4??)=

2(sin¦Ð4cos??cos¦Ð4sin?)?cos(¦Ð¦Ð4?4??)

=2(22cos??22sin?)?cos?=2cos??sin?=5

µÚÎå½Ú ÕýÏÒ¡¢ÓàÏÒ¶¨Àí

£¨Ò»£©ÖªÊ¶»Ø¹Ë 1£®Èý½ÇÐÎABCÖУº

¢ÙA+B+C=¦Ð£¬sin(A+B)=sinC£»cos£¨B+C£©= -cosC£» ¢Úa+b>c,a-b

¢Ûa>b?A>B?sinA>sinB. 2.ÕýÏÒ¶¨Àí£º

absinA?sinB?csinC 3.ÓàÏÒ¶¨Àía2?b2?c2?2bccosA

b2?c2?a2?2accosB c2?a2?b2?2abcosC

4.¶¨ÀíµÄ±äÐΣº ¢ÙÕýÏÒ¶¨Àí£º

a=2RsinA, b=2RsinB, c=2RsinC »ò sinA : sinB : sinC = a : b : c

20