高考数学一轮总复习课时质量评价-20.pdf

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1 . 5, 7, 8  !"#!$%&( )
A. 90° B. 120°
C. 135° D. 150°
2 . 1234567 8 2 a ~ 2 c = b , 9:;=( )
A 3 3 B
- 8 - 7
c 7 D 8
- is - n
3 . ZXRa'56 A, B, C BCDE a, b, cr 78 b = c f a =2Z>2(1 Gsin A), K A = ( )
3n n
A - T B - 3
C n D n
- 4 - 6
4 . 123O 5 6P  Q B, C RBCDa, b, c , T 2&acos C-3bcos ; 3 c c o s
B , KC  " $  ( )
5 . XYZ
12 /a'56\]^_`aE
A . T a cos A = b cos B , K23bcd
B . T a=40, 6=20, Q25° , K23ghijk
C . T % E m 6K sin J>cos B
D . T cos 23+cos 28Gcos 2 C < 1 , K238Cm
6 . 78249pP4 B, C BCDa, b, a q r + + s = t u v K  8 =
7 . 1 5 6 BC=a, AB=cf N 4 8 C mxqr lg a-lg c=lg sin B = T g ,
K 2 3 { '  | E .
8 . 782/1O P  /!, B , pBCDa, b, c , 9:~a =
6qr€”6
= 2 , 1=30° ” ‚ i j ƒ . „…†ƒ‡ˆ‰Š‹Œ
9 . 245pP36B, C BCD& 9 c , 78cos[Q + 6
+cos[
‘
2
T’†p= 4 “,”•–23bE— . : .
10 . 2022 ˜™š›
1238c56sin 2 C = & s i n C.
  N Q
2
T 6 = 6 , x238pœ6ž6 623Ÿ .
B ¡¢£b
11 . XYZ
12/1¤ 5 6¥¦\]€k 6§5i†kE
A. b = 7 , p= 3, 830° B. 6=5, c=4, 8=45°
C. a=6, b=34 , ^=60° I
. a=20, 6=30, 4=30°
12 . XYZ
Bª2/«¬i­\®¯6§5`aE
A . T cos A=cos B , K248pcd
B .  A > B , K sin J>sin B
C .  a=8, c = 1 0 , °=60° , ±!²³€2´µijƒ
D . T sin
+ sin'ZYsin'a K E ·   
1 3 . XYZ
¸23{'P4 B, C BCDa, b, c ,  a = 2 & , 6K  8
¹E
A. 15° B. 30°
C. 45° D. 75°
14 . 12 48C56P 4 B, C BCD a, b, c , x a cos 8GcGg=0, a = \bct b
> c t K:= .
15 . 124%?5636B, 6'RBCDa, b, ct 78sin 3+ sin 8 = ¬sin C , "#4BC
 9, 23gœ3sin C , K p= , cos C = .
16 . 2022 ˜¼½¾
78248pP36B , pBCDa, b, c , x b s i n U c c o s : .
‚ 3
À
(2)T 6 = 4 , 238p !"‹.
17. (2022 , Á¾)1Ã(26Gc)cos A = a cos C , Äa sin B = # b cos A , Åa cos C
+ J 3 c sin / = b + c , ƃ€5ÇY†ƒ6ÈÉ1\œÊZ56ËÌÍkÎ.
ÊZ–782 49CP4, B, C RBCDa, b, c , q r , x c=4, b=
3.
(1)23%œ¬
(2)T p a '56/ÏÐÑҋ.
ӖTYÔXƒ€CDÕÎ6Ö׆ƒkÎØC.

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25 + 64 - 49
1. B kٖ9 , K!"#!$&E180° - 8 , ÚÑÒÐۍÜ6COS 8 = 2x5x8
= –6ß Ü 9=60° , K!"#!$&E180° - 0 = 120p6àYB.
2. B kٖ¥¦ÑÒÐÛÜcos 600 =
 áâÜ36†10ã + 7c2 = 0 , K
(3aG7c) (aGcaG2 c = ä0 , i aåc , R¹–= ¬6àY B.
3. C kٖÚÑÒÐÛÜa=l)-\-c(2bc cos 4 = 2 æ†2b%os1 = 2 æ(1Gcos A). ç
a =2Z>2(1 Gsin A), R¹ cos J=sin A . ç cos 3W 0 , R¹ tan AAE. (0, n ), R¹ A
= ¬.àYC.
4. A kٖç 2 4 a cos C(3b cos C=3c cos B , R¹ Z^sin A cos CG3sin B cos
6^=3sin C cos B , R¹ 2j5sin A ˜ cos C=3sin (C+/!)=3sin A . ç36 (0, n ),
R ¹ sin 4#0, c o s ì í î CW (0, n ), R ¹ ï 6àYA.
5. BC kٖBªA , Ú`ÒÐۍÜsin3cos 1=sin 8 cos 8 , R¹sin 24=sin 28 : .
R¹4= 8 ð 4+Q90° , R¹2/1%cdð— 6à A ñò¬B ª B, a sin 8=
40sin25° <40sin 30° = 4 0 X ¬= 2 0 , Œ a s i n ^ V b V a , R¹2/%hijk6à B `a¬
BªC , ç  a 'Em 6R¹3+õ>– g|J^>J>~ZC>0,Ú`ÒøŠùú³
ûüýþÜsin O s i n g-B)=cos 8 , à C `a–BªD , ÿ

1
2sin2J + l 2sin2i?l+2sin26'<l, sinM+sin*sin?) +!">0 , %&
c o s O O ,  C +,-./01 4 % +,456 D 89.
6. I ;<=> + ? + @ = - + % & B = # + 2  GH
cos B =
q +7 ~ - = ^ J (0, H , ;
8=g.
Zac / 0
7 . QRS45 ;<=FT Ulg alg c=lg sin B = - lg
>+ 1g alg c=lg p lg a =lg ( $ ) ” = lg y,
%& lg ?=lg sin B=lg 4 ,
Zg=sin 4.
>+N H \,%&NQ45° , cos 8 = 0.
>+`=4,
% & a =b 
6 = 2-\~c-2ac c cos B=\c -be(2 4 ^-c 4 ^ = \c -\~c(c = ^ c ,
%&a = d= g d , %&a+ d =/
>f45g5h\QRS45.
8. (1,2)ij!k ;<=F l  G H
m =n % & sin 6 = o = ! qrstu1gv
wxyz J { | = 2 , % & 1<{}~+(1, 2)ij!k.
9. (1);=F€U
sin+cosg= 1 
BP cosZ cos4+==0.
%&(cos4 - …) =0, cos A=\.
F†0V/1V n , 6g='
(2)ˆ0=FlGH‰€Utu
sin 8sin C = Šsin A.
F(1)U 6 + C - ‹,%& sin 8(sin( T - ^)=ysin g , :sin 6- Ž os B = 6,
%& s i n (8-7)==
. . 2n n n lf n
F†0 V 8 V 8!5 = - 6 8 =  : .
‘14’\S45.
10.;=“1”>+ sin 2C=y/3sin C,
%& 2sin C cos U j S s i n C9
E sin C ^ O , %& 2cos C = # ,
%& cos C = 4 , >+ OVCVJI,
%&C=\.
(2)>+1g˜™š+6^3,
%&gab sin C=6;,
E 6=6, C=g,
%&;X a X 6 X == 6 Ÿ,
%&a = A # ,
X7 r 02 \3\ \*\ \5\ + 1,2
E cos C = Å z-7
4>/32 + 6 -
%&?
2 X 45/3 x 6 '
% & (7=2^3,
%& a + b + c = 6 + 6 4 ,
%&1g ¡¢+6+ 6 £
B ¤¥¦§¨©ª
11. B C ;<=«†A , >+b = 7 , = 3, 6^30° , %&FlGH
sin 4 !
=g
3
= % > 1 , ­;…«†B , >+g= 5 . c=4, 8=45° , %&FlGH
sin 6 ^ ®> ? x 2
5
= ¯ < 1 , J c V 8 , w!;…«†C , >+a=6, 6 = 3 " , ±=60° , %&FlGH
sing =² ³ =´ ^=1, J=90° , f µ = 30w!;…«†D , >+a = 2 0 , |=30, A
b ¶
= 30° , %&FlGH
sin 8 = * 3 0 · = ¸ , J % & 8 wxy¹wx
20
;.
12. A B D ;<=«†A ,  cos4=cos B , z 4 = 8 %&1 /a'+QR456lº…«
† B , qg> 6 , z a > 6 , F l  G H ¦ =n =2»
2" sin G>2" sin 6 ,  sin
sin 8 ½¾6lº…« † C , F   G H
¿ w
!;689…« † D , q +sin2^<sin26 zÀÁlGH
a+ dV1, cosC=
 à - <0 , % & +Ä%&1g&\Ä456lº. : .
Ç A B ;<:cos 8 = - = A = B = C + È É Ê Ë = Ì Ã J Í Ã * = Ã
= ”6µQν¾% & cos [Ð1], 8`(0° , 30° ] , % & ABÒÓlºC D ÒÓ8
9 .6 Ò AB.
14 . 2 ;<=F a cos 8c== 0 ‰lGH
singcos 8sin C!^ ^ = 0 .>+sin
C=sin U+/0 =sin A cos 8+cos gsin B , %&!Î^!cos A sin 6 = 0 .>+ sin D 0,
%&cos / = g ,  J = y . FGH
M =^)c= S + G + b e ,  2|J 5 A + 2 / = 0 , E b
> c , %&=2.
15 . 4 … ;<=>+sin 4+sin Q ^ s i n C , %&FlGH
a + b =
>+1 Ô ¡¢+9 , %&a + 4 + c = c + ^ = 9 , ;
Õ /1 % ™šQ†3sinC,%&Ö
sin 6^=3sin C ×H
a A a + b = ? = 5 , 6ØÙ 2 6=' ;
Ø = 4 ÚØ` = 9=%& cos C
_a2 + b2-c2_ 1
2ab !-
16 . ;=(1)FlGH‰ b sin C= c cos(B-g), U sin B sin C=sin C cos (“- ),
>+ sin Ì 0 , %& sin 4 c o s (8-g)=#cos 4 + =sin B ,  sin (8-9=0,
>+8W(0, n ) , %&4 2
(2)FGHUlH= a + c - 2 a c cos B,
%& 16=+ 1 Þ = (a+c)-3ac2 (a+c)?3 , (c?+ c)2 (a+ d 2,
%&(a+c)2W64, a + c W 8 , ÃJÍÃa = c = 4 µQν¾
%&1gv¡¢+a + 6 + e W 8 + 4 = 1 2 ,
61gá¡¢âã¹+12.
17 . ;=(1)qÒä=>+(2bc)cos A = a cos 3
FlGH
(2sin 8sin 6)cos J=sin A cos C ,  2sin B cos J=sin C cos J+sin
A cos 3
%& 2sin B cos /f=sin B.
>+0 V 8 V n ,
%&s i n I 0,

cos J=2>
>+0 V gV n , 6 4=g.
qÒæ : .
a sin B=