LTUR Q X 01 LTUR LTUR K 6 5, 6, 6, 7, 8, 9, 9, 9, 10, b= =: :=8.5 a+b= cm , = =: 7 := a+b+c 0 =1 a+b+

Transcription

1 우공비 중등 수학 (하) 특강편 SLUTIN LTUR K WRK K 0

2 LTUR Q X 01 LTUR LTUR K 6 5, 6, 6, 7, 8, 9, 9, 9, 10, b= =: :=8.5 a+b= cm , = =: 7 := a+b+c 0 =1 a+b+c= =: 5 :=11. 5 LTUR K 7~9 0 10_7+15_ = =600 = 18<a 0 a+0 a+0 19< 0. a+8+b+c+1 = =8 5 8+=0 = aæ18 19 a 18 a= aæ a <90 a< a<9 a 90, 91, 9, _91=910( ) 910-5=905( ) 905 =90.5( ) , 8, 8, 9, 9, 9, 10, 10, 10, 10 a= 9+9 =: := = = = = SLUTIN

3 Q X 1 a= a=: 1ª0 :=9. 1,, 5, 8, 8, 50, 51, 5, 55, b= = =9 8 kg c=8 a-b+c=9.-9+8= LTUR LTUR K , 0, 5, -, ' LTUR =1.5 = = = =;1*0);=8 1,,,,,,, 5, 7, 9 + = = - = + 0. = LTUR K 11~1 01 0cm 160 cm =16-160= y=160+7= cm = y=167 0 (-)+(-5)++1++0=0 = 6 1-= (-1)+(-)++(-)+(-)+=0 = =;&; ;&; = = (-8) (-5) = = 5 =' 87 ' (-)+=0 =-1 5 -(-1)=5 (-1) (-) + = =6 5 ='6 5'6

4 LTUR Q X +(7-) = =: 6 :=6 6 7 (-) +(1-) + + +(-6) = =0, (-)(-)=0 = = 7 10 (æ) ( ) = _+1_8+1_9+16_6+18_ 0 =;; 0º;;=1(æ) =; 0;{(-) _+(-) _8+0 _9 + _6+ _} 07 y z w 10 +y+z+w =10 +y+z+w=0 (+)+(y+)+(z+)+(w+) = +y+z+w+8 8 = = =1 y z w (-10) +(y-10) +(z-10) +(w-10) = 1 = {(+-1) +(y+-1) +(z+-1) +(w+-1) } 1 = {(-10) +(y-10) +(z-10) +(w-10) } =. +, y+, z+, w =;; 0 ;;=5.6 =' 5.6(æ) ( ) ( ) = =: 0º:= _+15_7+17_11+19_5+1_ 0 =; 0;{(-) _+(-) _7+0 _11 + _5+ _} =: 0º:=: : : : a+b+c+8 08 =8 a+b+c= yy (a-8) +(b-8) +(c-8) = a +b +c -16(a+b+c)+19=1 yy a +b +c -16_+19=1 a +b +c =0. _ 1 ( ) ( ) a b 0 ++a+b+=0 a+b=11 yy 55_+65_+75_a+85_b+95_ = a+17b=179 yy a=, b=7 5+1+m+n 09 =8 m+n=15 yy (5-8) +(1-8) +(m-8) +(n-8) =;; ;; m +n -16(m+n)+15=0 yy m +n -16_15+15=0 m +n =117 (m+n) =m +n +mn 5=117+mn mn=5 5 =; 0;{(-0) _+(-10) _ +0 _+10 _7+0 _} =;; ;$0);º;;= _5 +0_ 0 =: 0º:=17 SLUTIN

5 Q X 1 10_5+0_9 0 = = 0 0 ' 69 ' 69 = a b a<b = =7 5 (-) +0 +(-) +1 + = 5 =6 =' = = (-1) +(-) = 5 =.6 ='.6 > >. (a+)+(b+)+(c+)+(d+) 01 =7 (a+b+c+d)+1=8 a+b+c+d=8 a, b, c, d a+b+c+d =;*;= _5=5 5+ =89 =99 6 0, 8 0_=0 15_8= = = (-)+5+a+8+(-1)+6+ 0 = 7 19+a=8 a=9 -, -1,, 5, 6, 8, 9 5 LTUR LTUR K 1~ kg =7, y=1, z= '5m 1 ' 0 kg ;; º;; cm 6. a<b a=16, b>16 bæ = = <b< kg 51+ =5 =5 5 kg 5 5 kg 5 kg a= <b<19 16+b =17 b=18 a+b= 5

6 LTUR Q X 07 5_+6_5+7_6+8_7+9_ 08 = = = = 09, y, z , y, z 0 =0, y=0 0<z< 15, 0, 0, 0, z,,, 1 0+z =1 z= +y+z=0+0+= = = = = = z 0 =0 zæ 0+ = =1.5 0<z< (-1) +1 +(--1) = =1 -+11=0, (-7)(-16)=0 =7 =16 <z =7, z=16 =7, y=1, z= y+z+w=80 y z w +y+z+w =: º:=0 y z w (-0) +(y-0) +(z-0) +(w-0) = +y +z +w -0(+y+z+w)+1600=16 +y +z +w -0_ =16 +y +z +w =1616 +y +z +w 1616 = = a+=0 a=11 5_1+15_5+5_9+5_11+5_ b= 0 b=: 0º:=9 c=; 0;{(-) _1+(-1) _5+(-) _9 +6 _11+16 _} 11 1+(-)+++=0 = (-)=1 1 1 y=1 = +1+z =1 z=- 0 = - = - c=;:#!0@:);=10 a-b+c= _16+_1 0 =5.6 = 6 SLUTIN

7 Q X 18 7 æ (-1) +(-1) '6 = 6 æ (-5) æ (-) + + +(-) ='5 =' = = = a a y a º a +a +y+a º =10 10 a +a +y+a º= ;!;a ;!;a y ;!;a º {;!;a +;!;a +y+;!;a º}_;1 0; LTUR =; 0;(a +a +y+a º) =;; º0º;;=;; º;;(cm) 19 9 y z 9 =9, y= z =7 z=10 5 (-5) +(-) = 5 =: 5 := d m (d+100)m, (d+00)m, (d+00)m (d+00)+(d+00)+(d+100)+d = d+600 = =d+150(m) =;!;{ (-50) +(-150) } =;:%:)):):);=1500 =50'5(m) 1 50 kg 60 kg 0-(+++)=8 = =;:!!0):);=55(kg) 50'5 m 5_+5_+55_8+65_+75_ 0 d+00-(d+150) =150(m),, 50 m, -50 m, -150 m. ;; º;; cm (-)+y+(-1)=0 +y=5 yy (-1) (-) +y +(-1) = 6 +y =1 yy (+y) = +y +y 5 =1+y y= a+8 =10 a=9 9+b++16 =10 b=11 (-1) +1 +(-6) +6 =18.5 ' (-1) +(-) =.5 '.5 > =; 0;{(-0) _+(-10) _+0 _8 =;:@$0):);= _+0 _} =' 10=' 0(kg) ' 0 kg 7

8 LTUR Q X 0 LTUR 06 = =øπ1 +1 =' = =øπ(') +1 = = =øπ() +1 = =øπ +1 ='5 LTUR K cm =øπ +() =6 =øπ6 - ='5 Â =, S= =" 7-5 ='6(cm) =;!;_5_'6=5'6(cm ) 0 (+) = +8 ++= +6 =60 =15 LTUR K 19~1 5'6cm 0 =" 1-10 =' 11(cm) =" 8 -(' 11) ='5(cm) '5cm = + =øπ - =, = ' =' ' (RS ) 08 =9 =" 15-9 =1 = =16-1= 09, ' ' =7 cm =' =;!;_(11-7)=(cm) =øπ6 - ='(cm) =9 cm =" (') +9 =' 11(cm) 9 6`cm 7`cm ' 11`cm 6`cm ' 11 cm 0 = cm =6 -(+) =('6) - -- =- =8 = 05 =øπ + =' =øπ(') + = =øπ() + = F F =øπ + ='5 FG G =øπ('5) + ='6 cm '6 F=;!; - F =;!; 10 =øπ8 +6 =10(cm) ;!; =;!;_10 ;!; =50(cm ) 11 =6-8=16(cm ) =(cm) =' 8=(cm) =;!; =8(cm ) 50 cm 8 cm 8 SLUTIN

9 Q X 1 = yy F =, =F, = F F SS F K F= JF=;!; FKJ = = F= JF F K J I G yy yy =90 + = F F = +(6-) 1=0 =: º: : º: cm 17 =;!; =(cm) = cm = = cm =(10-)cm =(10-) + 0=116 =: 5ª: LTUR =;!; FKJ 1 =9-=6(cm) =6 + =5 F GF G FG FG= =5(cm ) 1 Q =R =9 cm Q Q =" 15-9 =1(cm) PQ =1-9=(cm) PQ =QR =RS =SP PQRS PQRS= =9(cm ) 9cm =F =GF =G, F = F = =90 90 FG.. 18 = = = cm =(8-)cm =(8-) + 16=80 =5 =" 8 + ='5(cm) =;!; ='5(cm) =øπ5 -('5) ='5(cm) '5cm =" 8 + ='5(cm) =;!; ='5(cm) Fª F =F 8 '5= ='5(cm) 15 = =90 ;!;_ =6 =5 =" 5-6 =(cm) =;!;_(+6)_(+6) =50(cm ) + = + =90 =90 0 LTUR LTUR K 1 16 = =10 cm =" 10-6 =8(cm) =10-8=(cm) F = cm F =F = cm F =(6-)cm ;; 5 ;; '6 80 8p cm cm 9

10 LTUR Q X () = + =(') 6 +8 = =1 0 1 =6 +(6) 1 ;!;_6_6=18 0 +(+) =(+) --1=0, (+)(-6)=0 =6 ( >0) 0 = m =1-(5+)=7-(m) =90 +(7-) =5, -7+1=0 (-)(-)=0 = ( > ) LTUR K ~5 m. 08 <9+1 1 <1 <9 +1 0< <15 1 <15 1< +9 < 1 1 < +9 >'7 '7< 1 '7< <15 8, 9, 10, 11, 1, 1, =k k>0 =k =" k +(k) ='5k '5k_=k_k k=' 15 =' 15, =' 15 =;!;_' 15_' 15=15 05 cm cm =" 6 +8 =10 8 cm =" 8-6 ='7 '7 cm, 10 cm 06 k, k, k k>0 (k) +(k) <(k) k, k, 5k k>0 (k) +(k) =(5k) k, 5k, 6k k>0 (k) +(5k) >(6k) 5k, 5k, 8k k>0 (5k) +(5k) <(8k) 5k, 1k, 1k k>0 (5k) +(1k) =(1k) 07 = +() =6 y =17-8 =5 z =(9') z =81 5>6+81 y > +z, y, z a, b, c(cæa, cæb) c <a +b c =a +b c >a +b M MN N MN =;!; =8, y=15, z=9 9-8<15<9+8, y, z. 10 =" + =5 _= _5 =: 5 : = _5 =;5(; =;!;_: 5 :_;5(;=;%5$; 11 =8 +6 =100 + = = +('5) - =0 ;%5$; 1 =;!; =;!;_8= + = + = +8 =80 1 (') +('5) = + =9 =øπ9-() ='6 10 SLUTIN

11 Q X 1 = + = + =('6) +, =11 ='ß11( >0) 15 () + =('5) +(+1) =6 = 16 S +S =15p+10p=5p(cm ) 5p cm ;!;_p_{ }=5p, =00 =10'(cm)( >0)... LTUR K 7~9 01 F= =8 +15 =89(cm ) 0 cm cm _=, =16 = ( >0) 8cm cm " 8 + ='5(cm) LTUR 17 =k, =k(k>0) k k S =;!;_p_{ }= p 8 k k S =;!;_p_{ }= p 8 S =S +S = k p k k k S S S = p p p 8 8 S S S =1 18 =('6) =(+) +-96=0, (+1)(-8)=0 =8 ( >0) =øπ1 -('6) = = =;!;_'6_ 1 =' ' a 'a 0 = =8 cm = = cm =" 8 - =(cm) =_ =16(cm ) 0 cm '=10 =5' _5'=0'(cm) 05 r cm pr =16p r =16 r= ( r>0) 16cm 8cm cm '=8 =' 8 cm 'cm 05 LTUR LTUR K ' ' 8' _ = _ = _ F (R ) a a 06 =" 8-6 ='7(cm) 6_'7= _8 '7 = (cm) 07 =" + =5(cm) = _5 =;5(;(cm) F = =;5(; cm F =5-_;5(;=;5&;(cm) 08 a cm a =9, a =6 a=6( a>0) 11

12 LTUR Q X 09 = _1=6(cm) = _(6) =7(cm ) 7 cm a a 15 = =6-= _8= =;!; = 10 G =;!; =6(cm) a cm a=6 a= = _() =1(cm ) 11 P = P+ P _8 Q P 8 R 1 G G = 1. =øπ +() =' (8-) '5 17 = 15 =1- =15-1 =1 -(1-) 8=5 =9 =" 15-9 =1 '7 =;!;_1_1=8 8 1 =;!;_8_PQ +;!;_8_PR 16=(PQ +PR ) PQ +PR = 1 M = M =a cm 75=_ a a =100 a=10 ( a>0) 5_10=50(cm) M 50 cm 18 = cm =(10-)cm =6 - =('6) -(10-) 0=0 = =" 6 - ='(cm) M =5 cm M =5-=(cm) M M =ø(π') + =' 1(cm) 06 LTUR LTUR K 0 1 6cm 6 6_{ _6 }=5(cm ) 1 7`cm = =5(cm) =" 7-5 ='6(cm) =;!;_10_'6 =10'6(cm ) 10`cm 7`cm 5, 5, ' 0, 60, =, y=' =, y=6 =, y= '5 5 '5 5' ' ' 1 LTUR K 1~ 01 =1 =(cm) =1 ' ='6(cm) 1 SLUTIN

13 Q X 0 16 = =8 8 y= 1 y= +y=1 0 = =5 ' =' 1 =, = = =6+=10 =" 10 + =' 9 0 = = cm (+) = 1 =+, (-1)= = -1 = `cm 8 = 7`cm = (cm) =7_=8 (cm ) _(8-) 8 = 15 ' 9 =5 =1 ' =' +' = = 6 = 1 = = = =+ ;!;_(+)_=;(;(+) 5æ 5æ ;(;(+) =1 1 (, y ), (, y ) øπ( - ) +(y -y ) Q1 y. y 0. n 180 _(n-) n y=a(-p) +q (p, q) 08 ' 6`cm r`cm ' r cm ' =(r+6)cm, ' =(6-r)cm ' (r+6) (6-r)= 1 r+6=1-r r=6 r= ' = cm =1 =(cm) ;!;_(+6)_=16(cm ) 09 " {-1-(-5)} + (0-) =5 " {1-(-)} + {-(-)} =' 65 " +7 =' 5 " (-0) + (-1-) =' " (6-) +(-) ='5 10 PQ =" (5-1) + {a-(-)} =' 1 a +a-=0, (a+8)(a-)=0 a= ( a>0) 16 cm 11 (a, 0) " (a-) + {0-(-)} =" {a-(-)} +(0-5) (a-) +=(a+) +5 1a=-8 a=- (-, 0) (-, 0) 1 y=+ =, y=a a=_+=7 (, 7), (-1, 1) =" (-1-) +(1-7) ='5 1 y=- +6+=-(-1) +7 y=;!; ++=;!;(+) -5 (1, 7), (-, -5) " (--1) +(-5-7) =1 1 LTUR 1

14 LTUR Q X 1 =" (8-) + (--) =' 1 =" (6-8) +{ --(-)} =' =" (6-) +(--) =' 1 = < + <90 = 15 ="{ --(-)} +{ -- (-5)} =' 10 ="{ -(-)} +{ 0- (-)} =' 10 =" (--) +(-5-0) =5' = + =90 a a 07 LTUR LTUR K 1 7 5' 5 6'6 ' LTUR K 5~7 16 =;!;_' 10_' 10=10 `cm P 1`cm 6`cm ' ' P +P =P +P' æ' =" (+1) +6 ='5 (cm) P +P '5 cm '5 cm. 01 " + +5 =' 10 =9 =7( >0) 0 k cm, k cm, 5k cm k>0 " k +(k) +(5k) =' 0 k' 0=' 0 k= cm cm 10 cm 10=80(cm ) 80 cm 17 ' '(, -) P +P =P +'P æ' =" {-(-)} + (--1) =' P +P ' 18 ' ' ' 8 +F +F =' +F +F' F æ'' ' =" (++) +8 =10 +F +F y - 1 P ' (a, b) (a, -b) 0 cm " = =10800 =150 =15'6( >0) 15'6 cm 15'6cm 0 a cm 6a =150 a=5 ( a>0) _5=5 (cm) 05 a a='6 a=' F ='_'= F=;!; '=' ' 06 M =MG =GN =N =" + ='5(cm) MGN 1 SLUTIN

15 Q X G = cm, MN =F ='cm MGN=;!;_'_=8'6 (cm ) 07 r cm pr =108p r=( r>0) 6 cm a cm a=6 a=6 a, b ;!;ab a '6 = a ' = a 1 =øπ('5) -π(') =6' MN=;!;_'_6'= 1 a cm _ a =1 a =1 a=( a>0) '6 = _=' LTUR 08 -F ;!;_{;!;_6_6}_6=6(cm ) ' y= _() ='6 1 +y = F 6'cm F= _(6') =18 (cm ) -F ;!;_18_P =6 P 6 P =6 P = (cm) cm 1 M = _6=(cm) '6 = _6='6(cm) M = 1 ' = _6 =18'(cm ) 1 09 F =" +6 =' 1 (cm) P =;!; F =' 1 (cm) P P =øπ6 +(' 1 ) =7(cm) 6' 1 7_I =' 1 _6 I = (cm) 7 6' 1 7 cm P _I =P _ 1 =;!; =;!;_{ _'6}='(cm) '6 = _'6= (cm) =;!;_'_=' (cm ) 10 FR FGR P FR =" + ='5 (cm) QFR QR =øπ('5) + QR ='6 (cm) RP =PQ ='6cm Q F R `cm G PQR _('6) =6 (cm ) = 1 = 15 =;#; =;#;_=6(cm) 'cm a cm a=6 a=1 ' 1 _1 =1'(cm ) 1' cm 11 M =N =" +8 ='5 MN =" + =' MN M =;!; MN =' Â5 Â5 M Â N MN MN MN. 16 N N =N = _10 N =5(cm) N N =N M =M MN M 10`cm N 15

16 LTUR Q X M =;!; =5(cm) MN MN =øπ(5) -5 =5' (cm) N MN =5 5' N MN = ' 6' G F 6 17 P =Q = _1=6 (cm) M N MN MN =;!; LTUR K 9~1 PQ =;!; =6 (cm) PQ =øπ(6) - =' 11 (cm) PQ=;!;_6_' 11 PQ=9' 11 (cm ) 6Â`cm 6Â`cm P 6`cm Q 9' 11 cm 01 =;!; =;!;_8' =' (cm) =øπ1 -(') ='7 (cm) =;!;_8'_'7=16' 1 (cm ) 8`cm 1`cm 8`cm 18 a cm M = _a M =a(cm) M =;!; =a(cm) M 0 =;!; =;!;_1 =6(cm) =" 10-6 =8(cm) 10`cm 6Â`cm M =øπ(a) -a ='a(cm) M 'cm ;!;_(6') _8=19(cm ) 8 cm, 19 cm ;!;_a_'a=' a = a= a>0 cm 0 Â10Ề cm 8`cm = =" 8 -(' 10) ='6(cm) =" (' 10) -('6) =(cm) ;!;_('6) _=18(cm ) 18 cm 08 LTUR LTUR K 8 1 6' ' ' 6' 6' 18'p 0 `cm =;!; =;!;_' `cm `cm ' M = (cm) ' ' =æ -{ }= (cm) 16 SLUTIN

17 Q X ' _{;!;_ _ }=9' (cm ) 05 =øπ('6) -6 =' 15 (cm) ;!;_p_6 _' 15=' 15p(cm ) ' 15pcm p cm ;!;_p_5 _ =100p =1(cm) =" 5 +1 =1(cm) + =1+1=5(cm) 5 cm 07 r cm r cm " (r) -r =r(cm) 9pcm ;!;_p_r _r=9p r =7 r= 08 r cm 10 p_6_ =pr r= 60 " 6 - ='(cm) 09 ' =8' =8(cm) r cm 90 p_8_ =pr r= 60 " 8 - =' 15(cm) 8' 15 ;!;_p_ _' 15= p(cm ) 8' 15 p cm 10 =øπ(' 55) + =8(cm) p_8_ =p_ = =1 =(cm) = = (cm) =M.. 0, 60, 90 1: : p =p_ = =;!;_p_ _= p(cm ) 1 =" 9-6 ='5(cm) p_('5) =5p(cm ) 5p cm 1 r cm pr=p r=1 " 15-1 =9(cm) 1 =" 10-6 r`cm M 10`cm =8(cm) rcm =8-r(cm) M Mª (8-r) 10=r 6 10r=8-6r 6`cm r= cm 15 ' 5 ' ' =" (++5) +5 =1 F 5 ' 16 ' =10p cm ' 10π`cm ' 6π`cm =" (10p) -(6p) =8p(cm) ' r cm pr=8p r= cm 17 0æ 6`cm M = _6 M =(cm) M M M=90 M =øπ() +6 ='7(cm) 15`cm r`cm LTUR 17

18 LTUR Q X 18 p_1_ =p_ =10 60 ' ' 1`cm ' 1 = =6(cm) ' = =1(cm) LTUR K ~ cm 0 cm cm cm 16 cm ' cm 1 +'5 '6 cm 10'cm ' ' =' a, b, c(cæa, cæb) c <a +b c =a +b c >a +b = _ 0 I=0-=16(cm ) =(cm) 0 =' 58 (cm) =øπ(' 58) - =7(cm) F =7-=(cm) FG FG= =16(cm ) cm 05 F = 15`cm =15 cm F `cm `cm 15`cm 9`cm F F =" 15-9 {9-}`cm F =1(cm) F =15-1=(cm) F = = cm =(9-)cm F (9-) + = 18=90 =5 06 > + >90 07 =øπ() -6 =(cm) () =6_ =(cm) =;!;_8_=8(cm ) 8 cm 01 =" 10-6 =8(cm) =" 17-8 =15(cm) 0 =;!;_(10-6) =(cm) =" - =(cm) =;!;_(6+10)_ =16(cm ) `cm 6`cm 10`cm 16 cm = km. 000 m 60_ P P +P =P +P =100+P, P =900 P =0(m)( P >0) km 0_60_60 = S S +S = S +S = S 8 S 1 + S = =8_1= SLUTIN

19 Q X 10 acm a =9, a =6 a=6 a>0 = _6= (cm) G =;@; = (cm) 11 5cm = cm =(7-)cm cm 7cm =5 - =(') -(7-) 1= = =" 5 - =(cm) =;!;_7_=1(cm ) 1 ' =' 1 =(cm) = = y =1 y= +y= 1 =" 1-6 =6 (cm) = = cm = =6cm 6`cm 1`cm =øπ9 +(6) =' 1 (cm) 1 = cm = cm = =" + + =" +5 =90 ( +5)=() =5 =5 ( >0) =10(cm) 15 -G 56 ;!;_{;!;_8_8}_8= (cm ) Â cm `cm a a. 5, 5, ' 0, 60, 90 1 = =5 =P _ G= _(8') = (cm ) 56 ;!; I = 8 8 I = (cm) cm 16 a cm '6 a='6 a=9 ' ' ' _9 = (cm ) cm 1 17 =;!; =;!;_6'=' (cm) =øπ5 -(') ='7 (cm) ;!;_6 _'7=1'7 (cm ) 18 = 1 = (cm) ;!;_p_ _=9p(cm ) 19 =" 10-6 =8 =5 =8_;8#;= =" +6 ='5 0 =" 6 +8 =10(cm) 6 =P _10 P =;; 5 ;; (cm) Q =;; 5 ;; cm PQ =10-{_;; 5 ;;}=;; 5 ;; (cm) 6_8=P _10 P =;; 5 ;; (cm) 6`cm 5`cm 6`cm 8 '5 LTUR 19

20 LTUR Q X PQ= PQ =_{;!;_;; 5 ;;_;; 5 ;;} 6 = (cm ) 5 1 y= --=(-1) - P(1, -) --=0 (+1)(-)=0 =-1 = (-1, 0), (, 0) = P =øπ{1-(-1)} +π(--0) ='5 P =øπ(1-) +(--0) ='5 P +'5+'5 =+'5 =60 6 = = (cm) =;!;_8_=1 (cm ) cm +'5 6`cm r`cm '6 = _6='6(cm) =;@;_{ _6} =(cm) r cm =('6-r)cm r =('6-r) +() '6r=6 '6 '6 r= cm =_0 =90 =øπ =10'(cm) 6`cm 6 5 8`cm 10`cm 10`cm 0æ 0æ 0æ 75æ 75æ 10' cm = =60 = = LTUR 1 ;1!@; ;1 ; ;; 5 ;; ;1 ; ;1!@; ;1 ; '5 '5 ' 0 ;!; LTUR K 6 '5 =, y=' =, y= 01 =" 9-6 ='5 '5 sin=;@; cos= '5 '5 sin= tan= 0 = k, =k(k>0) =øπ(k) +k =k cos=, cos=;!; cos = _= cos '5 0 sin= =;@; ='5 =øπ('5) -('5) =5 5 5 sin_tan= _ =;6%; '5 '5 0 tan=;$; =" + =5 cos+sin=;5#;+;5$;=;5&; cos-sin=;5#;-;5$;=-;5!; LTUR K 7~9 cos+sin =;5&;_(-5)=-7 cos-sin 0 SLUTIN

21 Q X 05 17sin-15=0 sin=;1!7%; =" =8 tan=;; 8 ;; ;; 8 ;; 1 sin0 = cos0 = tan0 = ' cos_sin= _ = sin0 +cos0 = sin0 +tan0 = + 6 ' ' LTUR 06 =90 - = = 5 tan= =;; 5 ;; 5 =1 =" 1 +5 =1 1 6 = =-1+(-) = =0 (-1) =0 =;!; sina=;!; a= ==y y 5 =øπ5 +(5) =10 y 5Â 5 sin= =, siny=;1 0;=;!; 10 sin = _= siny 08 ª = =" 10-6 =8 sin=sin( )= =;5$; tan=tan( )= =;#; sin_tan=;5$;_;#;=;5#; ;5#; + =90 +=90 = =, = =90 ª 1 sin60 = = = sin5 = = ='6 6 1 cos0 = = = cos0 = = =8 15 = =8 ' cos5 = = =' 8 = =' ' tan= = ='-1 8+' '-1 ' 09 G =', = G G ' '6 cos= = = 10 M =N = _6= MN N =;!; MN = N =øπ() - =' M Â Â N a a a tana 8 16 tan0 = = =8 (cm) ' cos5 = = 8 ='6 (cm) = ='6 cm =;!;_'6_'6=8(cm ) 17 5-y+10=0 y=;%;+5 tana=;%; 8 cm 1

22 LTUR Q X 18 tan60 = y= +b 0=+b b=- y=- -y-=0 06 -y+=0 y=+ tana=1 a=5 cos5 _sin90 -cos90 _tan5 ' ' = _1-0_1= ' 07 sin 0 =0, cos 60 =;!;, tan 5 =1, 10 LTUR LTUR K ' LTUR K 51~5 01 tan= = = 1 0 tan= = = 1 =y siny= = = 1 0 cos50 = = 1 = - =1-cos50 0 cos5 (sin90 -sin0 ) ' ' = _{1-;!;}= 05 p=cos90 -cos0 _tan0 p=0- =-1 q=cos0 -cos0 _tan0 =1-0=1 p-q=- 0 <90 tan 0 90 sin cos 1. " a = a =[ -a(aæ0) -a(a<0) sin 60 = tan 70 >tan 5 =1 08 cos0 =, sin70 >sin60 = cos0 <sin70 sin60 =, cos50 <cos0 = sin60 >cos50 tan5 =1 cos80 <1 tan5 >cos cosæsin 0 60 ;!; cos 1 5 <90 tan>sin 10 0 <<90 0<sin<1 sin-1<0 =-(sin-1)+sin= <<90 0<cos<1 tan>1 cos+1>0 1-tan<0 =cos+1-cos-{-(1-tan)} =-tan -tan 1 0 <<5 sin<cos<1 cos-1<0 cos-sin>0 -(cos-1)+(cos-sin)=;!; 1-sin=;!; sin=;!; 0 <<5 =0 cos=cos0 = SLUTIN

23 Q X 1 = = sin8 =0.71 =8 tan7 =1.07 y=7 +y=95 15 cos87 =0.05 =87 sin89 = y=89 -y=85 tan(-y)=tan85 = cos =;1 0;=0.71 =7.1 sin =;1 0;= y= y= = =180 -( )= tan = =0.5 0 = = =1 = sin= = =1 =cos1 =0.757 = - = = = _. 0 =5cos7 =5_0.8=(cm) =5sin7 =5_0.6=(cm) ;!; 6=6(cm ) 0 =0tan =0_0.97 =9.1(m) 0+9.1=9.1(m) 0 =_50=100(m) =100sin5 =100_0.=0(m) 6 cm 9.1 m 0 m 05 Q Q = tan0 =100_ =00(m) PQ PQ =Q tan60 =00_=100(m) 06 =6sin60 =6_ = (cm) 6`cm 0`m æ 0`m 8`cm LTUR =6cos60 =6_;!;=(cm) 11 LTUR LTUR K 5 1 =5.7, y=8. 6 'ß1 h h 7(-1) LTUR K 55~57 01 sin70 = = sin70 =øπ + =8-=5(cm) =øπ() +5 ='ß1 (cm) 07 = =5 15æ Â`cm `cm 5æ ' =sin5 =_ =' (cm) ' =cos5 =_ =' (cm) ='+'=' (cm) =øπ(') +(') ='ß10(cm) 08 =6sin5 =6_ ='(cm) ' 75æ 5æ 6`cm

24 LTUR Q X ' = ='_ ='6(cm) sin60 09 æ =y sin60 = y = sin = = y = y 6 5 k= 6 y 5 6 =180 -(75 +5 ) =60 + =1 1 =h =htan60 =h 5æ =htan5 =h 5æ h+h=1 1 1 h= =6( -1) +1 1 =h =htan0 = h =htan5 =h h+h= h=_ =(-) =;!; (-)=(-) 0æ + 5æ 5æ 10 6`km =6sin5 5æ ' =6_ ='(km) 7Â`km ' =6cos5 =6_ ='(km) =7'-'='(km) =øπ(') +(') =5'(km) 5'km 11 =6sin60 =6_ =(m) =6cos60 =6_;!;=(m) 7`m =7-=(m) =øπ() + ='ß (m) 6`m 'ß m - =6 15 =h =htan5 =h =htan60 =h h-h=6 6 h= =(+1) =h cm =htan60 =h(cm) =htan0 h- h=6 (-) = h(cm) h=6 h=9 5æ 0æ 15æ 5æ 6 =;!;_6_9=7(cm ) 0æ 6Â`cm 0æ 7 cm 1 =8' cos5 ' =8'_ =8(m) 5æ 8Â`m ' =8'sin5 =8'_ =8(m) 8 = =8_=8(m) tan0 = + =8(1+ )(m) 0æ - = h h 17 = (m), = (m) tan0 tan55 h h - =500 tan0 tan55 18 =h m 0æ =htan0 = h(m) 5æ =htan5 =h(m) 5æ `m h+h= h=_ =11(-) + SLUTIN

25 Q X 1 LTUR 1 10' ' 15' LTUR K =180 -_75 =0 =;!;_8_8_sin0 =16(cm ) 0 ;!;_8_1_sin= sin= = = = + = + = =;!;_6 sin5 =;!;_6 =6'(cm ) 0 M =M =, N =, N = MN= - M- NM - N MN= =15 M =" +6 ='5 N =" +6 =' 10 ;!;_'5_' 10_sin =15 sin = ' LTUR K 59~61 ' 05 =6 6 1 sin=;1 ;=;!; =0 = = =. a, c ;!;acsin (0 < 90 ) M, N = =60 6 = = sin60 =;!; 1_sin 0 =;!; 1_;!; =1 06 =;!; '_sin( ) =;!; '_ =(cm ) 1 07 ;!;_6_8_sin(180 -)=1 sin(180 -)= =60 = = cm =sin0 =_;!;=(cm) =60 = =150 =;!; sin( ) =;!; ;!; =(cm ) 09 = + =;!; =_sin( )+;!; sin60 cm 7 = += = =1, = =1' tan5 sin5 = + =;!;_1_1'_sin0 +;!;_1_1 ='+7 ' Â 150æ '+7 LTUR 5

26 LTUR Q X = =5 8 8_{;!; sin5 } =8'(cm ) 1 = =5 8_ _sin5 =, ' = =' 1 = =60 = =;!;_16=(cm) `cm 8.. LTUR K 6~ ;5$; 'ß ('+'6)m ;!; 0 1 5cm + 15cm = sin60 =8(cm ) 01 = sin=;5{; 1 =6_10_sin60 =0(cm ) =;!; sin=;6{; sin =;6{;_;[%;=;6%; sin =;!;_0=15(cm ) 15 =6_8_sin60 =(cm ) M=;!; M=;!; M=;!;_=6(cm ) 16 0æ =180 -( )=5 =;!;_10 sin5 =60'(cm ) 17 ;!;_8_ _sin90 =0 =5(cm) 6cm 18 ;!;_7 sin=1 sin= =60 cos=cos60 =;!; 105æ 10`cm `cm ;!; =;!; 0 90 sin 0 1 cos 1 0 tan =" 10-6 =8 =90 - = = sin=sin=;1 0;=;5$; ;5$; 0 '6 = ='6_'= cos5 1 =tan0 =_ = 0 1 =tan60 =, = = cos60 = = + = =0 = =15 =75 tan75 = = cos= = 1 = cos 06 tan 07 = = SLUTIN

27 Q X 08 = cos= = =9 =sin =tan + =sin9 +tan9 = = sin50 = =8sin50 8 cos0 = 8 =8cos0 10 =000sin60 =1000(m) =1000tan0 =1000(m) 11 =sin0 = =cos0 =6 Â 0æ =9-6= =øπ() + ='ß1 1 G =6sin 60 = G =G =6cos60 = =++=10 G =;!;_(+10)_=1 1 1 ;!;_1_ =70 =10 1 =øπ1-10 ='ß11 'ß11 'ß11 'ß11 cos= = =180 -( ) =0 - =6 = G=90, =, = G G (R ) 15 =h cm =htan0 5æ 0æ = h(cm) 5æ =htan5 =h(cm) 6`cm h- h=6 18 h= =(+) - 16 =;!;_ _ _sin =;!;_1. _0.6 _sin =0.78_{;!;_ _ _sin} =0.78 % 17 P=;!; =;!;_(8_1_sin5 ) =1'(cm ) 18 ;!; (+1)_sin60 = +-1=0, (+)(-)=0 = >0 19 M =M = _1=6 M M =;!; M M =;!;_6= 6Â M Â Â M cos= = =;!; M 6 ;!; LTUR 1 90`m =90cos5 =5'(m) 5æ =90sin5 =5'(m) 5' 1 = =5'_ =15'6(m) tan60 =5'+15'6=15('+'6)(m) 15('+'6)m 0 -y+8=0 y= +;*; tana= a=0 sina_tana-cosa =sin90 _tan60 -cos0 =1_- = 7

28 LTUR 1 I=90 +;!; =10 I=;!;_5 sin( ) I=5(cm ) 5cm F F ='6 cos5 = F Â6 F ='6sin5 = 5æ 5æ F = =1 =1+ tan60 F ='6 tan60 =' ª F (1+ )=' '6 '+'6 = =+ '6 =(+)+(1+)=+ + ' '= '=;!; ' '=0 =tan0 = (cm) '= '=_{;!; } 16 '= (cm ) =10_8_sin60 =0(cm ) M=;!;_5_8_sin60 =10(cm ) N=;!;_10 sin60 =10(cm ) = =10 ' `cm 0æ MN=;!;_5 sin( ) ' ' Q X I, I=90 +;!;. I = F = F ª F '= =90 ' =, ' (RS ) 1 LTUR ' =;!; =;!;_=1(cm) LTUR K 66 =" 1-1 =5(cm) = =1 cm = - =1-5=8(cm) 0 =" =17(cm) = =17 cm =17-8=9(cm) = =15 cm =" =' (cm) 0 N =;!; = N =" +() = = = M M =" -('6) =' 10 =M =' 10 LTUR K 67~69 8`cm 15`cm  M N Â6 MN=5(cm ) MN = - M- N- MN = =15(cm ) 15cm 0 =1 cm ;!;_6_ =1 =(cm) 6`cm 8 SLUTIN

29 Q X =;!; =(cm) =" + =5(cm) 5cm =10 cm 10 cm 05 r cm 6`cm 1`cm 1`cm r`cm =r cm {r-6}`cm =(r-6)cm r =(r-6) +1 1r=180 r=15 06 =" 8-6 ='7(cm) = ='7(cm) 8`cm `cm P P=;!;_'7_='7(cm ) 6`cm. = =. 09 M M =;!; ='6(cm) =r cm M =;R; cm M r =('6) +{;R;} r = r=' r>0 10 =;!; =10(cm) =;!; =8(cm) = - =10-8=(cm) 11 T=90 T T =" 7 - =' 10(cm) =T =' 10(cm) Â6`cm r`cm 16`cm 0`cm M cm LTUR 07 r cm =r cm M =(r-)cm M =;!; =8(cm) M r =(r-) +8 8r=80 r=10 10_=0(cm) 08 M =6 cm M =;!; =(cm) M 16`cm r`cm 0 cm M `cm 6`cm `cm. 1 M M 18`cm M =;!; =9(cm) y`cm `cm = cm, M =y cm M -y =9 p_ -p_y =p( -y )=81p(cm ) 81p cm 1 M M =M N N =N M =N M =M =N =N = M =N = = μ=μ M M =" 6 - =(cm) =M =6(cm) M=;!;_M _M =;!;_N _N = N 9

30 LTUR Q X 1 M M =;!; =9(cm) =15 cm M M =" 15-9 =1(cm) _1=(cm) 15 N N =;!; =(cm) N N =" 5 - =(cm) M =N = cm = =8 cm =;!;_8_=1(cm ) 16 M =N = =;!;_(180-6 )=58 17 = = = cm =;!;_6_ =6(cm ) 9`cm M 15`cm `cm 18 M =N = = =;!;_( )=60 1 cm 6`cm 6cm = M =16(cm) _16=8(cm) 1 LTUR LTUR K 70. P _ =P _ =. + + = +R +R + = +P +Q + =P +Q 01 TP=90 PT T =(6) -6 =7 p_t =7p(cm ) 0 P=90 P P =" 6 + ='5(cm) 6_='5_ 6'5 = (cm) 5 = = 0 P =P y=9 P =" 9 +() =6 y=5 1'5 5 (cm) 7p cm 5 0 P=90 P=90 - =68 P =P P P=180 -_68 = 05 F =, = F + = +F + + F + = F + = + + F + =6+5+7=18(cm) F = F =9(cm) 06 P=90 P P =" 10 - =' 1(cm) + + =P +Q =P =_' 1=' 1(cm) LTUR K 71~7 ' 1 cm 1 10 ' =T, =T + =T +T = =11(cm) _ =(cm) 0 SLUTIN

31 Q X 08 T = = =T =6-= = = =-= =" 6 - =' =;!; =;!; =' T = + 9+P ++R =8+15 P +R =11(cm) = + =5 =10, =1 _ =10 LTUR ;!;_p_(') =p 09 = = cm, =F = cm F = = cm (++)= =5 p 15 =_=8(cm) + = + =8+11 =19(cm) =;!;_19_8=76(cm ) 76 cm 10 = = cm F = =(5-)cm F = =(8-)cm (5-)+(8-)=9 = = 11 =" 10-8 =6(cm) F r cm = =r cm F = =(6-r)cm F = =(8-r)cm (6-r)+(8-r)=10 r= r= =" 10-8 =6(cm) r cm ;!;_8_6=;!;_r(6+8+10) =1r r= F r`cm 10`cm 8`cm 1 =F =6 cm =F = cm = = cm (+6) =(+) +9 6=5 =9 =_{;!;_9_}=7(cm ) 7 cm F +F = = = =r cm = + + +<(-)+(5-) <;%; = =90, =, RS 16 =" 5 - =(cm) = cm = =(+)cm +(+)=+5 =6 = 17 =cm 6+=7+ =(-1)cm =7-(-1)=8-(cm) =(8-) +6 16=100 =;; ;; 18 ' cm ' P Q P =;!;_8=(cm) ;; ;;cm ' =(+)cm ' P =(-)cm ' =9-(+)=5-(cm) ' (+) =(-) +(5-) -6+5=0, (-1)(-5)=0 =1 { 0<<;%;} 8`cm `cm 9`cm P ' `cm Q 1

32 LTUR Q X 15 LTUR LTUR K 7 μ 06 = = P = +0 Q ( +0 )+ =100 =70 = Q Q=90 Q=90-7 =6 P= Q=6 P Q 7æ 01 = =66 = =6 =66 +6 =11 0 = =60 = cm 0 P= P=90 P =60 -( ) =10 =;!;_10 =70 y=;!;_(60-10 )=110 y- = =0 0 P P=180 -( +6 )=9 = =9 05 =;!; = = =70 - =6 LTUR K 75~77 æ æ 70æ 0æ 0 8æ 6 =_ μ. 08 =90 =90-5 =65 = =65 P =180 -(65 +0 )=75 09 =;!; = =90 P =90 - =58 10 ' '=90 ' ' 5 8 ' =" 10-8 =6 = ' tan=tan'= =;6*;=;$; ' 11 ' ' '=90 6 = ' tan=tan'= =;#; ' 6 =;#; ' = ' ' ' =" +6 =' 1 p_(' 1 ) =1p æ 6æ 1 μ=μ = =8 =180 -( )=59 P 1p SLUTIN

33 Q X 1 =90 =90-8 = μ=μ = =;!;_ =1 = =1 1 P P=80-55 =5 μ μ= 5 μ=5 55 μ=11(cm) 180. μ. 01 F F=10-0 =7 =180-7 =108 0 =90 =180 -(90 +5 )=55 = =15 LTUR K 79~81 LTUR 15 =μ μ μ =6 7 5 =180 _;1 8;=50 16 =180 _;5!;=6 6 =μ μ= = P P=6 + = ,,, = =68 P =9-68 = =,,, = =70 P P=70 +5 =115 æ P 6æ. 0 = =60 = =5 =60-5 =5 =180-5 =15 0 = =110 =110-5 =65 = =5 y=180 -(5 +0 )=105 y- =0 05 = =10 = =10-65 =55 =90 =90-55 =5 5æ LTUR LTUR K 78 =P P 06 = P P Pª P 10 =P 6 P =15(cm) 15 cm P P=105 - =6 = P=6

34 LTUR Q X 08 Q= P PQ=6 + Q 8 +(6 + )+ =180 =116 = = =70 P= P Q= +70 Q 1 +( +70 )=110 =19 + = = =85 = =180 -( )=70 + = = =65 + =180 =180 -(65 +5 )= = =80 =15-80 =65 =_65 =10 11 F = =50 = =75 = =15 1 =;!; =0 80æ y + =180 + y = + + = = =180 = = æ 100æ 10æ 105æ F + =180 F+ =180 Q+ PQ= PQ' 110æ PQ= Q =110 QP Q= =70 = Q= PQ PQ ' PQ= Q =100 QP Q= =80 18 Q= Q=160 Q+ Q=0 7æ 80æ Q P S R 0 RS RS S= PRS PQ PQSR PRS= PQ QP PQ=180-7 =106 S= PQ= P 70æ ' 110æ Q P Q ' 100æ SLUTIN

35 Q X 17 LTUR =60, y=75 =70, y=70 LTUR K 8 01 =μ μ μ =5 6 =180 _;1 5;=8 T= =8 0 P =T TP= PT=8 T= TP=8 PT (8 + )=180 =96 0 = = =;!; =56 =56 - = LTUR K 8~85 11æ æ 0 = =110 =180 -( )=50 = =50 90 T =T =;!;_ _ =_sin (0 < 90 ) 180 P =75 - = T= TP=0 T=90 T=180 -(0 +90 )=70 μt μt= T T =0 70 = 7 08 T= = T= =90 T =90 - P (90 - )+ = =1 =61 09 T T T=90 T= T Tª T T =T 8, T = T ='6 (cm)( T >0) T T =øπ('6) - =' 15 (cm) ' 15 cm 10 = P=5 =;!;_9_1_sin5 =7' (cm ) 11 T= TP=0 T=90 =1 cm T T =1cos0 =1_ `cm 8`cm T =6 (cm) æ P 7'cm LTUR 05 = =50 =95-50 =5 T= =5 06 P= = P = =75 T 10æ æ 105æ T =1sin0 =1_;!;=6(cm) T=;!;_6_6=18 (cm ) 1 = Q = tan=;$; 16 = =16_;#;=1(cm) tan =" =0(cm) 16`cm Q 5

36 LTUR Q X 10 cm p_10 =100p(cm ) 100pcm 18 LTUR LTUR K 86 1 F= F=70 =F F= F=70 F =180 -_70 =0 1 F =F F=;!;_( )=55 F= F=55 F F=180 -( )=65 15 P P =P P=;!;_( )=65 Q= P=65 Q=μQ μq= Q=;#;. P _P =P _P LTUR K 87~89 01 P =P = cm =5_9=5 ='5 >0 =P =_'5=6'5(cm) 0 _(+1)=_(+7), +1-0=0 (+15)(-)=0 = >0 0 P = P =5 5_=_10 = = >0 P = Q +;#; +65 =180 ;%; =115 = P= PT'= PT= P=8 P P=180 -(8 +8 )=60 17 P= P= PF= P P= PF= P= P P P P= PP= P Pª P Pª P P P =P P = 0 P = cm P =(9+)cm P =(9-)cm (9+)(9-)=_8 =9 =7 >0 05 =6 cm = = cm =_6=1 = >0 06 P =8+=1 _1=6_P P =8 `cm `cm 6 P 8 18 P= PT'= P= P =105 - = P =7-, P =7+ (7-)(7+)=_8 =5 =5 >0 6 SLUTIN

37 Q X 08 =60 = = =10 cm = =0(cm) 10`cm `cm P P = cm (+10)=_(+0) =0, (+16)(-6)=0 =6 >0 09 7_(7+)=9_(9+5) =11 ' 6_(6+y)=9_(9+5) y=15 +y= =' -' =7-6=1 P = P = +P =5+ P = -( +P )=-(1+)=- P = -P =1- ' P _P =P _P (5+)(-)=(1-) 1=15 =;1!%; 11 _= _6 =(cm) P = cm () =(+8) +8-8=0 (+1)(-)=0 = >0 cm 1 PT= T= P PT P =T = cm PT =_(+6)=0 PT ='ß10(cm) PT >0 = =;!;_( ) =60 PT =P _P PT =P _P ' PT' =P _P P _P =P _PF ' P _P =P _PF 15 P = 6 =(+9) +9-6=0 (+1)(-)=0 = >0 PT PT P PT= PT PTª PT 6=T 10 T =5 16 PT =_(+6)=16 PT = PT >0 PT PT P PT= PT PTª PT T = T =6 17 PT =P _P =P _P =_(+8)=8 PT = PT > PT =PT' =6_(6+9)=90 PT =PT' =' 10(cm) PT >0, PT' >0 TT' =6' 10(cm) LTUR K 90~ '7cm ;; ;; cm ' 85 cm ' 1 6'5cm 100 LTUR 1 = cm =(8-)_8, 8=8 =6 1 ('5) =(+8) +8-0=0 (+10)(-)=0 = >0 6cm P T Â5. 01 =;!; =10(cm) =;!; =8(cm) =;!; F =(cm) = - =(cm) F = = - =(cm) F 7

38 LTUR Q X 0 cm = cm =(-)cm =(-) +6 6=5 `cm 6`cm `cm {-}`cm 09 =μ μ=1 =;!; P =;!; +8 =57 =;; ;; 0 L =M = =180 -_55 =70 LM LM=60 -( )=110 0 TP=90 T = =9 cm TP PT =" 1-9 ='7(cm) '7cm PT =P _P PT =_(+9+9)=6 PT ='7(cm) PT >0 05 = F = F = + + = +F +F + = = + = 06 =F = cm =F =(11-)cm = =(8-)cm (11-)+(8-)=7 =1 =6 07 μ 110æ =50 =;!;_50 =15 =60 -( )=65 08 = =, =90 =180 -(90 + )=8. 10 y= =75 = y=75 P = = y- =75 - = 11 P =180 -(85 + )=7 P= =7 1 F F + F=180 + = F = F = = =;9!;_60 =0 μ P P=;!; =0 T= P=0 =;9!;_60 =0 =;!;_(180-0 )=70 T=90 T= T- =0 1 = =6 =90 T =180 -(90 +6 )=8 T= =8 P 118æ T 8 SLUTIN

39 Q X 15 P = cmp =(1-)cm 8_5=_(1-), -1+0=0 (-)(-10)=0 = =10 P >P P =10(cm) 16 6 =_(+ ) =5(cm) TP=;!;_6_9_sin0 TP=;!;_6_9_;!;=;; ;;(cm ) TPª TP TP P =6 = 9 ;; ;; cm TP=;!;_6 sin0 =6(cm ) a, b ;!;absin (0 < 90 ) TP= TP, P TPª TP P ( +7 )+( +7 )+ =180 =50 1 P =P =0- (0-) =7 10=60 =6 P =1_6=8 P =' 1 P >0 P = =10 cm P = =8 cm =10+8=18(cm) = cm 10`cm P 50 ' 1 8`cm LTUR TP 6=9 TP=;; ;; (cm ) =" 18 - =8'5(cm) P =;!; =;!; ='5(cm) 17 =" 10-8 =6(cm) = =1(cm) PT =_(+1)=6 PT =8(cm) PT >0 18 =_(+6)=0 =' 10 >0 ' 0=_(+y) y=18 y=' 10_18=6' 10 = F =;!;_18_'5=6'5(cm ) 6'5cm F = F' ' F= + F = + =160 + F+ =60 = M M =;!; =6(cm) M M =" 11-6 =' 85(cm) `cm ' 85 cm ' 85 cm M =90 =;!; =5(cm) _15=5_10 =: º:(cm) 15`cm 10`cm 15`cm 0 = =7 = = 9

40 WRK Q X 01 LTUR WRK K _ b= a+b= = = =87 5 a a =87 a= , a= 0_+1_5+_7+_+_10+5_ 9 WRK K ~ +y+z+w 05 =1 +y+z+w=8 (-1)+(y-1)+(z-1)+(w-1) (+y+z+w)- = =;; ;$;º;;= = = 7 18+=1 = _51=550(kg) kg 550- =9.8 = , 17, 1,, 6, 7, 0 <<6 5 + = = = =18 = a= 1 1+ = 1< + < æ6 +6 =.5 <<6 a=;&9*;=. 15 b= c= a<b<c = = = = a<b<c 1 0 LTUR ' 10 ' ' 7. 5 WRK K 7'6 0 =, =11, =, =, =16. '. 0 SLUTIN

41 Q X WRK K ~5 0 (-5) (-)=0 =5 = - >0 6 1-(-5)= (6+++1)=8 15_6+5_8+5_+5_+55_1 = 0 =: 0º:=7 =; 0;{(-1) _6+(-) _8+8 _ =;:@%0@:);= _+8 _1} (a-)+(a+)+a+(a-)+(a+1) 0 = 5 5a = =a 5 (-) (-) +1 = 5 =: 5º:=6 6 a+b+c 05 =9 a+b+c=7 (a+)+(b+)+(c+) = (a+b+c)+9 _7+9 = = =9 (a-9) +(b-9) +(c-9) =5 1 = {(a+-9) +(b+-9) +(c+-9) } (a-6) +(b-6) +(c-6) = 16{(a-9) +(b-9) +(c-9) } = =16_5 =00 =' 00=0 9_0=780 = a+, b+, c =' 16=' 1 ' _5+_9 =;; 8 ;;= _1+65_+75_8+85_6+95_ = 0 =; %0*:);=79 =; 0;{(-) _1+(-1) _ WRK (+y+z) 06 =6 +y+z=18 yy 1 (-6) +(y-6) +(z-6) = 1 +y +z -1(+y+z)+108=1 yy +y +z -1_18+108=1 +y +z =10 10 =; )0*:);=10 +(-) _8+6 _6+16 _} 55_+65_6+75_+85_+95_ = 0 =; $0*:);=7 =; 0;{(-19) _+(-9) _6 5_6+55_10+65_ 07 = =5(kg) 0 (-9) _6+1 _10+11 _ = =9 0 =' 9=7(kg) 7kg _ +1 _+11 _+1 _} =; #0*:);=

42 WRK Q X 0 LTUR WRK K 6 01 ' 0 =6, y= =' 17, y=8 =', y='5 =', y= F GF G FG. F G, FG. 09 FG ='ß1 (cm) =øπ('ß1 ) - =(cm) =5 cm 5 =5(cm ) 10 =169 =1 FG=169-_0=9 F =7 =, =+7 +(+7) =1, +7-60=0 (+1)(-5)=0 =5 >0 0 =" 1-6 =6 =;!;_6= =øπ() +6 ='7 WRK K 6~7 05 =øπ1 +('6) ='7 =øπ('7) +('6) =' 1 =øπ(' 1) +('6) =' 19 F F =øπ(' 19) +('6) =5 5'6 FG=;!;_5_'6= 5'6 = + =øπ - + = + =90 =90 11 = =8 cm =" 6 +8 =10(cm) = =10 cm =" =10'(cm) 10'cm 1 G = cm FG =G =(9-)cm F = =6 cm FG =6 +(9-) 18=117 =;; ;; G=;!;_6_;; ;;=;; ª;;(cm ) ;; ª;; cm 06 = =" + =' = =øπ(') + = = =øπ() + = =;!; = 07 = =5 cm =7-5=(cm) =" 6 - ='(cm) 5`cm 6`cm 7`cm. 0 LTUR WRK K 8 =;!;_(5+7)_' =' (cm ) ' cm 08 =" 5 - =(cm) FM=;!; FMN=;!; 0 <' 1 ' 9<< '7 FM=;!;_ =8(cm ) 08 ;; ;;p cm 7 cm SLUTIN

43 Q X 09 + =('5) + =(') WRK K 9~ ('ß15) =5 + = =" -6 =' =;!;_6_'=6' 6' 10 =" +8 ='5 8 =" 8 - = 11 <<15 yy >6 +9 >' 1 >0 yy ' 1<< = a <b +c <90 a <b +c <90 <90 a >b +c a >b +c >90 <90 P +P =P +P.. a, b, c(cæa, cæb) c <a +b c =a +b c >a +b 17 P + =P +, P =11 P ='ß11 (km)( P >0) 18 S =;!;_p_8 =p S +S =S S +S +S =S =_p=6p 19 ;!;_p_ =8p(cm ) ;; ;;p-8p=;(;p(cm ) 0 = = cm + =10 =50 =5' ( >0) = =;!;_5'_5'=5(cm ) ;(;pcm WRK 1 =øπ(6) -9 = () =9_ = 9 =;!; = 1 = cm5 ={+;; ;;} =0, (+10)(-5)=0 =;%; ( >0) 05 LTUR WRK K '5 5' ' 0 h= S=9 h=6 S=1 =æ 5 -{;%;}= 5 (cm) 0 h= S=1 h='5 S=8'5 5 cm WRK K 11~1 15 =" 1 +9 =15 + =5 +15 =50 + = + 0 " +8 =" 5 +7 =10 =' 10 ( >0) ' 10

44 WRK Q X 05 =" () + =' 10 ' 10=' 0 = =øπ() +() =' a ' a=10' a= p 10p 07 =" =17 15 = _17 =;; 1 7 ;; 08 a cm a=6' a='6 _('6) =(cm ) ;; 1 7 ;; = _ a = a = a 1 = =9- =6 -(9-) =('7) - 18=108 =6 =øπ('7) -6 = 06 LTUR =;!;_6_=9 01 =5 y=5 =' y=' 0 = y= = y='6 WRK K 1 09 = cm G= = _() = - G= G= 7 =7 = = ( >0) cm cm cm =;(; = (a, b), (c, d) øπ(c-a) +(d-b) 0, 60, '5 10 'ß 'ß10 0 ' 6' 5 'ß 05 = = =' 1 ='6 '6 = 1 = WRK K 1~1 '6 06 = 1 =(cm) =1 = (cm) =;!; =8 (cm ) 8cm 11 ;!;_1_ =8 =8(cm) =" 8 +6 =10(cm) =(cm) 1`cm cm = =6(cm) = = = =5 =øπ() +5 =' 7 5 SLUTIN

45 Q X 08,, ' 5æ ' = 1 = = = ' ' =' = = =++=+ =;!;_(6+)_ = " a + ='5 a =6 a= =" (-5-) + {--(-)} =8 =" (1-) + {-(-)} =' 10 =" (-1-) +{-(-)} =' 1 =" {1-(-5)} + {-(-)} =6' =" {-1-(-5)} +{-(-)} =' 1 11 y=-;!; ++=-;!;(-) + (, ) =0 y= (0, ) =" (0-) +(-) =' ' 1 =(-0) +(-1-1) =1 =(a-0) +(-1) =a +1 =(a-) +{-(-1)} =a -6a+18 =90 = + a +1=1+a -6a+18 6a=0 a=5 1 ' P +P =P +'P æ' `km =" (+) +8 =10(km) P 8`km `km `km ' a '6 = a ' = a 1 y=a(-p) +q (p, q) a, b ;!;ab 07 LTUR 10 km 01 ' 17 '6 0 0 h=, V= '6 h=, V= 0 '6 ' 16' 05 øπ F =5'5 61+F =15, F =6 F =8(cm)( F >0) 5_6_8=0(cm ) 06 " + +6 =' 1 " + +6 ='6 " =5 " =' 6 " + +5 =5' WRK K 15 0 cm 07 MF =FN =N =M MFN a cm F =a cm, MN =G ='acm MFN=18'6cm ;!;_a_'a=18'6 a =6 a=6 a>0 6_6_6=16(cm ) WRK K 15~16 16 cm WRK 5

46 WRK Q X 08 G =cm G =I _ I = (cm) 09 a cm F =F = ='a cm F 1cm _('a) =1 a = a='6 a>0 =I _G 1 P =P = _1 P =6 (cm) P Q Q =;!; =6(cm) PQ PQ =øπ(6) -6 =6' (cm) P=;!;_1_6' P=6' (cm ) P 1`cm Q 6' cm 10 G =6cm M M =" 6 + ='5(cm) MG MG =" 6 + ='5(cm) GM M G I I =GI = cm MI MI =øπ('5) -π() MI ='(cm) GM=;!;_6_' GM=9'6(cm ) M Â5`cm Â5`cm I G 6Â`cm 9'6cm 11 a cm 8 cm '6 a=8 a='6 ' _('6) =6 (cm ) 1 MG M =MG I =GI 08 LTUR '7 01 h='7, V= h=, V= 0 h=8, V=96p h=' 1, V= 0 π ' π '5 p 50' 1 WRK K 17 p ' 1 a cm cm '6 a= a=6' =øπ(6') -π() ='6(cm) =;!;_'6_ =1'(cm ) 0 ='_'6= =;!; = WRK K 17~18 6 Â6 6 SLUTIN

47 Q X =øπ6 -() ='6 ;!;_('6) _'6=16'6 16'6 05 =;!; =;!;_6'=' (cm) =øπ(5') -(') =' (cm) =;!;_'_'=1 (cm ) =;!;_6 _'=8' (cm ) M M =;!; =(cm) M 6`cm M M =øπ(5') - =' 1 (cm) =6 +_{;!;_6_' 1} =1(+' 1)(cm ) 06 ;!;_p_8 _ =0p =15(cm) = =øπ8 +15 =17(cm) =50(cm) 07 ( +5)= 8 +0=8 =5(cm) =" 5 - =(cm) =" 10-8 =6(cm) 5Â`cm 5`cm 8`cm 50 cm `cm 8`cm 5Â`cm =;!;_ =_ ª ( ) = = =. a a r cm pr=6p r= =;!;_8_6p=p(cm ) =" 8 - =' 55 (cm) =;!;_p_ _' 55 =' 55p (cm ) 09 =" 6 - = (cm) p_ =6p(cm) 10 P =" 5 - =(cm) = =5 cm P =5+=9(cm) ;!;_p_ _9=7p(cm ) 11 FM FM =" 7 +(') =' 57(cm) 7pcm ' 57 cm 1 M Â`cm M = M =_{ F P M Â`cm `cm G`cm _}=1(cm) 5`cm `cm WRK ;!;_p_8 _6-;!;_p_ _=11p(cm ) 11p cm 08 =p_8_ =6p(cm) 7

48 WRK Q X 09 LTUR WRK K =" +6 ='ß1 =90 - = = 6 'ß1 sin= = = ' 1 1 'ß1 1 '5 '5 '5 01 ;!; ;5$; ;#; ;$; ;5#; 0 sin = =;5$; 15 =1 =" 15-1 =9 1 G =" + =5 G =" + +1 =1 G sin-cos=;1!@;-;1 ;=;1 ; ' ' 1 =;!; { _ }- _ ' 0 05 ;!; - -;!; 06 =, y=1 =', y=' =5, y=5 =6', y=6 WRK K 0~1 07 =" 1-1 =5 cos= =;7%; '5 08 cos= = ='5 5 =øπ('5) - = =;!; = 8 09 sin= =;5$; =10 =" 10-8 =6 cos_tan=;5#;_;$;=;5$;, sin=;5#; cos_tan+sin 10 =90 - = = tan= = =10 10 =" 10 +(10) =0.. =;!; ' 1 sin5 = -15 =5 =60 sin60 +cos0 = + = 15 ' sin5 = = =6' 1 6' tan60 = = ='6 '6 16 =60-0 =0 = =6 cm cos60 = =;!; =(cm) 6 sin60 = = =(cm) 6 7 =;!;_9_= (cm ) 17 sin0 = =;!; =6 tan0 = = = =0-15 =15 = =6 8 SLUTIN

49 Q X tan15 = = = tan5 =1 a=1 y=+b -6 0=-6+b b=6 a-b=-5 10 LTUR WRK K 01 < > < < > < "ça = a a(aæ0) "a =[ -a(a<0) 0 90 sin 0 1 cos 1 0 tan =(tan-cos)+(sin+cos) -{-(sin-tan)} =sin sin 10 sin15 =0.588 =15 tan17 =0.057 y=17 +y= 11 sin56 +cos5 = =1.168 tan57 =1.599 =57 sin57 = = tan= =0.877 =6 =sin6 =0.8 =cos6 = =.7.7 WRK 0 cosz=cosy= = 05 sin6 = =0.59 WRK K ~ 06 =6_;!;_1-1= cos0 =1 0<cos10 <1 0<sin6 <1 tan 55 >tan 5 =1 sin90 = <<90 cos<sin<1 tan>1 cos<sin<tan 09 5 <<90 0<cos<sin<1 tan>1 tan-cos>0, sin+cos>0, sin-tan<0 11 LTUR WRK K 01 =', y= =5.5, y= ' 0 (+1) WRK K ~5 0 =1sin0 =6 =60 =;!;_60 =0 =6tan0 =6_ = 6 05 = =6_ =1(m) cos0 =6tan0 =6_ =6(m) + =18(m) 18 m 9

50 WRK Q X 06 Â`cm 0æ 10`cm = sin0 =(cm) = cos0 =6(cm) =10-6=(cm) =øπ() + ='7(cm) 07 =asin= sin = asin sin a. asin sin =. 1 =h m =htan60 =h(m) =htan0 = h(m) h- h=0 1 LTUR h=0 h=0 0æ 0`m 0æ 08 =7' sin5 =7(m) =7' cos5 =7(m) =10-7=(m) =øπ7 + =' 58(m) ' 58 m 09 5æ 8`m =8sin0 =(m) 0æ = ='(m) cos5 10 =h cm =htan5 =h(cm) =htan0 = h(cm) h+ h=18 h=18_ + =9(-) 10`m 5æ 5æ 7Â`m 0æ 18`cm 9(-)cm G= G = G =;!; + =18 cm WRK K 6 01 ;; ;; 5 6 0' 0 15' ' WRK K 6~7 0 ;!;_8_ _sin5 =1 ' =1 =' (cm) 05 =;!; 9_sin5 =9'(cm ) G=;!; ='(cm ) 06 =180 -( + )=150 =;!;_1_9_sin( ) 11 =h cm =htan5 =h(cm) 5æ =htan0 = h(cm) 0æ 5æ 10æ h- h= `cm (+) h=_ = - - = cm =;!;_1_9_;!; =7(cm ) 07 =180 -_.5 =15 p_ _;!6#0%;=6p(cm ) 50 SLUTIN

51 Q X =;!; sin( ) ' =;!; ='(cm ) (6p-')cm (6p-')cm 08 =;!;_10_ _sin60 5 = =;!;_'7_'7_sin( ) =;!;_'7_'7_ =7(cm ) = =7, =0 =8(cm) 09 =60 _;1 ;=0 1_{;!;_1_1_sin0 } Â7`cm 10æ Â7`cm 10`cm 1`cm LTUR 01 6 ' M M =;!; =9 =15 M =" 15-9 =1 WRK K 8 WRK K 8~9 0 =;!; =(cm) =" 8 - = (cm) = =8(cm) M WRK =1_{;!;_1_1_;!;} =(cm ) = =5 8 1 '_'_sin5 =' 8_'=8' 11 =8_8_sin60 =8_8_ =96(cm ) M=;!; =(cm ) 1 = =6 cm =;!;_6_6_sin 60 =;!;_6_6_ =9(cm ) Â 9 cm. M M =M M=;!; M=;!; M M (RS ) M= M 05 M =;!; =6(cm) M M =" 10-6 =8(cm) M =10-8=(cm) 06 =M =10(cm) M M =" 10-5 =5(cm) =M =10(cm) 07 M r M =;R; M M cos( M)= =;!; M=60 = M=10 10`cm M M M 5`cm 1`cm 10 51

52 WRK 08 =P =11 Q Q =" 11-5 ='6 =Q =8'6 09 =;!; =00(m) =;!; =50(m) = - =00-50=50(m) 10 M =N = = cm M =;!; = (cm) M=;!; = (cm ) 11 MN =60 -( )=70 M =N = =;!;_( )= P Q 5 8' L =M =N = = = _() =1(cm ) 1cm Q X... a a 0 =T =r P =+r TP=90 PT (+r) =r +(') 8r=16 r= 05 P P = 1 P =(cm) P=60 P =P P 0æ P =P =cm WRK K 0~1 06 =, =F + + = +( + )+ = +( +F )+ = +F = = 07 = + 1`cm = + =15(cm) `cm =1-=9(cm) =" 15-9 =1(cm) = =1 cm P Â T `cm 10æ r 1 LTUR WRK K 0 =F, =, F = F =;!;( + + ) =;!;_(7+10+9) =1(cm) 09 = = cm F = =10 cm =F = cm =(+)cm =(+10)cm 1 =(+) +(+10) +1-0=0, (+15)(-)=0 = ( >0) 5+1+1=0(cm) 0 cm 5 SLUTIN

53 Q X 10 G = =5 cm =1 cm =( + ) =_(9+1) =(cm) 11 + = + 6`cm G 5+ +8=6+11 8`cm 5`cm =(cm) F = =90 11`cm = cm p_ =16p(cm ) 16p cm 1 = cm +8= +1 =-(cm) =1-(-)=16-(cm) 8 +(16-) = =0 =10 15 LTUR WRK K = =10 P= P =90 P 65æ =60 -( )=50 07 Q= P=6 Q Q= Q= Q=6 - = Q= Q= = - =18 08 = = P =5 + Q +(5 + )=115 =80 = =90 6æ =90-6 =6 1æ =6-1 = = =66 66 = =6 = =5 =180 -(6 +5 )=66 P 6æ æ Q æ P WRK ' '=90 '= =60 ' ' = =_ sin60 ' =8(cm) Â`cm ' WRK K ~ 05 P=;!; =55 P P æ P= P= 110æ P=55 - = = P= ;!;. =;!; ' =(cm) 11 P= P = + æ μ=μ=μ = = = + μ = = +( + )=180 =8 P 5

54 WRK Q X 1 = =;1 ;_180 =0 =;1 ;_180 =5 = + + = =105 1 = = P y= +6 =68 + y=90 16 LTUR = =76 P P=180 -( +76 )=8 05 =;!;_(180-6 )=7 =180-7 = WRK K WRK K ~5 =μ μ μ μ μ = =180-8 =96 P P=96-6 =70 08 = =50 F =50 + = =180 =8 09 =;!; =5 = =7 =5 +7 = = P=75 = =75 - = 11 PQ QP P QP= Q 9æ 88æ =88 Q PQ ' Q= =9 1 P=;!; P' P P=8 PQ PQ ' PQ= P=8 Q QP P=180-8 =96 70æ 108æ ' 168æ 70 ' 06 + =180 ;$; +( -70 )=180 ;; º;; =50 =75 = = LTUR WRK K 6 5 SLUTIN

55 Q X 0 =85, y=85 =65, y=6 =, y=7 =70, y=8 09 =90 =180 -( )=0 = =0 =60-0 =0 = = cos60 0 =;!; =70 = =70 0 PT TP= T T= T TP= T+ TP = T+ T = T=65 WRK K 6~7 65. =10_;!;=5(cm) 10 F =F F=;!;_(180-5 )=6 5cm F= F=6 F F=180 -(0 +6 )=77 11 = PT'= TP= P=5 P= P=70 P y=180 -(5 +70 )=56 WRK 05 = =8 =180 -(5 +8 )= P= = LTUR WRK K 8 06 = = =90 =180 -(90 + )=7 = =7 æ = T= P P= P=;!; = ;!; =180 =60 08 P=90 P= PT=60 P =P cos60 =1_;!;=7(cm) P T P _P =P _P WRK K 8~0 05 _=_8 =6 1_(1+8)=y_(y+1) y +1y-0=0, (y+)(y-10)=0 y=10 y>0 y-= 06 _(++8)=(-1)_(-1++1) -1=0, (-6)=0 =6 ( >1) 55

56 WRK Q X 07 = =+=6(cm) P =6+=9(cm) P =P = cm =9_=7 = >0 =;!;_1_=18(cm ) P =9 cm=90 P =9_=7 P =(cm) P >0 =;!;_1_=18(cm ) 1 PT =5_(5+7)=60 PT =' 15(cm) PT >0 TP=90 PT T =" 1 -(' 15) =' 1(cm) PT=;!;_' 1_' 15 PT=6' 5(cm ) 1 r cm P =(r+)cm () =_(r+) r= p_=6p(cm) 6' 5 cm 08 r cm r P = cm, P =;#;r cm ;!;r_;#;r=6_15 r =10 r=' 0 r>0 p_' 0=' 0p(cm) ' 0p cm TP= =0 PT PT =180 -( ) =0 15 T T T = sin0 =(cm) PT=0 P P =T = cm PT =_(+)=1 PT =(cm) PT >0 0æ `cm 0æ T 0æ 09 P =P =+1 _(+1)=_(+) +1-8=0, (+1)(-)=0 = >0 10 r cm P =(1-r)cm 7_(7+)=(1-r)_1 8r=16 r=;(; p_;(;=9p(cm) 11 P = _(+5)=_(+16) +5-6=0, (+9)(-)=0 = >0 PT P =T T PT =P _P =PT' PT =PT' P _P =PT =P _P P _P =P _PF =P _P 16 PT =_(+9)=6 PT =6(cm) PT >0 PT PT PT= PTP PTª PT 6 1=6 T T =1(cm) 1 cm 17 PT =PT' =;!; TT' = =(+6), +6-16=0 (+8)(-)=0 = >0 18 r cm 6_(6+6)=_(+r), 8r=56 r=7 p_7 =9p(cm ) 1 PT =_(+9)=6 PT =6 PT >0 6 =_(+ ) =5 +PT =11 56 SLUTIN