(001~042)개념RPM3-2(정답)

- 0 0 0 0 6 0 0 06 66 07 79 08 9 0

000 000 000 000 0 8+++0+7+ = 6 6 = =6 6 6 80+8+9+9+77+86 = 6 6 = =86 86 6 8+0++++6++ = 8 76 = = 8 80 80 90 00 0 + = 90 90 000 7 8 9 6 6 = += 7 +7 =6 6 0006 6 7 9 0 8 8 = += 6 +6 =.. 0007 68 69 76 8 87 9 97 7+ = 8 8 0008 0009 000 00 9 0 00, 9 9., 9 +6+7+8+9 00 = = =7 - - 0 - - 0 0+6+7++ 70 00 = = = - - 0 - - 0 8+77+9+7+97 00 = = =8 0-8 9-0 -8 9-9+++7++ 6 006 = = =6 6 6-7 - 8 - -7-8 - ++6+8+0 0 007 = = =6 (-) +(-) +0 + + 0 = = =8 ='8=' 8 ' ++6+6+7 008 = = = (-) +0 + + + = = =. ='.. '. 8+9+6++ 0 009 = = =0 (-) +(-) +(-) + + 0 = = =0 ='ß0 0 'ß0 000 = 7+0+++8+9 60 = = =0 6 6 0 = = 6 =Æ (-) +0 + + +(-) +(-) 6 0 0 = 'ß

++7++7++9+ 0 00 = = = 8 8 (-) +(-) + +0 + +(-) + +(-) = 8 = =. 8 ='.. '. 78+8+96+76+90+86+7+7 00 = 8 66 = =8 8 (-) + + +(-6) +8 + +(-8) +(-0) = 8 96 = =6 8 ='ß6 6 'ß6 00 ~ ~ ~ ~ 60 = =8 8 0 00 00 = = =70 70 = =86 0 ='ß86 006 86 'ß86 0 7 8 0 'ß a= 8 9 0 0 _ 0_=0 0_=00 0_8=0 0_=00 60 _ (-8) _=68 (-8) _=0 _8= _=70 70 + = b= a+b=+=8 8 007 6 7 8 8 8 _++_+_+6+7+8_ a= 60 = = 6 7 + b= = a+b=+=0 0 008 +++(0+a)+(0+a)+9+0+++ = 0 0+a = 0+a=0 0 a= 6 9 +9 009 =7 7 p q r p q r 9 7 8 9 p q r 8 8 000 7 8 8 9 0 7+8_+9+0+_++ m= 0 00 = =0 0 6 0 0+ a= =0. b= m+a+b=0+0.+=..

RM 00 0 8 8 7 7 8 8 8 9 9 8+8 b= =8 8 c=7 a=b>c 00, 7, 0,, 6, 6, 0,,, 00 +7+0++6+6+0+++ +++6+=0 a= 0 _+_+7_+9_6+_ = 67 0 = =6.7 0 6 = =7. 6 6 6 0 6+6 6 6 8 b= =6 6+8 =7 c=6 6 8 a+b+c=6.7+6+6=8.7 8.7 6+8 =7 00 6 _+_+7_+8_+9+a =6 0 +a =6 +a=60 a= 0 7 7 8 8 9 6 7 +7 =6 6+= 00 0 +6++x+=0 x= 6_+7_6+8_+9_+0_ a= 0 60 = =8 0 a 0% 0% 0% 0% 006 7. 7 7 0 +a+b++=0 a+b= yy _+_a+_b+_+6_ = 0 a+b+ = a+b+=80 0 a+b=8 yy a=6 b= 0 + = +=7 7 a b 0% 0% 0% 0% 007 a 7 9 a 7

a +a = +a=8 a= 7+9++ 6 = = =6 6 008 8 b=8 6 6 7 6 a+8 =6, a+8= a= b-a=8-= 009 7 a<b a=9 +8++++a+b = 0+a+b=77 7 a+b=7 a=9 b=8 b-a=8-9=9 000 0 a++b =0 a++b=0 a+b=8 yy a< <b<8 yy a b (a b) ( 7) ( 6) ( ) ( ) ( ) b-a 7-=6 -=8 b-a 6+8= + +(-) +0 +(-) 00 = 0 = = =' 00 00 0 --++6+x=0 x=- E 76-=7 00 0 --+x++=0 x= (-) +(-) + + + 0 = =0 0 00 m =(m-) =(m+) 0 (-) +(-) + +0 + 0 = = = =' 006 9 7+8+x+(x+)+(x+) =9 8+x =9 8+x= x=9 7 8 9 0 (-) +(-) +0 + + 0 = = = =' 007 a= b= a b c ' 0% 0% 0% ++++c = +c=0 c=6 (-) +(-) + + + 6 = = =. 008 =(0+00)_76=00

RM =0_7=8000 =00-8000=600 600 = =8 00 009 80 70+8+x+90+9+6 =80 6 0+x=80 x=7 76 80+70+8+70+6+y+80_6 =76 6+6 80+y=9 y=6 x-y=7-6= 000 7 _0=00 7 _0=980 0 00+980=80 80 = =7 0 ='ß7 00 'ß7 ('6) a 6_8=8 a _=a 0 8+a =9 8+a =9 0 8+a =80 a = a='ß ( a>0) 00 7+6++x+y = 8+x+y= x+y=7 + +0 +(x-) +(y-) = +(x-) +(y-) =0 x +y -0(x+y)=- x +y =0(x+y)-=0_7-= x +y =(x+y) -xy 'ß =7 -xy xy= 00 a b c d 6 (a-6) +(b-6) +(c-6) +(d-6) = (a-6) +(b-6) +(c-6) +(d-6) =00 00 x+y = x+y= (x-) +(y-) = x +y -(x+y)+8= x +y =(x+y)-=_-= 00 0 a-+b+-=0 a+b=- yy 6.8 a +(-) +b + +(-) =6.8 a +b += a +b = (a+b) -ab= (-) -ab= ab=- 006 yy - 0 a+b 0% a +b 0% ab 0% x y z 8 x+y+z =8 x+y+z= x y z (x-8) +(y-8) +(z-8) = (x-8) +(y-8) +(z-8) = x+ y+ z+ (x+)+(y+)+(z+)+ x+y+z+ = = + 8 = = = = {(x+-) +(y+-) +(z+-) +(-) } 6

= {(x-8) +(y-8) +(z-8) } = _= 007 a, b, c, d, e a+b+c+d+e = a+b+c+d+e= a, b, c, d, e, (a-) +(b-) +(c-) +(d-) +(e-) = (a-) +(b-) +(c-) +(d-) +(e-) =0 a, b, c, d, e a+b+c+d+e (a+b+c+d+e) ( )= = _ = = ( )= {(a-) +(b-) +(c-) =+(d-) +(e-) } 9 = {(a-) +(b-) +(c-) =+(d-) +(e-) } 9 = _0=6 ( )='å6=6 a b c 6 a+b+c =6 a+b+c=8 a b c 8 (a-6) +(b-6) +(c-6) =8 a- b- c- (a-)+(b-)+(c-) a+b+c-6 = = 8-6 = = = {(a-)-} +{(b-)-} +{(c-)-} = (a-6) +(b-6) +(c-6) = =8, 6 8 008 a b c d 0 a+b+c+d =0 a+b+c+d=0 a b c d (a-0) +(b-0) +(c-0) +(d-0) = (a-0) +(b-0) +(c-0) +(d-0) = a- b- c- d- (a-)+(b-)+(c-)+(d-) = (a+b+c+d)- = _0-68 = = =7 = [{(a-)-7} +{(b-)-7} +{(c-)-7} +{(d-)-7} ] = {(a-0) +(b-0) +(c-0) +(d-0) } =(a-0) +(b-0) +(c-0) +(d-0) = 009 x x x x x 6 x +x +x +x +x =6 x +x +x +x +x =0 x x x x x = - x +x +x +x +x = -6 x +x +x +x +x =0 x x x x x 8 x +x +x +x +x ++8 = 7 0++8 6 = = =9 7 7 x +x +x +x +x + +8 = -9 7 0++ 789 = -8= -8 7 7 = 9 7 0060 0 ~60 60 ~70 70 ~80 80 ~90 0 _ _= 6_=9 7_=00 8_=70 70 _ 7 (-7) _=89 (-7) _=7 _=6 _=8 80 7

RM m= 70 0 =7 80 s = =8 0 770 m= =77 0 80 = =8 0 m-s =7-8=-9 s='ß8=9 m+s=77+9=86 006 { _ } 0 (-)_+(-)_+0_+_x+_=0 x=6 x= (-) _+(-) _+0 _+ _+ _ = ++++ 6 = =6. 0 006 0 +a+b+6+=0 a+b=9 yy 6 0_+0_a+60_b+70_6+80_ =6 0 0a+60b+70=0 a+6b=0 yy a= b= s = {(0-6) _+(0-6) _+(60-6) _ 0 +(70-6) _6+(80-6) _} = _90=6 0 a+b+s =++6= 006 0% 0% a b 0% s 0% a+b+s 0% ~6 6 ~7 7 ~8 8 ~9 0 _ 60_=60 70_=0 80_=0 90_=80 770 _ (-7) _=89 (-7) _=7 _=6 _=8 80 006 ~ ~ 6 6 ~ 8 8 ~0 0 ~ 70 = =7 0 8 = =.8.8 0 006 0 0-(++)= ~ ~ 7 7 ~ 9 9 ~ 60 = =6 0 6 = =.6.6 0 0066 0 0 _ _= _=0 7_=8 9_=8 _= 70 _ _=0 6_= 8_=8 0_=0 60 _ (-) _=6 (-) _=8 0 _=0 _=8 _=6 8 _ (-) _=0 0 _=0 _= _= 6 6 8 -(+++)= ~ 6 6 ~ 8 8 ~0 0 ~ ~ _ _= 7_=8 9_=7 _= _=6 08 _ (-) _=6 (-) _=6 0 _=0 _=8 _= 7 8

08 = =9 7 = =6 ='6 0067 '6 6 8 0% 0% 0% '< 0068 0069 0 ++8+a+0 =0 +a=0 a=6 9++b+8+ =0 +b=0 b=6 (-0) +(-0) +(8-0) +(6-0) +(0-0) 8 = =7.6 ' 7.6 (9-0) +(-0) +(6-0) +(8-0) +(-0) 0 = = 'ß 0070 007 007.,.,.,, 6,. 007 0 + =. a=. b= a+b=.+=9. 9. 007 0 +++a++=0 a=6 0 + =..+=7. 007, +_+_ 0 = + 7 7 a(a+) +_+_+a +a = = 7 7 +a= a=0 7 0 0 0076 0 0 9

RM a=0 0 0 0+b a=0 =0 b=60 b-a=60-0=0 0 0077 0 -+x-+(-x)=0 --x=0 x=- E 7+x=7-=69 7+(-x)=7+7=79 E 69+79 8 = =7 { _ } 0078 = (-) _+(-) _+(-) _+ _+ _+ _ = 0 96 = =.8 0 ='.8 0079 '.8 6 7 8 9 0 6 7 8 9 0 ' 6 7 8 9 0 6+7+8+9+0 0 = = =8 (6-8) +(7-8) +(8-8) +(9-8) +(0-8) = 0 = = =' 0080 7 s s s s <s <s 008 x 0 ++0+x-=0 x=- + +0 +(-) +(-) = 0 = =8 8 008 x - x - x - x - 8 (x -)+(x -)+(x -)+(x -) =8 (x +x +x +x )-0 =8 x +x +x +x = x x x x x +x +x +x = =. 008 6, 7, 8, 9, 0 6_+7_+8_+9_+0_ 80 ( )= = =8( ) 0 0 (6-8) _+(7-8) _+(8-8) _+(9-8) _+(0-8) _ ( )= 0 = =.. 0 008 0 7 a 6, 7, a, 6 7 a 7+a =0, 7+a=0 a= +7++6 80 = = =0 m=0 a-m=-0= 008 0 70 80 0-(++)= 0 ~60 60 ~70 70 ~80 80 ~90 0 _ _= 6_=0 7_=7 8_=70 70 _ (-8) _= (-8) _=8 _=0 _=88 760 0

70 = =7 0 760 = =76 76 0 0086 a>b b= 8-+8+a+--+- = 9 +a=8 a=7 = {(8-) +(--) +(8-) +(7-) +(-) 9 +(--) +(--) +(-) +(--) } 00 = 9 00 0' 0' =Æ = 9 0087 0 +x+7+y+9 =0 x+y+=0 x+y=9 ' (-0) +(x-0) +(7-0) +(y-0) +(9-0) = x +y -0(x+y)+= x +y =0(x+y)-0=0_9-0=60 xy=(x+y) -(x +y ) =9-60=8 0088 0 0_0=00 _0=80 0 00+80=80 80 = = 0 ='ß=' ' 0089 a, b, c, d, e, f 8 a+b+c+d+e+f =8 6 a+b+c+d+e+f=8,, (a-8) +(b-8) +(c-8) +(d-8) +(e-8) +( f-8) = 6 (a-8) +(b-8) +(c-8) +(d-8) +(e-8) +( f-8) = a+, b+, c+, d+, e+, f+ ( ) (a+)+(b+)+(c+)+(d+)+(e+)+(f+) = 6 (a+b+c+d+e+f)+8 = 6 _8+8 = = =9 6 6 ( ) = [{(a+)-9} +{(b+)-9} +{(c+)-9} 6 +{(d+)-9} +{(e+)-9} +{(f+)-9} = {(a-6) +(b-6) +(c-6) +(d-6) 6 +(e-6) +(f-6) } {(a-8) +(b-8) +(c-8) +(d-8) +(e-8) +( f-8) } = 6 _ 96 = = =6 6 6 ( )='å6= 9+= 0090 a, b, c 6 a+b+c =6 a+b+c=8 a, b, c ', (a-6) +(b-6) +(c-6) = (a-6) +(b-6) +(c-6) =6 a +b +c -(a+b+c)+08=6 a +b +c =(a+b+c)-0 =_8-0= (a+b+c) =a +b +c +(ab+bc+ca) 8 =+(ab+bc+ca) ab+bc+ca=0 ab, bc, ca ab+bc+ca 0 = = 009 g 90 00 0 8 9 0 8 7 0 0 g 0 g 0 6 8

RM 0 g 0 g 90_+00_+0_8+0_8+0_+0_ 6 90 60 = = (g) 6 90_+00_+0_9+0_7+0_+0_ 8 60 8 = = (g) 8 7 8 0+0 0 g 0 g =(g) 0 g 009 må vå a_+a_+a_ må= =a (a-a) _+(a-a) _+(a-a) _ vå= = a mı vı b_+b_+b_ mı= =b 0 (b-b) _+(b-b) _+(b-b) _ vı= = b 0 vå=vı a = b a=b a>0 b>0 k= 70+80+70+8+70 009 = 7 = =7 60+60+6+00+90 7 = = =7 70+7+7+7+80 7 = = =7 (-) + +(-) +0 +(-) = 00 = =0 (-) +(-) +(-0) + + = 00 = =80 (-) +0 +0 +0 + 0 = = =0 < < 009 0 x++0+(-)+=0 x=- = - =0-(-)= (-) + +0 +(-) + 0 = = = ' 009 ' x 0% 0% 0% x y 8 0 x y 9 8+0++x+y =9 0+x+y= x+y= 8 0 x y (-) + + +(x-9) +(y-9) = +(x-9) +(y-9) =0 x +y -8(x+y)+7=0 x +y =8(x+y)-7+0 =8_-7+0=7 (x+y) -xy=x +y -xy=7 xy= 0096 0 +a+b++=0 x+y 0% x +y 0% xy 0% a+b=9 yy

9 0_+0_a+60_b+70_+80_ =9 0 0a+60b+670=80 a+6b= yy a= b=6 {(0-9) _+(0-9) _+(60-9) _6 0 +(70-9) _+(80-9) _} ++6+60+88 = 0 80 = =9 0 9 0% 0% a b 0% 0% 0097 a+b+c = a+b+c= ' (a-) +(b-) +(c-) = (a-) +(b-) +(c-) =9 a +b +c -8(a+b+c)+8=9 a +b +c =8(a+b+c)-9 =8_-9=7 a p b p c p a p+b p+c p (a +b +c )p = 7p = =9p 0098 9p a+b+c 0% a +b +c 0% 0% a, b, c 0 0 a, b, c 0., a, b, c 0, 0, x,,, 7, 0, 0, 0, x 8 8., 7 x 0 7+x ( )= =8 x=9 a+b+c=0+0+9=9 9 0099 6 70_6=0 0-70 0 = =70 6 0_6=0 0 [{6 }-{ }] = (0-0) = 000 9 x x y xª kg 0 kg x +x +y+xª+ =0 0 x +x +y+xª= 0 x +x +y+xª+ + 90 = = =9(kg) 0 0 0 kg 6 = - x +x +y+xª + -0 =6 0 0 x +x +y+xª + -9 0 x +x +y+xª +(-0) = -(0-) 0 x +x +y+xª + = -0 +(-00)+00-0 =6-00+00- =

RM 0 00 a b c d 7 8 7a+76b a+b =7 a= 8c+90d =8 c=d yy c+d 8 76b+90d =8 d= b yy b+d 8 c=_ b= b 7_ ;@; b+8_ ;*; b 7a+8c x= = a+c ;@; b+ ;*; b b 00 x = +(') x = x= ( x>0) 00 0 =x +6 x =6 x=8 ( x>0) 8 00 8 = +x x =8 x='( x>0) ' 00 x = +(') x = x='ß ( x>0) 006 'ß x=" - =' = y=" 9 + =' = x= y= 790 b = =79 79 0 b 007 x=" + ='8=' y=" (') +(') ='ß6= x=' y= 008 SS FL FML LMG 009 =6+6=00(cm ) 00 cm 00 =-=7(cm ) 7cm 0 FE F =9-6=(cm) EF =" 6 + ='ß='(cm) EFG EFG =_'='(cm) EFG=(') =(cm ) ' cm cm 0 E E =" - =' =(cm) F =E = cm EF =-=7(cm) EFG EFG=7 =9(cm ) 7cm 9 cm 0 (') = +(') (') = + 7 + +(') 6 + + 0 =6 +8

+ + 0 0 06 07 08 09 00 > + ('7) =(') + 9 <6 +8 ('ß0) >(') + 7 < +6 ('ß0) = + -<x<+ <x<7 yy x < + x < 0<x< yy <x< <x< 0 6-<x<6+ <x<9 yy x <6 + x < 0<x<' yy <x<' <x<' 0 -<x<+ <x< x x> <x< yy x > + x > x>' yy '<x< '<x< 0 6-<x<6+ <x<0 x x>6 6<x<0 yy x > +6 x > x>'ß yy 'ß<x<0 'ß<x<0 0 = _ x =(6+9)_6=00 x=0 ( x>0) = _ y =6_9= y= ( y>0) 0 = _ 6 =x x=9 y=" 6 +9 =' 7='ß 06 x=øπ6 -(') ='å6= _ = _ x=0 y= x=9 y='ß 6_y=_' ' y= x=, y= 07 = _ 8 =0_(0-x) 6=00-0x, 0x=6 8 x= 8 =0- = y=æ 8 -{ } 76 8 =æ = x=, y= 08 6 + =7 +x x = x='( x>0) ' 09 6 +8 = +x x =7 x='( x>0) ' 00 +(') =x + x = x='ß ( x>0) 0 (') +x = +8 x =60 x='ß ( x>0) 0 +6 = +x x = 'ß 'ß x='( x>0) ' 0 x + =(') + x = x='ß ( x>0) 0 +8 =x +6 x = x='ß ( x>0) ' 'ß 'ß

RM 0 08 x= 09 (x+) =x +8, x=60 x m (0-x) m. (0-x) = +x, 0x=8 x=.(m) (0-x) m. m. m 00 ' cm =' ='(cm) =øπ +(') ='å6=6(cm) 0 =" 8 +6 =' 00=0(cm) m x m 6cm = = = = _0=(cm) 0 G = = _= (cm) 0% 0% G 0% 0 ('7) + = +x x = x='( x>0) ' 06 07 =6+ =9(cm ) = = _6_ =(cm ) =" - ='ß6=(cm) =" 6 + ='ß='ß(cm) 9 cm cm 0 cm 'ß cm 0 =" + ='ß=(cm) = = cm =+=9(cm) =" +9 ='ß90='ß0(cm) 'ß0 cm 0 =x cm =" -x (cm) (') =('+x) +(" -x ) 0=+'x+x +9-x ' ' 'x=6 x= = (cm) cm ' 0 = = 6= =" -6 =' 08=6'(cm) = = _6'='(cm) =øπ(') +6 ='å8='(cm) ' cm = 0% 0% 0% 0% = 06 =" x +x ='x =" ('x) +x ='x E =" ('x) +x =x F =" (x) +x ='x G =" ('x) +x ='6x G ='6 '6x='6 x= GF F =', FG = 9' GF= _'_= 9' 07 =a = = =E =EF =a 6

=" a +a ='a =øπ('a) +a ='a E =øπ('a) +a =a F =øπ(a) +a ='a F =' 'a=' a= x=' =øπ(') +(') =' =øπ(') +(') ='8=' E =øπ(') +(') ='å x=f =øπ('å) +(') ='å ' 'å 08 = ' =" + ='8='(cm) = ' =" (') + ='ß='(cm) ' cm 09 ' =x = ' =" x +x ='x = ' =" ('x) +x ='x = ' =" ('x) +x =x =6' x=6' x=' ' 00 cm = = cm cm =7-=(cm) 7 cm =" - =' =(cm) = _(+7)_=7(cm ) 7 cm 0 =" + ='ß=(cm) =" -(') ='ß(cm) cm cm ' cm = + _'_'ß =6+'ß9(cm ) (6+'ß9) cm 0 = = cm =-=8(cm) =" 0-8 ='ß6=6(cm) =" +6 ='ß='ß(cm) 0 E F EF = = cm cm cm cm 0 cm E =F = _(0-)=(cm) E E =" - ='ß6=(cm) = _(+0)_=8(cm ) cm E F 0 cm cm 8 cm EF 0% E 0% E 0% 0% 0 E I E= E E '7 cm E= F (SS ) F= E =øπ -('7) ='9=(cm) F= E= E F L cm M G 9 9 = = (cm ) cm 0 E E= E F E(SS ) F= E F M F= FL E= E= F= FL 7

RM 06 08 = + = GF+ E =0+9=69 =(cm) ( >0) cm 07 =" -6 =' 08=6'(cm) FG= GF= = _(6') =(cm ) cm 0% FG 70% EFG EF = EF =(cm) ( EF >0) FE F =" - ='ß8=9(cm) F =E = cm =9+=(cm) = = =(cm ) cm QRS QRS=QR =('-) =6-8' 06 Q = = cm Q Q =" - =' =(cm) Q= =0(cm ) Q = +Q =+Q Q =7(cm) QRS=Q =7 =9(cm ) = = =69(cm ) QRS+. 06 E =G = cm E E =" 6 - ='ß7='(cm) F =G = cm EF =('-) cm 6-8' EFG ('-) cm ('-)=('-)(cm) ('-) cm 09 =E =8 cm =-8=6(cm) E E =" 8 +6 =' 00=0(cm) EFG EFG=E =0 =00(cm ) 00 cm 06 QRS 9 Q =9 Q = ( Q >0) Q = = =+=6 =" +6 ='ß=' = =(') = 060 E E =" x +y ='ß EFG EFG=E =('ß) = 06 E =x cm E E =" x +x ='x(cm) EFG 8' cm _'x=8' x=(cm) =E =_=(cm) = =_=6(cm) 6 cm 06 Q = = Q Q =" - ='ß=' R = = QR ='- 066 E =E =0, =80 ='8å0='(cm) ( >0) =øπ(') - ='6å=8(cm) = = cm =8+=(cm) E = =8 cm E= _(+8)_=7(cm ) 067 E =E = = cm =øπ(') + ='å='(cm) E= _'_'=6(cm ) 068 E =E 8

=E =x cm x +x =(0'), x =00 x =00 x=0(cm) ( x>0) =" 0-6 ='6å=8(cm) E = =8 cm, = =6 cm E= _(6+8)_=98(cm ) 069 =90 x+ (x+) =x +(x-) x -x=0 x(x-)=0 x=0 x= x->0 x> x= 070 = +(') (6') +6 +6 ('ß) = + =('7) + (') +(') + 6 +('ß) + 07 yy yy x+ x+<x+(x-) x> (x+) =x +(x-) x -8x=0, x(x-8)=0 x=0 x=8 x> x=8 _8_=60 60 07 6 6 = +x, x =7 x=' ( x>0) x x = +6, x = x=' ( x>0), x=' x=' ', ' 6 x 0% x x 0% 07 7 < +6 9 > +8 9 <6 +7 0 <6 +9 =9 + 07 a <b +c <90 a 07 (') + =('7) (') + >('å0) + >6 6 +8 < 9 + =, 076 x 8<x<6+8 8<x< yy x <6 +8, x <00 0<x<0 ( x>0) yy, 8<x<0 x >6 +8, x >00 x>0 ( x>0) yy, 0<x< 8<x<0 0<x< x 0% x 0% x 0% 077 -<x<+ <x<9 yy x < + x < 0<x<'ß yy <x<'ß <x<'ß 078 079 (a+x) x +y b > -<a<+ 7<a<7 yy 9

RM a <90 a < + a <69 0<a< yy 7<a< a 8 9 0 =k cm k 0% 0% 0% 080 8-<x<8+ <x< 8 x<8 <x<8 yy 8 > +x x <8 0<x<' yy <x<' <x<' x 0% x 0% x 0% 08 x=" +6 ='ß=' = _ (') =y y= x=' y= 08 = _ 6 =x_(-x) x -x+6=0 (x-)(x-)=0 x= x= > x= = _ 6 = _' ='(cm) ='-'='(cm) = _ x ='_'= x=' ( x>0) ' 08 =k cm(k>0) =k cm = _ (') =k_k, 8=k k =9 k=(cm) ( k>0) = cm =øπ +(') ='å7='(cm) ' cm 08 =øπ(') + ='6å=8(cm) = _ = _8 =(cm) =" - ='å='(cm) M = = _8=(cm) M =-=(cm) M= '='(cm ) ' cm 08 =" -0 =' =(cm) _ = _ _0=_ =(cm) 086 =øπ(6') + =' =8(cm) _ = _ 6'_=8_ ='(cm) 087 =" 0-6 =' =(cm) = _ 6 =y_0 y= (cm) _ = _ 8 _6=0_x x= (cm) ' cm 8 6 x-y= - = 088 = =k cm, =k cm(k>0) =" (k) +(k) ='åk _ = _ 'å k_k='åk_8 k= (cm) 'å =k=_ ='å(cm) 'å cm 089 =" + ='ß + = + ('ß) +(') = + =8 ='( >0) 0

090 + = + + = +6 = ='( >0) ' 09 + = + (') + =('ß) +('ß) = = ( >0) =" - ='ß6= = =6 6 09 = + = + =(') +6 = ='ß ( >0) 09 E + =E + +(') = + = ='6( >0) 09 E + =E + 6 + =(') +0 =76 ='ß9 ( >0) 'ß 'ß9 098 + = + + = + =8 ='(km) ( >0) ' km ' km 099 + = + - = - =6 - = 000 =" (') + ='ß6=8 _ = _ _'= _8 =' = _ = _8 = =8-=6 + = + (') + = +6 =8 ='7( >0) '7 0% 0% 0% 0% 09 E = = _=6 E + =E + =6 + =80 80 00 +Q=R +Q+R=R=_{ _p_6 } =6p(cm ) 096 E E =" + ='ß E E =" +(+) ='ß68='ß7 E + =E + - =E -E =('ß7) -('ß) = E 0% E 0% - 0% 097 + = + +('å0) =('å) +, = ='6(cm) ( >0) 00 00 S +S = = _p_8 =p(cm ) p cm =p+p=7p(cm ) _p_{ } =7p =6 =6'6(cm) ( >0) 00 6'6 cm r cm _p_r =8p, r =6 =_=8(cm) r=(cm) ( r>0)

RM =" 6 +8 =' 00=0(cm) R= _p_ = p(cm ) p cm 00 =" 8 - ='ß8='(cm) = = _'_ =8'(cm ) 8' cm 006 = =0 cm _ _=0 =(cm) =" + =' 69=(cm) 007 008 ( )= =_{ _8_6} =8(cm ) + =0 = =00, =0 ='(cm) ( >0) ( )= = _'_' =(cm ) 009 F = = cm F F =" -9 =' =(cm) cm 8 cm cm F =-=(cm) E =x cm EF =E =x cm E =(9-x) cm EF x =(9-x) + 8x=90 x=(cm) 00 =x cm = =(6-x) cm (6-x) =x +8 x=9 x=6(cm) 6 cm 0 F =x cm EF =F =(-x) cm E = = _=6(cm) FE (-x) =6 +x x=08 9 9 x= (cm) cm 0 F F =x cm F =F =(8-x) cm (8-x) =x + 6x=8 x=(cm) F= =6(cm ) 0 Q = =0 cm Q Q =" 0-8 ='ß6=6(cm) Q =0-6=(cm) =x cm Q = =(8-x) cm Q (8-x) = +x 6x=8 x=(cm) 0 F= F= F= F F F =F F =F =x cm F =(0-x) cm F x =6 +(0-x) 0x=6 cm x= (cm) 0 F= F= F= F F F =F F =F =x cm F =(8-x) cm F x =6 +(8-x) 6x=00 x= (cm) F =F = cm =" 6 +8 =' 00=0(cm) F =F +F + = + +0 = (cm) cm F F 60% 0% F 0%

06 =" 0 - =' 6=6(cm) =-6=(cm) =" + =' 69=(cm) 07 =x cm =(+x) cm =(') -(+x) =-0x-x yy = -x =-x yy -0x-x =-x 0x=0 x=(cm) cm 08 = =" + =' = =" (') + =' = =" (') + ='= = - =-' -' 09 + = + (') +x =(') +('ß) x = x= ( x>0) y=" - ='9= x+y=+=8 8 00 =" + ='å=(cm) + =, + = cm cm cm cm =90. = + = + =0+6=6(cm ) 6 cm 0 +Q= 7 cm Q cm = =_{ _7_}=8(cm ) 0 EE E + E= E E= F= LF= = G= GL= FML LMG E= FG= + E+ FG 0 EF = EF =(cm) ( EF >0) F =E = cm E =+=9(cm) E =" +9 ='9å7(cm) = =('9å7) =97(cm ) 06 =" (') +(') ='= =" +(') ='6 =" ('6) +(') ='8=' E =" (') +(') ='ß0 97 cm FE= _'å0_'=' 07 E = = _0=(cm) E + =E + 7 + = +0 =76 ='ß9(cm) ( >0) 'ß9 cm 0 =6 =6(cm) ( >0) =00 =0(cm) ( >0) =" 0-6 ='6å=8(cm) = _8_6=(cm ) cm 08 x x = + x = x='ß ( x>0) =x + x =9 x= ( x>0) x 'ß 'ß 0 +Q=R p+q=0p Q=8p(cm ) _p_{ } =8p, = =(cm) ( >0) 09 x= > + x='7 =('7) + x=' (') > + x=6 6 > +

RM 00 = _(0-6)=(cm) =" 8 - ='6å0='å(cm) = _(6+0)_'å =6'å(cm ) 0 L FG M =" -7 =' 0='ß0(cm) F= LF= FML = E= 0 8cm 6cm 0 cm 6'å cm = _('ß0) =60(cm ) 60 cm : = : =0:6=: =a =a(a>0) (a) =6 +(a) 6a =6 a =6 a= ( a>0) E F I 7 cm L cm =_= 0 x+y= x y = = =" + ='ß= _ = _ _=_ = 0 E =x cm 'E =E =x cm E =(-x) cm 'E (-x) =x + 0x=00 x=8(cm) 0 = E = E E= E E E =E M G 8cm E =x cm E =E =(8-x) cm E (8-x) =x + 6x=8 x=(cm) E= =6(cm ) 06 E =x cm E =E =(6-x) cm = = _6=(cm) E (6-x) =x + x=7 x= (cm) 9 7 7 E= = (cm ) cm 8 8 07 + = + 0 +70 = +(0'å0), x =00 x=0(m)( x>0) 0 000 08 _60_60=60( ) 9 60 E =E =, = =(cm) ( >0) =øπ -(') =(cm) = =' cm, E = = cm E= _(+' )(+') =+'(cm ) 09 = E, = E E= E, E E =E. E =E =x cm E =(8-x) cm E x =(8-x) +, 6x=80 x=(cm) E= =0(cm ) 0 cm 00-9<x<+9 <x< x> <x< yy <90 x <9 +, x <

0<x<, <x< <x< x 0% <90 x 0% x 0% 0 + = + (') + = +6, =9 = ( >0) =" - =' = '=' ' 0% 0% 0% 0 =x cm = _ (') =x(x+), x +x-8=0 (x+8)(x-6)=0 x=6 ( x>0) = _ =_6= ='(cm) ( >0) ( )= = _8_' =8'(cm ) 8' cm 0% 0% 0% 0 =" ('6) +(') =' = = _ (') =_ = =" (') - ='ß=' M = M = M = = _=6 MÚ =6-= M _MÚ = M _ ' '_=6_ = ' 0% 0% 0% 0% 0 -<a<+ 7<a<7 a>, a > + a> ( a>0), <a<7 a<, > +a 0<a<' 9, 7<a<' 9, <a<7 7<a<' 9 a 8, 9, 0,,, 6 8+9+0+++6=7 7 0 S +S = S +S = = + S = =_= 06 MÚN M MÚN = =x MÚN = x MN M +N =MÚN + 6 +8 ={ x} +x x =00 x =80 S S S N 6 x='( x>0) '

RM 07 M N M =Q =Q =a N 6 8 =E =E =b a a Q a N (a) +b =8 yy MQ a +(b) =6 yy b b E b + a +b =00 a +b =0 MÚN =" a +b ='ß0=' ' 08 09 00 0 0 " + ='ß0='(cm) ' cm " 8 +6 =' 00=0(cm) 0 cm '_='(cm) ' cm '_='(cm) ' cm 0 x=" 7 - ='ß0='ß0 'ß0 0 'x=' x= 0 ' h= _6='(cm) ' S= _6 =9'(cm ) h=' cm S=9' cm 0 ' h= _'=(cm) ' S= _(') ='(cm ) h= cm S=' cm 06 ' h= _8='(cm) ' S= _8 =6'(cm ) h=' cm S=6' cm 07 ' h= _'='6(cm) ' S= _(') =8'(cm ) h='6 cm S=8' cm 08 ' a a=' a=0 0 09 ' a a =' a =6 a= ( a>0) 6

060 6:x=: x=6 078 M 6:y= : ' y=6' x=6 y=6' ' M = _6=' ' 06 x:= : ' x=' y:= : ' y=' x=' y=' 06 8:x=: x= 8:y= : ' y=' x= y=' 06 x:'= : ' x=6 y:'= : ' y= x=6 y= 079 = M = _'=' ' 080 =øπ - =øπ6 -(') ='å='6 '6 06 ' :x= : ' x=8 8:y= : ' y=' x=8 y=' 06 : x= : ' x=6' 6' : y= : ' y=6'6 x=6' y=6'6 08 = _ _ ' = _{ _6 }_'6 =8' 8' 066 067 068 069 070 07 07 =" + =' ' Q =" + ='å 'å Q =" (-) + (-) ='ß8=' ' R =" (-) + (-) ='ß7 'ß7 =" +(-) ='ß0=' ' =" (--) + {--(-)} ='ß= =" (--0) + (0-) ='ß9 'ß9 08 '6 ' _'=' ' 08 ' _ =' ' 08 '6 a a='6 a= 08 a ' a =8' a =6=6 a=6 6 07 =" (-7) +( --) ='ß=' ' 086 = = _6'=' ' 07 07 076 " +8 +6 =' 6='ß9(cm) 'ß9 cm '_='(cm) ' cm " x + + ='ß x += x =6 x= ( x>0) 077 'x=6' x='6 '6 087 V V =øπv - =" -(') ='7 '7 088 = _ _V = _6 _'7 ='7 '7 7

RM 089 = = _'=' V V =øπv - =øπ6 -(') ='å8='7 ( )= 09 = 09 = 09 09 =" - ='ß6= =" 8 - ='ß _ _ = _(p_ )_ =p _(p_ )_'ß='ßp p 'ß 'ßp =" (+) + ='ß80=' ' 09 x cm " 6 +x ='å, 6+x = x =6 x= ( x>0) 6_=(cm ) _ _V = _ _'7 = '7 090 = = _6= V V =øπv - =" 8 - ='å ( )= '7, '7 _ _V = _(') _'å =6'å 'å, 6'å 096 k cm k cm(k>0) " (k) +(k) =0 k=0 k=(cm) _=6(cm) _=(cm) =6_=9(cm ) 9 cm 097 a cm (a-) cm (a+) cm (a-) +a =(a+) a -a=0 a(a-)=0 a= ( a>) +=(cm) 098 x cm (x) +x =(0') 0x =00 x =0 =" (x) +x ="çx ='ƒ_0=' 00 =0(cm) 0 cm 099 ='_=' EFG G =" ('6) +(') ='ß7=6' +G ='+6'=9' 9' 000 x cm 'x=0 x='(cm) _'=0'(cm) 00 '_=6'(cm) '_6'=(cm) 00 a 'a='6 a=' _'=' =(') -p_(') =-p -p 0% 0% 0% 8

00 =" 0 + =' ='(cm) _ = _ 0_='_ ='(cm) 00 =" 6 + =' 00=0 = _ 6 = _0 = _ = _ 6_=0_ = ' cm 6 8 8 + = + = 00 =" 9 + =' =(cm) = _ 7 9 = _ = (cm) Q(R ) 7 Q = = cm 7 Q =-_ = (cm) cm 006 8 =" (') + ='ß6=(cm) _ = _F '_=_F F ='(cm) F F =" -(') =(cm) E F(R ) E =F = cm EF =-(+)=(cm) EF= ' ='(cm ) 007 ' cm a cm ' a =8' a =7 a=6'(cm)( a>0) ' = _6'='6(cm) ' E= _('6) 7' 7' = (cm ) cm 008 a cm ' a =9' a =6 a=6(cm)( a>0) ' = _6 ='(cm) 009 = G = _=6(cm) 6cm a cm ' a=6 a='(cm) ' = _(') ='(cm ) ' cm 0% 0% 0% 00 E =E =F = _8=(cm) GE cm ' GE= _ ='(cm ) ' = _8 =6'(cm ) =_( - GE) =_(6'-') ='(cm ) ' cm cm 6 ' 6_{ _ }='(cm ) 0 8cm cme 8cm 6 ' 6_{ _8 }=96'(cm ) G F 9

RM 0 0 0% 60% 0% 0 a cm ' 6_ a =' a =6 a=(cm)( a>0) 6_=(cm) cm a cm ' a= a='(cm) ' = _(') ='(cm ) 6 =6_' =8'(cm ) a cm ' _ a =' a =6 a=8(cm)( a>0) _8=(cm) 60 60 60 cm 8' cm 06 = = _=7(cm) =" 0-7 ='ß(cm) = 'ß =7'ß(cm ) 07 = =_=0(cm) cm _0_ = =(cm) G G = = _=(cm) G G =" + ='å6(cm) 08 0 cm cm 0 cm 7'ß cm 'å6 cm cm = cm = = _(-)=0(cm) 0 cm = = _=6(cm) cm =" 0-6 ='ß6=8(cm) = 8 =8(cm ) 8 cm 0 = = 8' cm _8_ =8' ='(cm) = _8=(cm) =" +(') ='ß6=6(cm) + + =6+8+6=0(cm) 8cm 0 cm 09 =x =-x = -x yy =0 -(-x) yy -x =0 -(-x) x=0 x= =" - =' = = =6 0 x -x 0

00 =x =6-x = -x yy x 6-x = -(6-x) yy -x = -(6-x) 9 x=7 x= 9 7 '7 =æ -{ } =Æ = '7 6 0 =x cm =(8-x) cm =9 -(8-x) yy =7 -x yy 9 -(8-x) =7 -x 6x= x=(cm) =" 7 - ='ß='(cm) M = M - =-=(cm) M M =" (') + ='ß9=7(cm) 7cm 0 : = : ' : 6= : ' ='(cm) : = : ' :'= : ' ='6(cm) = = ='6 cm = _'6_'6 =(cm ) cm 0 : =: : =: =6(cm) = = _60 =0 : = : ' : 6= : ' ='(cm) ' cm 0% 0% 0% 0% M 0% M 0% 0 =x =h h =('ß) -(+x) yy h =(') -x yy ('ß) -(+x) =(') -x x= x= h=" (') - ='= = = ' ' x h 06 = E=90 EF ' = _=6'(cm) : = : ' :6'= : ' ='6(cm) 07 : =: : =: =6 : = : ' 6: = : ' =6' 0 '6 cm 0 : = : ' : = : ' ='(cm) : =' : ' : =' : ='6(cm) 08 : =: 8: =: = 8 60

RM : = : ' 8: = : ' =' = =8 =+8= = _(8+)_'=0' E= = _90 =0 E :E =' : 9:E =' : E ='(cm) E = -E =9-'(cm) (9-') cm 09 =80-0 =60 : = : ' 6: = : ' ='(cm) : =: 6: =: =(cm) =" (+) +(') ='ß9(cm) 00 6cm E F "6 cm 60 E :E :E =' :: '6 :E :E =' :: E =E ='(cm) F =E =' cm E F F F :F = : ' F :'= : ' F =(cm) = _{6+('+6+)}_' =+'(cm ) 0 60 = 8 a cm a : = : ' a='(cm) +a=+_' =+'(cm) 0 a cm cm cm a cm a =8 a=9(cm)( a>0) 6cm 0 60 cm 'ß9 cm (+') cm (+') cm 0 : =: :8=: =(cm) : =' : :8=' : ='(cm) = = ' =8'(cm ) yy 8' cm 0% 0% 0% 0 : =: :=: =(cm) : = : ' : = : ' ='(cm) Q = = cm Q = -Q ='-(cm) QRS QRS=Q =('-) =-'(cm ) 0 " (-) + (-) =' " + ='ß " (0-) +( --0) ='ß9 " {-(-)} +(--) ='ß= " {--(-) } +{-7-(-)} ='ß7 06 (-') cm =" (a-) +( --) =' (a-) +(-) =(') a -a-=0 (a+)(a-8)=0 a=- a=8 a<0 a=-

=" {-(-)} + (-) ='ß =" {(-a)-} +(-a) =" a -a+ = =a -a+ a -a-=0 a -a-6=0 (a-)(a+)=0 a=- ( a<0) x (a, 0) = y 7 " {a-(-)} +(0-ç) =" (a-) +(0-7) - x (a+) + =(a-) +7 a=60 a= (, 0) - - (, 0) 00 =" (--0) + (-) ='8=' =" {--(-)} +(--) ='ß6 =" {0-(-)} + {-(-)} ='ß7 > + 0 =" {7-(-)} + (8-) =' 00=0 =" (-7) +(-6-8) =' 00=0' =" (--) + {-(-6)} =' 00=0 = = + =90 = _ _ = _0_0=0 07 y= x y=x+ x =x+ x -x-8=0 (x+)(x-)=0 x=- x= x=-y= (- ) x=y=8 ( 8) =" {-(-)} + (8-) ='ß7=6' 6' 08 y=x -7x+7 y=x+ Q x -7x+7=x+ x -8x+=0 (x-)(x-)=0 x= x= x=y= x=y=7 ( ) Q( 7) ( 7) Q( ) Q =" (-) + (7-) ='8=' ' 09 =" {-(-)} +(--) ='ß7 =" (7-) +{ --(-)} ='ß=' =" (--7) + {-(-)} ='ß90='ß0 < + 0 =90. = + {-(-)} +{7-(-)} ={(--a) +(--) }+{(-a) +(7-) } a -a-=0, (a-7)(a+)=0 a=7 a=- a 7+(-)= 0 ' = ' + = ' + æ ' 9 ' ' ' ' '' ' =" +9 =' = + 0 x ' '( -) + ' =" (-) + {-(-)} ='ß='ß y x - '

RM 0 y y ' '(- ) ' + - x ' =" {-(-)} +(--) ='ß8 - 'ß8 06 ' ( ) 9 km 6 km km ' 0 km ' =" 0 + =' 6=(km) km 07 =x cm " + +x =' +x =0 x =6 x=(cm)( x>0) 08 =x cm " x + + =' x +=0 x =9 x=(cm)( x>0) G G =" + ='ß(cm) FG cm 'ß cm FG=_'ß='ß(cm ) 'ß cm 0% G 0% FG 0% 09 00 k, k, k(k>0) ( )=k_k_k=8 6k =8, k =8 k= cm, cm, 6cm " + +6 ='å6='å(cm) 'å cm x cm = =" x +6 +8 =" x +00 =x+x=x =90 + = (x +00)+(x +00)=(x) x =00 x=0(cm)( x>0) =x=_0=0(cm) 0 a cm EG =" a +a ='a(cm) EG= _E _EG = _a_'a ' = a ' a =8' a =6 a=6(cm)( a>0) G ='a=6'(cm) 0 a cm 'a=' a='6(cm) '6_'6_'6=6'6(cm ) 0 0 cm a cm 'a=' a=(cm) F ='_='(cm) F F F= _F _F = ' =8'(cm ) 8' cm 0 MGN M =MÚG =G N =N =" +0 =' ='(cm) MGN MÚN =F ='_0=0'(cm) G ='_0=0'(cm) MGN= _MÚN _G MGN= _0'_0' =0'6(cm ) M F E 0 cm G N 0'6 cm

MGN 0% MÚN 0% G 0% MGN 0% 0 F F =F = ='_='(cm) ' F= _(') =8'(cm ) I =h cm _ F_h= _ _F _8'_h= _{ }_ ' ' h= h= (cm) cm 8' 06 G =G = ='_='(cm) G ' cm ' G= _(') =7'(cm ) E =øπ(') +6 ='6å='7(cm) F =" 6 +6 ='7å=6'(cm) (6') =('7) +, F =E +EF EFEF=90. EF= _E _EF = _'7_ 9'7 = (cm ) 07 7' cm G =" + +(') ='ß6=(cm) EG =" + ='8='(cm) EG E _EG =G _EI 9'7 cm '_'=_EI EI =(cm) cm 08 M =MÚF =xcm E E =" 6 +(x) =" 6+x M M =" +x =" +x EM E = M " 6+x =" +x 6+x =+x x =08 x =6 x=6(cm)( x>0) M =MÚF =6 cm M +MÚF =6+6=(cm) cm 09 '6 a cm a=6 a='6(cm) ' = _('6) =7'(cm ) 7' cm 060 9cm = '6 _9='6(cm) E, E ' 9' E = _9= (cm) 9' = E = _ ='(cm) 7' = _'_'6= (cm ) ' ' _9 = (cm ) 9 cm 7' ' cm cm ' 06 MÚ =MÚ = _ M ='(cm) M ' cm ' cm = = = _=(cm) cm M MÚ =" (') - ='8='(cm) M= _ _MÚ = '='(cm ) ' cm 06 M = = ' '6 _'='(cm) _'=(cm) MÚ = M = _=(cm) M= _MÚ _ = '='(cm ) E

RM ' = _(') ='6(cm ) 06 ='_6=6'(cm) = ='(cm) =" 9 -(') ='ß6='7(cm) = _6 _'7 =6'7(cm ) 06 ' =æ -{ } ' = (cm) =_ ' =_{ _ _ } =9'(cm ) h cm E 6 cm 9 cm 6 cm E cm E ='_='(cm) ' = = (cm) 06 ='_=' = =' =" 8 -(') ='ß6='ß = _ _'ß= M M =" 8 - ='ß60='ß = 'ß='ß =_+'ß_ =6(+'ß) 066 'ß 'ß E MÚN = E = _=(cm) M =N = ' _='(cm) 9' cm 8 6(+'ß) M MN Q =MÚN = cm =Q = _(-)=(cm) M MÚ =" (') - ='ß(cm) MN= _(+)_'ß ='ß(cm ) 067 M r cm pr=6p r=(cm) =" 6 - ='ß7='(cm) = _p_ _'=9'p(cm ) 068 r cm pr =6p r =6 r=6(cm)( r>0) " 0-6 ='ß6=8(cm) _6p_8=96p(cm ) = 6= ' = =' cm 069 _p_(') _'=8'p(cm ) = = cm = - =9-=(cm) =" - ='9=(cm) _p_ _9=7p(cm ) cm N ' cm ' cm cm Q cm 'ß cm 9'p cm 0 cm r cm 6cm 96p cm 8'p cm 7p cm 0% 0% 0% 6

070 : = : ' 8: = : ' ='(cm) : =: 8: =: =(cm) l 6' _p_ _'= p(cm ) 8cm 0 cm 6' ' cm p cm 07 " +('ß) ='ß6=8(cm) x p_8_ 07 x 60 =p_ x =90 " 0-6 ='ß6=8(cm) p_8 =6p(cm ) 8cm x cm 90 07 x x p_6_ =p_ 60 x =0 6cm =" 6 - ='ß='(cm) = _p_ _' cm 6' = p(cm ) 07 0 ' cm r cm pr=p r=(cm) =" 0 - =' 6 =6(cm) 07 r= p_9_ 0 60 =pr =" 9 - ='ß7=6'(cm) 6' p cm 0 cm cm 6 cm = _p_ _6' 9cm =8'p(cm ) cm 6' cm 8'p cm 076 r cm p_r =00p r =00 r=0(cm)( r>0) =" -0 =' =(cm) 077 = =7 cm =" 7 - ='ß='6(cm) p_('6) =p(cm ) 078 =" (+6+) + =' 69=(cm) 079 cm 6cm cm 7cm 7cm G F cme cm cm G G G =" (8+) + 8 F =' 69= 080 F F =" (+) +7 ='ß98=7' E F 7 7' 7

RM 08 ' F' 7 F' =" (+8++8) +7 F E 8 G 8 F' =' 6= 08 ' ' =p_8=6p(cm) ' =" (6p) +(p) ' =" 00p =0p(cm) 08 ' =p_=8p(cm) =" (0p) -(8p) =" 6p =6p(cm) 08 6p cm p_=6p(cm) " " =" (p) +(6p) =" 00p =0p(cm) 0p`cm ' p cm ' 8p`cm ' '' ' ' 6p cm 6p`cm 6p`cm ' '' 6p`cm 0p cm 0% " 0% 0% 08 : = : ' 6: = : ' ='(cm) = =_'=6'(cm) 6 cm 60 60 0 0 086 x x p_0_ =p_ 60 ' x =90 ' ' ' =" 0 +0 =' 800=0'(cm) 087 x p x =90 x 60 =p_ M M M =" + ='ß0='(cm) 088 0 cm x : = : ' ' : = : ' =6(cm) : = : ' : 6= : ' ='(cm) 089 ' 0 cm cm x cm M a cm a =9' a =6 a=6(cm)( a>0) = ' _6='(cm) G cm 0' cm ' cm ' cm G = = _'='(cm) ' cm 090 a cm (a) +a =('), 0a =0 a = =" (a) +a ="ça ='ƒ_=(cm) 09 : = : ' 8: = : ' =8' = =8 = + =8'+8=8('+) = _8('+)_8=('+) ('+) 8

09 = ' _8='(cm) ' E= _(') ='(cm ) 09 =" {-(a-)} +(a-) =' (-a) +(a-) = a -a+0=0 a -7a+0=0 (a-)(a-)=0 a= a= a +=7 09 =" (--0) + (-a) =" a -0a+0 =" (-0) + (-a) =" a -6a+0 = a -0a+0=a -6a+0 a=0 a=0 09 '_='(cm) = _'=6'(cm) 096 ='_8=8'(cm) = = _8'='(cm) =" 9 -(') ='ß9=7(cm) 7cm 097 y= x y=x+6, x x =x+6, x -x-=0 (x+)(x-6)=0 x=- x=6 x=-y= (-, ) x=6 y=8 (6, 8) =" {6-(-)} +(8- ) =' 0=8' 8' 098 =" (-) +(--) ='å7 =" (--) +{-(- )} ='å =" (--) +(-) ='å7 = + = =90. = _ _ = _'å7_'å7=. 7 099 =x =x = =" + +x =" +x = =90 : = : ' " +x : x= : ' x=" 0+x x =0+x x = x= ( x>0) 000 = = = _0= =" - =' = = _0_=60 60 00 a b c =a +b = yy G =a +c = yy G =b +c = yy + + (a +b +c )= a +b +c =6 " a +b +c ='ß6 00 ' =p_=8p(cm) =" (8'p) -(8p) =" 6p =8p(cm) 00 l ' ' ' =" +0 =' ='ß6 00 E =6 cm E =', E 6=' E ='(cm) E, F, G EF F E =' 6 ' 8"p cm 8p cm E ' ' 8p cm 0 F 6cm l 0 G 9

RM 9 F '=' F = (cm) 9 E= _ _G = _6_ 7 7 = (cm ) cm '6 00 = _='6(cm) ' M = _=6'(cm) = M = _6'='(cm) = _'_'6 ='(cm ) 006 E =" 6 + ='ß='(cm) F =" 6 +6 ='ß7=6'(cm) EF =" 6 - ='ß7='(cm) ' cm F =E +EF EFEF=90 EF= _E _EF = _'_' 9'ß 9'ß = (cm ) cm 008 ' a cm a =8', a = a='(cm)( a>0) ' cm. E E ='_'=8(cm) = E = _8=(cm) =øπ(') - ='å6=(cm) ' cm ' cm 8 ( )= _(') _= (cm ) ' cm 8 6 6 _ = (cm ) cm 009. km km km (-)km ( )=x+=" 9 + +=' + =+=7(km) km x km E 7 km 007 : =: 6: =: =(cm) =p_ =9p(cm ) = =_=6(cm) : = : ' 6: = : ' ='(cm) ' cm = _p_ _'=9'p(cm ) x p_6_ x 60 x =80 =p_ 6 cm x cm 00 x p_0_ x =90 x 60 =p_ M M M =" 0 +0 =' 00=0'(cm) 0 = + + = + E =+ F =6( +E +F ) 0 cm x 0 cm M ' cm 0' cm F E cm 0

= ' 6( +E +F )=6' +E +F =6'(cm) 0 _ =6'(cm ) : = : 9:6=: = =9 -(++ ) yy =6 - yy 9 -(++ ) =6-0 =0 = =" 6 - ='ß=' 6' cm = _(+)_'=0' 0' 0% 0% 0% 0 G- _ _G = _{ _'_'}_' =9'(cm ) G G =G = ='_'=6(cm) ' G= _6 =9'(cm ) -G _ G_I = _9'_I =' I ' I =9' I ='6(cm) '6 cm G- 0% G 0% -G I 0% I 0% 0 r cm 0 p =pr r=(cm) 60 =" - =' 8=8'(cm) cm cm 8' _p_ _8'= p(cm ) 0% 0% 0% 0 = :=: =(cm) : =' : :=' : ='(cm) = = cm l _p_(') _=8p(cm ) cm cm 8' p cm l 8 _p_ _= p(cm ) 8 6 8p- p= p(cm ) cm 6 p cm,, 0% 0% 0% 0% 06 p_=6p(cm) ''' ''' =" (6p+6p+ 6p) +(9p) '''=" 0p =9'p(cm) ''' '' ' ''' '' ' 6p`cm 6p`cm 6p`cm 9p`cm 9'p cm

RM ' 07 M =N = _=6'(cm) MÚN = = _=6(cm) MÚN 6' cm 6' cm MÚ =N = MÚN =(cm) M M N cm 6 cm =" (6') - ='ß99 ='ß(cm) MN= _6_'ß=9'ß(cm ) 9'ß cm 08 =0 '=0 +60 =90 ' =" -6 =' 08=6'(cm) =" (6') + =' ='7(cm) 09 =0 : = : ' : = : ' =' Q = =' Q = = ='++'=+' ' ' = = _(+') =6'+ cm ' 60 cm 0 cm 0 '7 cm Q 6'+ 00 0 0 0 0 0 06 07 0 sin = = = 6 ' ' cos = = = 6 ' tan = = = ' ' ' sin = = = 6 cos = = = 6 ' tan = = =' ' =" - ='7 '7 sin = = cos = = '7 '7 tan = = 08 x sin = = 9 x=8 x=6 6 09 '7 x ' cos = = x=' x=6' 6' ' ' ' '7 00 0 ' tan = = x 'x=0 x=0' 0' 0 sin 0 +cos 60 = + = 0 ' +' tan +sin =+ = +'

' ' tan 60 -sin 60 ='- = ' 0 08 cos x= = = 0 ' sin +cos ={ } ' +{ } = + = 09 00 tan x= = = 0.79 0 ' ' tan 0 _cos 0 = _ = 0 0.6 06 cos 0 tan 60 = ' ' 0.8 ' = _ = ' 0 tan 0 +sin 0 =0+0=0 0 07 0 0 sin 0 +cos 0 =0+= 08 0 0 tan 0 +cos 90 +sin 90 =0+0+= 09 00 60 60 06 sin 90 _sin 0 =_ = 0 07 cos 90 +sin 0 _sin 90 =0+0_=0 0 0 08 < < 0 x ' tan 0 = = x=' 6 6 ' cos 0 = = y=' x=' y=' y 0 ' cos = = x=' x y tan = = y= x=' y= 0 x cos 60 = = x= y ' sin 60 = = y=' x= y=' 06 x sin 0 = = x=' ' y ' cos 0 = = y= x=' y= ' 09 060 06 06 06 06 06 066 067 > > < < > < < < = > 0.7 07 sin x= = = 068 0.69

RM 069.0 080 sin = = =60 0 070 0.77 = =" 0 - =' 6=6 07 07 07 07 07 076 0.680.98 0 9 =" + ='ß0=' ' sin = = ' ' cos = = ' ' sin = = ' ' cos = = ' tan = = 077 =" 0-8 ='ß6=6 6 8 sin = = cos = = 0 0 7 sin +cos = + = 7 078 =" ('ß) - ='ß= =" - =' = sin = = 08 tan = 6 = =6 = =" 6 + ='ß0='ß0 'ß0 sin = = = 'ß0 'ß0 0 0 08 =' ' cos = = =' =" -(') ='ß6=8 = _'_8=6' 6' 0% 0% 0% 08 =x =y y ' ' sin = = y= x x x =6 +y x =6+ x x =6 x =8 9 9 x=9( x>0) 9 08 sin = 6 =" 6 - ='ß 'ß 'ß cos _tan = _ = 6 0 6 079 =" - ='8å=9 tan x= = = 9 =" - ='å= tan y= = 6 tan x_tan y= _ = 6 08 tan -=0 tan = =" + ='ß sin = 'ß = 'ß

cos = = 'ß 'ß 'ß 'ß + sin +cos = = sin -cos 'ß 'ß - 086 cos -=0 cos = =" - =' ' ' sin = tan = ' ' 0 sin _tan =0 = cos 0% 0% sin tan 0% 0 sin _tan 0% 087 =90 sin(90 -)=sin = 7 =" 7 - ='6å=8 8 tan = 8 088 =" 9 + =' = ª ª ( ) 9 x= sin x= = = 9 y= cos y= = = 6 sin x+cos y= + = 6 089 ª ª ( ) = = sin = 7 090 =" 6 +8 =' 00=0 ª = x 8 sin x= = = 0 6 x 0 6 cos x= = = 0 sin x-cos x= - = 09 = _ =8_0=80 =' ( >0) ª ( ) = ' ' cos x=cos = = = ' 0 09 =" 8 + =' 89=7 ª E( ) x= 8 cos x=cos = = 8 7 7 09 =" 9-6 ='å=' ª E( ) x= ' ' cos x=cos = = = ' 9 09 E E =øπ('7) - =' ª E( ) = E '7 sin = = =, E '7 7 E ' 'å cos = = = E '7 7 '7 'å ' sin _cos = _ = ' 7 7 7 7 09 E E =" 9-7 ='å=' ª E( ) = E E ' E ' sin x= =, tan x= = 9 E 7 sin x ' 7 7 = _ = 7 tan x 9 ' 9 9 x 8

RM 096 x y x-y+8=0 y=0 x=-8 (-8 0) x=0 y= (0 ) =8 = =" 8 + ='ß80=' sin a_tan a= 097 _ ' = _ = ' ' 8 0 0 x y x+y-6=0 y=0 x= { 0} x=0 y= (0 ) = = tan a= = = 098 x y y y= x+ y=-x+ y=0 x=- (- 0) a x=0 y= (0 ) = = - x =" + ='ß9 7 sin a+cos a= + = 'ß9 'ß9 'ß9 7'ß9 sin a+cos a= 7'ß9 9 9 099 x y y=x- y=0 x= { 0} x=0 y=- (0 -) = =æ{ } + =Æ;%;= ' sin a= = = ' ' = y a a x y=x- ' cos a= = = ' ' sin a-cos a={ } ' -{ } 000 = - = EGEG=90 EG =" + =' E =" + + =' EG ' '6 cos x= = = E ' 00 FF=90 F =" 6 +6 =6' =" 6 +6 +6 =6' F 6 ' sin x= = = 6' F 6' '6 cos x= = = 6' F 6 ' tan x= = = F 6' ' '6 ' sin x_cos x-tan x= _ - ' ' = - ' =- - ' 6 6 00 FF=90 F =" 8 +6 =' 00=0 F =" 8 +6 + =' 6='ß9 'ß9 sin x= = = F 'ß9 9 F 0 'ß9 cos x= = = F 'ß9 9 'ß9 'ß9 0 sin x_cos x= _ = 0 9 9 9 9 00 EGEG=90 EG =" + ='ß= G =" + + ='ß0=' E sin x= = = G ' EG cos x= = = G ' ' ' E tan x= = = EG 6

tan x _ = = = sin x_cos x ' ' _ EG G 0% sin x cos x tan x 0% 0% ' +' 00 = + = ' ' ='_ -'_ = -= ' ='_ -_ =-=0 ' =' -=-= ' ' = _ - = - = 6 00 006 007 '- 6 ' ' ={- - } {+ - } ' ' ={ - } { + } = - =- - ' '_ -_ ='_'+ ' '_ +_ - =+ =- = + 80 =80 _ = ++ ' sin =sin = ' cos =cos = tan =tan = ' ' sin _cos _tan = = 008 cos 60 = x+0 =60 x= tan x-sin x=tan -sin 0 =- = 009 sin 60 = x-0 =60 x=0 ' sin =cos = x= tan x=tan = cos = ' x+ = ' x=0 tan x+ tan 0 + = = tan x- tan 0 - ' + ' - '+ = =--' '- tan 60 =' x-0 =60 x=0 sin x-cos(x+0 )=sin 60 -cos 0 ' ' = - =0 0 --' 0 00 tan = 60 -x= x= =cos _sin 0 ' ' = _ = ' 0 (x-) =0 x= ( ) cos = =60 60 ' 0 sin = = 6' = =6 6 ' sin 60 = = ' = =' ' 0 tan = = =6 6 6 ' sin 60 = = ' = =' 7

RM 0 =60-0 =0 = =x ' cos 60 = = x=' x y tan 60 = =' y=6 ' xy='_6=' ' 0% x 0% y 0% xy 0% 0. = =6. = =. 6 =. +. = ' sin = = 6 =6' =' ' cos = = 6 =6' =' ' tan. = = ='- '- 6+' 0='_(-)+b b=' ab='_'=6 6 09 =tan 60 =' y='x+b(' 7) 7='_'+b b= " - 60 y='x+ ' x - y ' 8' = 8' 0% 0% 0% 00 z= y sin z=sin y= = = 0 0.66. cos 9 = =0.66 tan 9 = =. y x cos 9 +tan 9 =0.66+.=.8.8 06 ( )=tan = y=x+b(0, ) =0+b y=x+ 07 y= =tan 0 = ' ' x+b(- 0) ' 0= _(-)+b b=' ' ' y= x+' y= x+' 08 a=tan 60 =' y='x+b(- 0) 0 = y (cos x sin x) (cos x cos y) (sin y sin x) (sin y cos y) 0 =80 -(90 +6 )= cos =0.9 cos = = =0.9 0 =.9.9 0 sin 0 +tan 0 +cos 90 =0+0+0=0 tan 90 sin 90 +cos 0 =+= 8

' ' sin 60 = cos 0 = sin 60 =cos 0 cos 90 -sin 90 =0-=- 0 06 07 ' =_'-_0+ ' ' ='+ = ' ' ' = _- _+ ' +' = - +'= +',,, ( )= = + 08 0 < sin <cos sin <cos < 90 cos <sin sin 7 >cos 7 0 90 cos cos 8 >cos 0 0 90 tan tan 0 <tan 0 tan = tan 0 > 0<cos 70 < tan 0 >cos 70 09 0 <x< sin x<cos x sin <cos <sin 80 <cos 0 <tan 6 sin cos sin 80 cos 0 tan 6 0 0 <<90 0<sin < sin +>0 sin -<0 =sin +-(sin -) = 0 0 << 0<sin <cos sin +cos >0 sin -cos <0 =(sin +cos )+(sin -cos ) = sin 0 << 0<tan < tan -<0 tan +>0 =-(tan -)+(tan +)= 0 0<cos x< <x<90, cos x<sin x sin x-cos x>0 -cos x>0 sin =(sin x-cos x)-(-cos x) =sin x- sin x- 0 ' <<90, 0<cos <sin cos -sin <0, sin +cos >0 " (cos -sin ) +" (sin +cos ) =-(cos -sin )+(sin +cos ) = sin sin =' sin = =60 tan =tan 60 =' ' ' 00 <<90 cos <sin < tan = <tan cos <sin <tan 06 = cos = 7.7 0 =0.77 0 0 x 90 sin x 0 cos x 0 sin <sin =cos <sin 80 < yy cos 0 = yy tan = tan x 0 tan <tan 6 <tan 6 yy 07 x=7 y=9 x+y=7+9=76 76 08 =80 -(90 +0 )=0 cos 0 = =0.7660 0 =7.660 7.660 9

RM 09 =80 -(90 + )= sin = =0.76 00 =7.6 cos = =0.89 00 =8.9 + =7.6+8.9=9.8 9.8 0% 0% + 0% ' ' = _ - ' = 6 ' ' ' ' ={- }{ + } ' ' ={- }{+ } =- = = - ' ' + - 00 ' sin = = ' = =' =" (') - ='ß=' ' sin = = = ' '6 = - +' -' (-')-(+') = (+')(-') -' = =-' ' -' 6 0 : =: =k =k k>0 =" (k) -(k) ='k 'k ' tan = = = ' k 8.9 0 sin = =0.89 0 sin =0.89 = cos = =0.76 0 =.76.76 0 sin = = =0 =" 0 - =' 6=6 6 cos -tan = - 0 6 = 0 0 0 ' ' = { } -'_ ' = - ' ' '- 0 cos 0 -cos 60 = - = '- x -ax+=0 x= '- { } '- -a_ +=0 (-')a=('-) ('-) a= = -' =' 06 cos x=0.7 ('-)(+') (-')(+') 07 sin = = 8 =8' =' ' tan 60 = =' '6 ' =' = 08 tan = x+ = x=0 ' 0

sin x+cos x=sin 0 +cos 60 = + = ' sin 60 = x-0 =60 x= tan x-cos x=tan -cos 90 =-0= ' sin =cos = x= tan(x+ )+tan(7 -x)=tan 60 +tan 0 ' ' ='+ = 09 x-y+6=0 x y (- 0) (0 ) = = =" + ='ß sin a+cos a= + 'ß 'ß ' x-y+6=0 a - y 'ß sin a+cos a= = 'ß 'ß 00 = = =80-0 =60 ' sin 60 = = =' =6' 6' 0 =tan = y=x+b(- 0) 0=-+b b= y=x+ x y=x+ 0 sin = =" - =' = 90 - tan(90 -)=tan = = 0 tan = sin = <x<90 cos x<sin x<tan x ' <sin x< 0<cos x< ' ' cos 0 <sin <sin 0 <tan <tan 0 0 sin x= cos x= tan x= x cos x sin x x=0 0 x=90 0 x< sin x<cos x <x 90 sin x>cos x 0 x 90 sin x>cos x tan = tan x 0 sin x x<90 sin x<tan x x= sin x=cos x= 0 ' =" - =' = ª ª = x = y x sin x+sin y= + 7 = + = 7 06 sin 0 = = 6 =6 = =60 = =0 y ' tan 0 = = y=' y=' ' sin 0 = = =' = =0. = =' x=' x-y='-'=' '

RM 07 <x<90 sin x<tan x sin x-tan x<0 tan x-sin x>0 =-(sin x-tan x)-(tan x-sin x) =0 08 = = =0 = = tan 60 = =+' _0 = = +60 =7 cos 60 = = tan 7 = = =+' 09 =' =' +' x -(+')x+'=0 (x-)(x-')=0 ' x= x= 0 <<<90 sin <sin ' sin = sin = =0 =60 +' ' cos(-)=cos 0 = ' 060 x-y+=0 y= x+ ª = a =tan = (0 ) (- 0) = = =" + ='ß= sin a=sin = = 06 = = =0 - =60 =7 - =0 60 0 0 0 ' cos = = ' =0 =0' cos 60 = = 0' =0' =' ' sin 60 = = 0' =0'6 ='6 = + = _'_'6+ _0_0 ='+0, 8, ' 6 60 8 ' sin 60 = = 6 =6' =' cos 60 = = 6 =6 = ' = = =' =--=8 = _(8+)_' =' 06 0 <x< 0<tan x< tan x+>0 tan x-<0 " (tan x+) -" (tan x-) =(tan x+)+(tan x-)= 6 tanx= tan x= 6 tan x= =" + =' 69= ' '+0 ' cos x= 06 =9_=6 =6( >0) =" 9 +6 =' 7='ß x

= y 9 tan x= = = 6 6 cos x= = = 'ß 'ß 6 'ß sin y= = = 'ß 'ß 'ß = _{ + } 'ß = _ 6'ß = 6'ß 06 x -x+ =0 {x- } =0 x= ( ) sin = sin 0 = =0 tan 60 + ( )= - sin 90 tan 60 - '+ = -_ '- ('+) = - ('-)('+) =+'-=' ' 0% 0% 0% 06 =" - =' ' E ª E ( ) x x y = x ' ' cos x_tan y= _ = 6 066 EGEG=90 EG =" + =' G =" + + =' E ' sin x= = = G ' E ' tan x= = = EG ' ' sin x+'tanx='_ ' +'_ ' = EG G 0% sin x tan x 0% ' sin x+' tan x 0% 067 =90 =_6= ' cos 0 = = = =6' ' cos 0 = = = 6' =9 sin 0 = = = 6' =' = _ _ = _9_' 7' = 7' 0% 0% 0% 6 0% = x 0% cos x_tan y 0% ' 068 sin = = ' =' = ' cos = =

RM ' =' = E tan = = E = E= E- ' = - 069 ' = E E = =x E 60. x 0 E =0, x E=60 x=' ='x = + ='x+x=('+)x ('+)x tan 60 = =' ' x= =8-6' '+ =('+)x=('+)(8-6')=' E= _ _E = _'_(8-6') =08('-) 08('-) 07 F EF= EF( ), EF= FE( ) EF= FE, EF. 6 E x x 6 x F G F =E =E =6, G = = FG FG =" 6 - ='å0=' =F =FG =' E =E - =6-' FE F +' tan x= = = +' E 6-' 070 6 6 ' M = _6=' x M =M =' M M = M = _'=' M =øπ(') -(') ='å='6 '6 ' sin x= = = M ' '6 tan x= = =' M ' ' 8 sin x_tan x= _'= 8

0 089 + =00 h(tan 0 +tan )=00 07 07 6 ' 6 ' ' ' 00 00 h= = tan 0 +tan ' + h=0(-') 0(-') 07 9 6' 9 ' 090 =60 =0 07 x=0 sin 0 =0_0.77=7.7 y=0 cos 0 =0_0.6=6. x=7.7 y=6. 09 =h tan 60 =h tan 0 076 =80 -(90 + )= x= sin =_0.7=.8 y= cos =_0.8=. x=.8 y=. 077 078 079 080 =8 sin 0 =8_ = ' =8 cos 0 =8_ =' ' = - =6'-'=' ' =øπ + =" +(') ='ß8='7 '7 09 - =00 h(tan 60 -tan 0 )=00 00 00 h= = =0' 0' tan 60 -tan 0 ' '- 09 09 = 6_sin 60 ' = 6_ =6' 6' = _'_8_sin ' = _'_8_ = 08 =80 -(0 +0 )= 08 = sin 0 =_ = 09 = 8_sin 0 = 8_ =8 8 08 08 ' = = =' sin ' =80 -(60 +7 )= 096 = _0_6_sin(80 - ) = _0_6_sin 08 ' =9' sin =9'_ =9 9 ' = _0_6_ =' ' 086 9 ' = =9 =6' 6' sin 60 097 = _6_6'_sin(80-0 ) 087 =0 = = _6_6'_sin 0 088 =h tan 0 =h tan = _6_6'_ =9' 9'

RM 098 = 0_sin(80-0 ) 0606 = 0_sin(80-0 ) = 0_sin 60 = 0_sin 60 ' ' = 0_ = 0_ =0' 0' ' ' = 0607 = _(+6) sin 60 099 =8_6_sin ' 9' = _9 = 9' ' =8_6_ =' ' 0608 = _(+8)_'_sin 0600 =_'_sin 60 ' = '_ =8 8 ' =_'_ =8 8 y x 0609 = = sin cos 060 060 060 = sin(80-0 ) = sin 60 ' = =0' 0' =6 sin(80 - ) =6 sin ' =6 =9' 9' = _6 sin ' = _6 =6' 6' =80 -(90 + )=6 x y = = sin 6 cos 6 060 sin = c b 06 c=b sin =0 cos =0_0.7=7. =0 sin =0_0.68=6.8 7.-6.8=0. 0. 06 ='6 tan 60 ='6_'=' ' = =' =6 6 sin 060 = _8_0_sin 60 ' = _8_0_ =0' 0' 06 EG =" + ='å8='(cm) EG G =' tan 60 ='_'='6(cm) '6=7'6(cm ) 060 = _8_8_sin(80 - ) = _8_8_sin ' = _8_8_ =6' 6' 06 G =6 cos 60 =6_ =6 sin 60 =6_ ' '='(cm ) =(cm) ='(cm) ' cm 6

(0~06)개념RM-(정답) 0.. 0:6 M 페이지7 다민 0I 7LI 본문 06 =8' cos =8'_ 06 ' =8(cm) 꼭짓점 에서 에 내린 수 선의 발을 라고 하면 0 cm ' =8' sin =8'_ =8(cm) =0 sin 60 =0_ 따라서 삼각기둥의 부피는 { 08쪽 ~ 08쪽 ' 60 _8_8}_6=9(cm ) ② =0 cos 60 =0_ cm ='(cm) =(cm) =-=7(cm)이므로 에서 066 ' =6 sin 60 =6_ ='(cm) =6 cos 60 =6_ =(cm) 06 _p_ _'=9'p(cm ) 9'p cm =QR =0 m이므로 =0 tan 0 =0_ 꼭짓점 에서 에 내린 수 선의 발을 라고 하면 따라서 원뿔의 부피는 067 ③ =øπ(') +7 =' ='å(cm) 6" = 6' sin =6'_ ' =6 =6' cos =6'_ ' =6 =-6=8이므로 에서 ' =" 6 +8 =' 00=0 0 =0'(m) 06 Q =0 tan =0_ =0(m) 꼭짓점 에서 에 내린 수선의 발을 라고 하면 Q = +Q (0'+0) m =0'+0(m) 0 =0 cos =0_ =6 =" 0-6 ='ß6=8 068 점 에서 에 내린 수선의 = cos 0 =_ =0-6=이므로 에서 0 발을 라고 하면 =" +8 ='ß80=' ' 06 = - 꼭짓점 에서 의 연장선에 내 린 수선의 발을 라고 하면 = 6 sin 60 =6_ = tan 60 =_'='(m) ' 0' m =6 cos 60 =6_ = 060 0æ =' ' =0'(m) =0' tan =0'_=0'(m) 6 yy` ③ =6(-')(cm) =80-0 =60 이므로 =-6' =0 cos 0 =0_ ' cm =6'(cm) 069 0 yy` yy` = + =+=6이므로 = tan =_=(m) yy` 에서 = - =('-)(m) yy` =" 6 +(') ='ß6='7 yy` ('-) m 단계 채점요소 배점 '7 단계 채점요소 배점 의 길이 구하기 0% 의 크기 구하기 0% 의 길이 구하기 0%, 의 길이 구하기 0% 의 길이 구하기 0% 의 길이 구하기 0% 0. 삼각비의 활용 7

RM 06 ' =9' cos =9'_ 60 =9(cm) ' =9' sin =9'_ =9(cm) 9 9 = = ='(cm) tan 60 ' =('+)(cm) 066 ' = sin 60 =_ =6' =80 -(7 +60 )= = 067 6' sin =6' ' 9' cm ('+) cm =6'6 6'6 = sin 0 =_ =6 0 0 =80 -(0 +0 )= 6 ' = =6 sin =6' 6' 068 =x = =x x x ' = = = x tan 60 ' = + ' '+=x+ x +' ={ }x ('+) x= ='(cm) +' ' ' = =' sin ='6(cm) 7 x 60 60 ("+) cm '6 cm 069 =h æ =0 = 0æ h ' =h tan 0 = h 60æ æ 0 =h tan =h = + ={ h=(-') 060 '+ =h }h=0 = =0 =h tan =h =h tan 0 = + =(+tan 0 )h= h= 06 +tan 0 =h m = =60 =h tan =h(m) =h tan 60 ='h(m) = + =(+')h=60 h= 06 60 +' =0('-)(m) =h cm =0 = ' =h tan 0 = h(cm) =h tan =h(cm) '+ = + ={ }h=6 h=(-')(cm) = _6_(-') =9(-')(cm ) æ æ (-') h hm 60 60 m 0 h cm 0 0æ 0æ 0('-) m 60 6cm 9(-') cm 8

06 =h m =60, =0 60 =h tan 60 ='h(m) 0 60 0 00 m ' =h tan 0 = h(m) = - ' h=00 h=0'(m) 06 =h =8 = =h tan 8 =h tan = - =(tan 8 -tan )h= h= 06 tan 8 -tan =h m =60 = =h tan 60 ='h(m) =h tan =h(m) = - =('-)h=0 0' m 8 6 0 0 m h 0 h= =('+)(m) ('+) m '- 066 =h cm = =0 =h tan =h(cm) ' =h tan 0 = h(cm) -' = - ={ }h=0 h=0(+')(cm) = _0_0(+') =00(+')(cm ) 60 0 cm 60 h m 0 h cm 00(+') cm =h cm h 0% 0% 0% 067 = _6_0_sin =' ' sin = = 068 = =7 =80 -(7 +7 )=0 = _8_8_sin 0 = _8_8_ =6 069 tan =' =60 = _9 sin 60 ' = _9 =7' 7' 060 = _8 sin ' = _8 =' G= = _'=8' 06 8' =80 -( +8 )=0 = _8_0_sin(80-0 ) = _8_0_sin 60 ' = _8_0_ =0' 06 = sin(80 -)= 80 -= = 06 ' _6 sin(80 -)=6' + = _0_ _sin 60 + = _0_6_sin(80-0 ) ' + ' _ _6_sin 60 =' ' =' = 9

RM 06 = =8 =8 sin 0 =8_ = =80 -(90 +0 )=60 =60 +90 =0 = 8_sin(80-0 ) = 8_sin 0 = 8_ =8 8 0% 0% 0% 06 cm " cm = + 0 cm 60 = _'_'_sin 60 " cm + sin(80-0 ) ' ' = _'_'_ + 7' ' = + ='(cm ) 066 ' = =' =' cos 60 = + = _'_'_sin 60 + _'_'_sin ' ' = _'_'_ + _'_'_ =6'+8' =' ' 067 6 cm = sin 60 ' = ='(cm ) F E =6 =6_' ='(cm ) 068 =6' cos ' =6'_ =6 = =6 =-6=8 =" 6 +8 =' 00=0 = + = _6' sin + _0_6_sin 0 ' = _6' + _0_6_ =+=7 6" ' cm 0 6 7 0% 0% 0% 069 x cm =x_x_sin(80 - )=8' x_x_sin =8' ' x_x_ =8' x =6 x=6(cm) ( x>0) 060 = =6 =8_6_sin(80 - ) =8_6_sin ' =8_6_ =' + =80 =80 -( +00 )= = 8_sin ' = 8_ =8' = =_8'=6' ' 6' 60

06 = =0 =_8_sin(80-0 ) =_8_sin 60 ' =_8_ =0'(cm ) = = _0'='(cm ) 06 + =80 =80 _ = + =0 sin ' =0 =60' ' cm M= = = _60'=' ' 06 = _6_ _sin(80 - ) = _6_ _sin ' = _6_ _ =' =8 8 06 = =8 = _8_8_sin(80-0 ) = _8_8_sin 60 ' = _8_8_ =6' 066 = x(0 <x 90 ) _8_0_sin x=0 sin x 0 <x 90 sin x x=90 0 0 067 cos 0 = x= x cos 0 y tan 0 = y= tan 0 068 = 7_sin(80 - )=7' ' sin(80 - )= 80 - = = ' 069 cos = = =80 -( + )=0 = ('-)_sin(80-0 ) = ('-)_sin 60 ' = ('-)_ =6-' ' 0660 FG =8 cos 0 =8_ G =8 sin 0 =8_ = =' =' =8' 6-' 06 =80 -(6 + )=0 = _6 sin(80-0 ) = _6 sin 60 ' = _6 =8' 8' 066 = cos 60 =_ =(cm) =+=7(cm) = _7 sin 60 ' = _7 =7'(cm ) 6

RM 066 =0 m =0 tan 60 =0'(m) = + =0'+.(m) 066 8 ' = =8 ='(m) cos 0 =8 tan 0 =8_ '+6'=8'(m) 066 066 ' =6'(m) = = cos ' =_ ='(cm) = =' cm cm " cm = + ='+'=6'(cm) =" (6') +(') ='ß80='(cm) 0666 =8 sin(80-0 ) =8 sin 60 ' =8 =8'(cm ) (0'+.) m M= = = _8'='(cm ) ' cm ' cm "7 = + 0 " = '_sin(80-0 ) 60 "7 + _'7_'7_sin 60 = '_sin 0 + _'7_'7_sin 60 ' = '_ + _'7_'7_ 9' 6' = + =8' 0667 = x(0 <x 90 ) _8_9_sin x=6 sin x 0 <x 90 sin x x=90, 6 cm 0668 = =x cm = _x_x_sin(80-0 ) ' = _x_x_ =9' x =6 x=6(cm) ( x>0) 0669 =N Q =0 m R =0 tan =0(m) Q =0 tan 60 =0'(m) RQ =R + Q =0+0' =0(+')(m) 0670 =60, = =x tan 60 ='x =x tan =x = - =('-)x=0 0 x= =('+) '- =60 =0 =x tan 60 ='x ' =x tan 0 = x ' = - = x=80 x=0' 067 =h =60 = =h tan 60 ='h =h tan =h 60 0 m R Q 0(+') m 0 0 0 80 60 x 60 0 ('+) 0' 0 x 60 60 h 0 6

= + =('+)h=0 0 h= =('-) '+ h ' = =('-) cos =('6-') 067 ' ' = =6 cm = _(0-6)=(cm) = tan 60 ='(cm) = _(6+0)_' =6'(cm ) 067 = =60 =0 sin =0_ ' = =' cos 60 =0'(m) 067 ='(m) =0 cos =0_ =0'(cm) ' = - =0-0' =0(-')(cm) 6cm 60 6cm cm ' cm æ 0`m 60æ æ 0 cm 0(-') cm 0(-') cm 067 + =80 =80 _ =0 + =_6_sin 0 =_6_ = = = _= ' 0676 ' =8 sin 60 =8_ ='(cm) E=0 +90 =0 E= _'_8_sin(80-0 ) = _'_8_sin 60 ' = _'_8_ =(cm ) cm 0677 =80-0 =60 =8 cos 60 =8_ =(cm) ' =8 sin 60 =8_ ='(cm) =8+=(cm) = '='(cm ) ' cm = _8_8_sin(80-0 ) = _8_8_sin 60 ' = _8_8_ =6'(cm ) =80-0 =60 =8 cos 60 =8_ =(cm) = _8 sin 60 ' = _8 =8'(cm ) =6'+8'='(cm ) 0678 = =x = _6_ _sin x= sin x= = _0_ _sin x = _0_=70(cm ) 0679 =0 + = = 0æ a a æ æ æ 6

RM = =a a ' = =a ='a sin a = =a =a sin 0 a ' = =a ='a tan 0 = - ='a-a=('-)a = _('-)a_a_ 0680 8 FE=60 _ = 8 EF E =F =x EF= _x_x_sin ' = _x_x_ ' EF= x =8 EF=0' ' 8_ x =0' x = x=( x>0) E =E =_=0 0 068 G x æ F x E = 6_sin(80-0 ) = 6_sin 60 ' = 6_ =8'(cm ) = + =x cm 8'= x_sin 60 + _6_x_sin 60 ' 8'='x+ x 9' _('-)a_a_sin 0 =('-) a = a= ( a>0) =('-) =('-) = =' =('-)++' ='+'+ '+'+ x=8' x=(cm) cm 0% 0% 0% 068 ' = sin 60 =_ =6'(cm) =80 -(60 +90 )=0 = 6'_sin 0 = 6'_ =8'(cm ) = _6'_9_sin 0 7' = _6'_9_ = (cm ) = + 7' 6' =8'+ = (cm ) 6' 0% 0% 0% 0% 068 cm 0 =0, = ' cm =' cos 60 ' ='_ =(cm) ' =' sin ='_ =(cm) ' = tan 0 =_ ='(cm) = + =+'(cm) = _(+')_ (+') = (cm ) (+') cm 6

0% 60% 0% 068 cm 0 = cm =60 ' = = sin 60 ='(cm) = = = = = _ _ _sin(80-0 ) = _'_'_sin 60 ' = _'_'_ ='(cm ) ' cm 0% = 0% 0% 068 = = =80 -( + ) =0 = - 0 =p_8 _ - _8_8_sin(80-0 ) 60 =p_8 _ - _8_8_ 80 80 = p-6(cm ) { p-6} cm 0 8cm = + =(+')h=0 0 h= =('-)(cm) +' E= _0_('-) =('-)(cm ) 0687 ('-) cm MN MN= -( M+ MN+ N) =_-{ + + } =6-0 =6(cm ) M =" + ='å0='(cm), x cm N N =" + ='å0='(cm) MN= _'_'_sin x=6 M 0 sin x=6 sin x= 0688,. ' = = sin ='(cm) ='_='(cm ) cm cm cm ' cm 0686 E E =h cm E=, E=60 =h tan =h(cm) =h tan 60 ='h(cm) E 60 0 0 cm h cm 6

06 0700 T=90 T x=" - =' = 0689 0690 M RS M M M =" 6 - ='ß7='(cm) M = M = M =_'=6'(cm) x=6' 6' 069 M MÚ =" - ='ß6=(cm) M = M x= 069 M = = _8=(cm) M =" + ='ß0='(cm) x=' ' 069 M = = _0=(cm) M M =" 6 - ='ß(cm) x='ß 'ß 069 069 0696 x= x=9 9 x= _6= 0697 x=_8=6 6 0698 = =90 x=60 -(90 + +90 )= 0699 = =90 x=60 -(90 +0 +90 )=0 0 070 T=90 T x=" (8+9) -8 =' = 070 070 = =0 cm 0 cm =90 =" 0 + =' ='(cm) ' cm 070 =90 + =(+) =0 ='(cm) ( >0) x= =' ' 070 0706 E E F +F = + + =8++7=0 =F x=0 0 0707 E = =-8= F = = E =F =-9= x=e +E =+=7 7 +F = + + =8+x+9 x=7 0708 E = =9-6= F =E =-= F = =9 x=f -F =9-=7 7 +F = + + 8=6++x x=7 0709 E =F =6-= =E =-= =F =6 x= - =6-= +F = + + =x++ x= 66

070 -x 6-x r cm =r cm, M =(r-) cm 07 E = =x M F = =7-x F =E =9-x r =7 +(r-), 0r=7 =F +F 7 7 r= (cm) 8=(7-x)+(9-x) x=8 x= cm 070 07 F =E =x =F =8-x =E =-x = + 0=(8-x)+(-x) x=0 x= 07 F = = E = =9-=6 E =F =0-=7 =E +E x=6+7= 07 =" - ='ß= E =F =x =F =-x =E =-x = + =(-x)+(-x) x= x= =" - ='ß= = 0=x x= _x_(++) 07 = =+=(cm) =" - ='ß6=(cm) = =_=8(cm) 07 =" - ='ß ='(cm) r cm =r cm, =(r-) cm r =(r-) +(') r=6 r=(cm) _=8(cm) cm cm cm cm 8cm cm 8cm 0% 60% 0% 07 076 077 078 079 x+8=6+9 x=7 7 +x=7+ x=8 8 7+x=+8 x=6 6 8+=(+x)+ x= M M = = _=6(cm) M =" 6 + ='ß='(cm) 07 = = _6 =8(cm) r cm =r cm =(r-) cm r =(r-) +8, 8r=80 r=0(cm) 07 = = _ =(cm) 8cm cm r cm (r-) cm 0 cm 67

RM =" 0 - =' 6=6(cm) = - =0-6=(cm) cm 07 r =r =r- r =(r-) +(') 6r=6 r=6 076 = = _8 =(cm) r cm =r cm =(r-) cm r =(r-) + r=0 r=(cm) p_=0p(cm) 077 " r r- cm cm (r-) cm r cm 0p cm M 8cm =8 cm cm M M = = _8=(cm) M M =" 8 - ='ß8='(cm) = M =_'=8'(cm) 078 0" M M = = _0'=' M r r r =r M = = M r ={ 070 M =N = =6 cm M = = _6=(cm) M ' = = ='(cm) cos 0 p_(') =p(cm ) 07 07 r N = } +(') r =7 r =00 r=0 ( r>0) N N =" (') - ='ß= =N =_=0 M = N N = M = cm N N =" - ='å=(cm) =N =_=0(cm) = =0 0 = _0_=60(cm ) 60 cm M cm cm 0 M 0% r M r 0% 60% 079 = = =_60 =0 0 μ=p_6_ =p(cm) 60 6cm N 68

07 M N = =6 cm M = N M = = _6=(cm) M M =" - ='ß6=(cm) MÚN = M =_=8(cm) 07 M = N = M 6cm cm N 6cm 8cm = (80-8 )=66 66 07 ML =60 -(90 +0 +90 )=70 M = N = = =70 =80 -(70 +70 )=0 076 MN =60 -(90 +0 +90 )=60 0 M = N = = = (80-60 )=60 = = M =_6= 0% 0% 0% ' ' = =' =8(cm) cos 0 p_8 =6p(cm ) ' E = _8'=(cm) = E = _=8(cm) p_8 =6p(cm ) 078 =90 Q = = cm =" (+) - ='ß0='ß0(cm) 079 r cm = =r cm =(9+r) cm =90 (9+r) =r + 8r= r=8(cm) 6p cm r cm 9cm r cm cm = 8=60(cm ) 60 cm 070 r cm T=90 T T r sin 0 =, = +r r=+r r=(cm) =0 cm, T = cm T =" 0 - ='7å='(cm) 0 cm T r cm r cm ' cm 077 =E =F = = = = =60 = = _8'='(cm) F(RS ) = = _60 =0 " cm E 0 F 07 T T=90 T=80 -(90 +60 )=0 T T =6 tan 60 =6'(cm) = T- TQ 60 = _6'_6-p_6 _ 60 =8'-6p(cm ) (8'-6p) cm 69

RM T T 0% T 0% 0% 07 = =90 =60 -(90 + +90 )= =60 - = =p_8 _ 60 =0p(cm ) 0p cm 07 = = _(80-70 )= =90 x=90 - = 07 = =90 (RS ) =0 =8 sin 0 =8_ =(cm) ' =8 cos 0 =8_ ='(cm) = ={ '} =6'(cm ) 07 = =90 =60 -(90 +60 +90 )=0, =, =60 =6 sin 60 =6_ ='(cm) ' = =_'=6'(cm) 076 E=90 E E =" 8 - ='ß8='(cm) 60 =E =_' =8'(cm) 6' cm 6cm 60 6' cm 8' cm 077 = 9+8+x=_ x=7 F = = F =6-= =E =9+= E =F = x=-=7 = x+6+9=(9+) x=7 078 7 7, =, E =E = =90, =, (RS ) = E = E= _ _ _E _, =E = E +E + E =, E =E, = ( E )=E +E + =E +(E + )+ =(E +E )+( + ) = + = 079 E (RS ) E= E = _60 =0 E 8 ' E = =8 =8'(cm) tan 0 =E =_8' =6'(cm) E 8cm 60 F 6' cm 70

070 = = cm =9-=(cm) E = =9 cm E = = cm =9+=(cm) =" - =' =(cm) = = cm 07 9cm = = + = + = =6(cm) = =_'='(cm) = ( + )_ = _6_' ='(cm ) 07 E cm cm ' cm = =8 cm = = cm 8cm = + cm =8+=(cm) = = cm =8-=(cm) =" - =' 60='ß0(cm) = ='ß0 cm 'ß0 cm ='ß0 cm = _ _ = 'ß0 ='ß0(cm ) 'ß0 cm 0% 0% 0% 07 EF =E =x cm E =(0-x) cm F = =0 cm E =(0+x) cm E (0+x) =(0-x) +0 80x=00 x=(cm) cm 07 0 cm = =0 cm =" 0 - ='ß8='ß(cm) = =_'ß ='ß(cm) 07 : =a cm =a cm = = _8' ='(cm) (a) =(') +a a =6 a=(cm)( a>0) a=_=8(cm) 076 6p cm p- p=6p - =6 =øπ - ='ß6=8(cm) = =_8=6(cm) 077 E =F =x cm =F =(-x) cm =E =(-x) cm = + =(-x)+(-x) x= x=7(cm) cm a cm a cm 8" cm 8 cm 6 cm 7

RM 078 =F =6 cm E = =9-6=(cm) E =F =0-6=(cm) =E +E =+=7(cm) 7cm 079 =E = cm E =F =9 cm =F =x cm + + = cm (x+)+(+9)+(9+x)= x= x=(cm) cm 0760 =F =6 cm E = =-6=7(cm) E =-7=8(cm) Q =E =_8 =6(cm) 6 cm 076 =" 8 +6 =' 00 =0(cm) E F EF {8-r}`cm E r cm E =F =r cm (6-r) cm F r cm r cm =E =(8-r) cm =F =(6-r) cm = + 0=(6-r)+(8-r) r= r=(cm) cm 076 F r cm F r cm cm =F =r cm cm E =E = cm F =E =6 cm =(+r) cm =(6+r) cm (+r) +(6+r) =(+6) r +0r-=0 (r+)(r-)=0 r=(cm)( r>0) p_ =p(cm ) 076 F EF E =F = cm E = =x cm =F =-=(cm) (x+) =(x+) + x=0 x=0(cm) =0+=(cm) r cm F 6cm 6cm cm cm x cm F cm cm x cm E cm = =0(cm ) 0 cm E F 0% 60% 0% 076 F = sin 0 =_ cm =(cm) r cm 0 E ' = cos 0 =_ r cm ='(cm) E E r cm =E =r cm F = =(-r) cm F =E =('-r) cm =F +F =(-r)+('-r) r='- r='-(cm) ('-) cm 076 =" - ='ß8=9 + = + +9=8+ = 0766 + = + x+8=0+(x+) x=7 0767 + = + + =8+=0(cm) = = _0=0(cm) 7

0768 G =F =x cm =E = cm E =F = cm G = = cm (+++x)=0 x=8(cm) 0769 + = + + =+0=(cm) 8cm =_ =(cm) cm 8 0770 F FG F =G =6 cm E =F =-6=8(cm) =E =-8 =(cm) 077 E cm F cm 6cm G cm =E =_=8(cm) + = + + =8+0=8(cm) = _( + )_ = _8_8=7(cm ) 7 cm 0% + 0% 0% 077 F, G cm E G =F = = _ G cm cm =(cm) I F cm =G = cm 6cm cm E =F =6-=(cm) E = =x cm I IF = =x cm I =(-x) cm I (+x) =(-x) + 6x=6 x= =+=(cm) 077 I I =" - ='9=(cm) =x cm = =x cm I = -I =(x-) cm = = cm +I = +I +=x+(x-) x= x=6(cm) 077 E =F =F =G = _8 =(cm) =E =-=8(cm) GI =I =x cm I =(8+x) cm I =(8-x) cm I (8+x) =8 +(8-x) x=6 x=(cm) cm cm 8cm E cm F 8cm cm 8cm G x cm cm I (8-x) cm x cm cm E G 0% 0% GI =x cm I I x 0% GI 0% 077 E =F =F cm 8cm cm E 6cm =G = _ 6cm cmf =(cm) cm G I =E =8-=6(cm) cm ( I ) =I +I + =( +I )+I + =E +(GI +I )+ =E +G + =6+6+ =6(cm) 7

RM 0776 9cm ' r cm 8 cm cm (9-r) cm 9 cm r cm ' =(9+r) cm =E -E E ' F =E - 'F (6-r) cm =(9-r) cm ' =FE = -(9+r) =-(9+r)=(6-r) cm ' (9+r) =(9-r) +(6-r) r -68r+6=0 (r-)(r-6)=0 r=(cm)( 0<r<9) 0777 x cm =(x+) cm =(x-) cm =(x-) cm (x+) =(x-) +(x-) x -8x+9=0 x=9 'ß7=9 6'(cm) > x=9+6'(cm) 0778 Q 8cm r cm Q =(8+r) cm =r cm Q =(8-r) cm =(6-r) cm Q -Q = - (8+r) -(8-r) =(6-r) -r 6r=6 r=(cm) 0779 + = + (x+)+(x+)=x+(x-) x=6 ( + )=(9+8)= x cm (x+) cm E F cm (x-) cm r cm cm (x-) cm (9+6') cm 8cm Q 6 cm cm 0780 F = =x cm E = =(9-x) cm E =F =(-x) cm =E +E 8=(9-x)+(-x) x=6 x=(cm) 078 E = =8 cm E =0-8=(cm) E =" 9 + =' =(cm) G = -G =-9=6(cm) 078 =F =9 cm =E = cm E =F =x cm cm 6cm (x+9+)=6 x= cm 078 = =90 x=60 -(90 +0 +90 )=0 =. y= (80-0 )= x+ y=0 + = 078 = E =F = cm E E =" - ='(cm) =E ='(cm) = _'_='(cm ) 078 =E ++=E E =6(cm) F =E =6-=(cm) 0786 M N = = cm M = N N = = _=6(cm) N N =" 0-6 ='ß6=8(cm) MÚN = N =_8=6(cm) cm cm M N 0 cm cm 7

0787 M = N = = =6 =80 -(6 +6 )= MN MN=60 -(90 + +90 ) =8 8 0788 = ='6 cm =x cm =(x-) cm x =('6) +(x-) x=8 x=7(cm) 7 cm 0789,, F, G, FG cm =G =9-=6(cm) E = =8-6=(cm) 0790 =90 =" - ='ß96='6(cm) E cm 8cm F cm G cm 9cm = + + = +F = =_'6 =8'6(cm) 079 =0 =60 =8 sin 60 =8_ 079 + = + =6+0=6(cm) = = _6=8(cm) ' =' cm = =_'=8' 8' 8 60 = (0-6)=(cm) =" 8 - ='ß60='ß(cm) 8cm 'ß cm 'ßp cm 079 =E =F = = = = =60 = = _6=(cm) F(RS ) = = _60 =0 ' = = ='(cm) cos 0 p_(') =p(cm ) 6cm 0 cm p cm =E =F = = E ' E = _6='(cm) = E = _'='(cm) p_(') =p(cm ) 079 M =MÚ r cm r =r cm M = cm M = = _6=(cm) M r ={ r } + r = r='(cm) ( r>0) cm E F cm r cm M - r cm 0 ' cm 7

RM 079 = = = _6'='(cm) =r cm =r cm (r) =(') +r r =9 r=(cm) ( r>0) r=_=6(cm) 0796 M = N 6' cm = =60 0 M N ' cm N N = = = _'=6'(cm) N=0 6' ' = =6' =(cm) cos 0 cm 0797 (RS ) = = = _60 =0 = =90 = = =(cm) sin 0 ' = = ='(cm) tan 0 = cm =' cm = =' cm =80-60 =0 =60 ' = sin 60 =_ ='(cm) = ='(cm) = =_{ _'_} ='(cm ) =0 = (80-0 )=0 r cm 6' cm r cm 6cm 0798 =F =_=0(cm) + = + + =0+=(cm) = _( + )_ = 0=0(cm ) 0 cm 0799 T =RT, QT =RT T =RT =QT RT = Q = _=6(cm) T =RT =QT TR, RTQ. RT= RT= TRQ= TQR= x RQ _ + x=80 x=7 0800 080 R =Q = = _6=(cm) R =8-=(cm) E =E +E + =E +EF +F + =E +E +R + = +R + =++6=6(cm) 6cm Q 6 cm 7 = = R cm r cm = _=6(cm) cm R cm r cm R -r =6 =6 =pr -pr =p(r -r ) =6p(cm ) 6p cm R 8cm E F 76

080 F r cm r(7+8+9)=' r='(cm) F =E =a cm =E =(9-a) cm =F =(8-a) cm =(9-a)+(8-a)=7 a=(cm) F =" +(') ='ß0(cm) 080 M r cm =r cm M =(r-) cm M r =(r-) + r=0 r=(cm) p_ =p(cm ) cm M cm r cm (r-) cm p cm r cm, M r 0% 0% 0% 080 = =9 cm = = cm = + =9+ =(cm) = = cm =9-=(cm) =" - =' =(cm) = = cm 7cm 9cm r cm F 8cm E 9cm cm 'ß0 cm = + + + =+++9 =8(cm) 8 cm 0% 0% 0% 080 =90 =0 =6 tan 0 =6_ ='(cm) = =90 ' =60 -(90 +60 +90 ) =0 =p_(') _ =p(cm ) 6cm 0 0 60 0 p cm 0% 0% 0% 0806 F F r cm r cm =F =r cm 6cm E =E =6 cm F =E =9 cm =(r+6) cm =(r+9) cm =(r+6) +(r+9) r +r-=0 (r-)(r+8)=0 r=(cm)( r>0) p_ =9p(cm ) F 9cm 9p cm 77

RM r cm, r 0% 0% 0% 0807 E E = =0 cm EF =x cm E = =x cm =(0-x) cm F = =0 cm E =(0+x) cm E (0+x) =0 +(0-x) x cm E F 0 cm 0 cm (0-x) cm 080 cm ' r cm ' =(+r) cm =E - E =E - 'F =(-r) cm ' =FE = -(+r) =0-(+r)=(6-r) cm ' (+r) =(-r) +(6-r) r -8r+6=0 r= 'ß0 0<r< r=-'ß0(cm) 8cm 0 cm (-r) cm cm r cm ' E F (6-r) cm (-'ß0) cm 0x=00 x= (cm) E =F +EF =0+ = (cm) cm 0808 E =8 cm E E =" 0-8 E F E (0-x) cm Fx cm x cm E 8cm 8cm ='å6=6(cm) F =EF =x cm 0 cm F =(0-x) cm F (6+x) =(0-x) +8 x=8 x=(cm) cm 0809 =Q =R =S =T =x cm =(0-x) cm Q =G =-(0-x) =x-(cm) 0 cm G cm T F J cm R S E I 7cm Q cm =Q R = =-(x-)=6-x(cm) I =R ES =EI =7-(6-x)=x-9(cm) EJ =ES FT =FJ =-(x-9)=-x(cm) F =x+(-x)=(cm) cm 78

07 08 = Q μ=μ x= 08 08 08 08 x= = _0 = x= =_0 =0 0 x= = _60 =0 0 x= =_ =70 70 08 =90 =80 -(90 +60 )=0 = μ=μ x=7 7 08 : Q=0 : 0 = : μ : μ= : x:=: x=0 x=0 0 08 x= =60 60 086 μ : μ=9 : = : : = : x : : 086 x= Q= x=7 7 087 =90 90 087 x= = x=80 -(90 + )= 088 x= =80 -( +70 )=6 6 088 Q=90 Q= =70 x=80 -(90 +70 )=0 0 089 = =0 x=80 -(80 +0 )=70 70 089 Q Q= = Q x R Q= R= x= Q+ Q = + =60 60 080 = =_0 =0 =00-0 =60 x= = _60 =0 08 μ=μ Q= = 0 x= 08 μ=μ = =0 x=0 0 0 Q x 00 080 = =0 = = x=80 -( +0 +0 )= 08 + =80 x+8 =80 x=9 9 08 08 x= =80 80 + =80 =80 -( +60 )=7 + +80 + =80 = + =80 E= 79

RM 08 + =80 087 x= T=6 x+0 =80 x=7 7 T= T= T 08 =80 -(0 + )=8 x= =8 086 =80-0 =0 x= =0 087 =80 -(90 + )=6 + =80 6 + x=80 x= 088 Q= =0 Q Q+ x=80 0 + x=80 x=78 089 080 x= =0 = T=0 x=80 -(0 +60 )=70 08 = T'= =90 x=80 -( +90 )= 8 0 78 0 70 y=80 -(6 + )=60 088 x=6 y=60 ` 0 _0 =0 y=60-0 =0 x= y= _0 =7 x+ y=7 +0 = 089 = =_70 =0 = x= (80-0 )=0 = =_ =70 = Q =_0 =0 x=70 +0 =0 x 70 0 Q x 0 0 0 08 = T'=70 x= =_70 =0 = = x x=70 x=0 08 08 x= =80 -(80 +0 )=70 =90 x= =80 -( +90 )= 08 086 x= TQ= T= y= T= x= y= 0 70 x= y= x= y= 080 =0 = _0 =70 70 =8 + = 08 60-08 = = _ =6 x=60 -(6 +08 +6 )=6 6 08 x 6 0% 0% x 0% 80

08 = =90 x 0 0 =60 -(90 +90 +0 ) =0 x= = _0 =6 08 = =_8 =96 = =90 =60 -(90 +96 +90 ) 96 8 =8 8 087 x= =0 6 =0 + y y= y- x= -0 = 088 = =0 = = x=80 -( +0 +70 ) = = =6 = =6 x=80 -(6 +6 + ) =7 7 08 = =90 =60 -(90 + +90 ) =8 8 = (60-8 )=6 6 08 =60 -_ =6 = =90 x=60 -(90 +6 +90 )= b= Q a=60 - b =60 - Q x Q Q a b 089 μ = =0 =0 + = x= +0 =6 6 0% 0% x 0% 0860 =90 = =6 =90-6 = 086 =90 = E=8 x=90-8 = 6 E 8 8 x 6 086 Q Q= = Q= R= x= + =7 Q x R =90 = = x= +90 = x 8

RM 086 =90 = = _6 = =80 -(90 + ) =8 086 = = _8 =9 =90 E E= E= x= -9 =6 086 ' '=90 = ' tan =tan '= ' ' =' ' =(cm) ' ' =' ' =øπ(') + ='å='å(cm) 'å cm 086 =90 sin 0 = = 8 =8 =(cm) ' cos 0 = = 8 =8' ='(cm) 8++'=+'(cm) 0866 ' '= =60 '=90 ' sin 60 = = ' ' ' =' ' =(cm) ' 6 ' cm 6 ' 'å cm (+') cm 60 ' cm ' 60 cm 0867 =90 90 = =x =" 0 - =' 6=6 6 sin x=sin = = = 0 cos x=cos = = = 0 sin x_cos x= _ = x x 0 = =x 0% sin x, cos x 0% sin x_cos x 0% 0868 μ=μ = =0 = =0 x=80 -(0 +0 + )= μ=μ = = x =90 x=80 -(90 + + )=6 μ=μ = =_0 =0 x= =80 -(0 +0 ) =0 = _0 =0 μ= μ = = = x 0 + x+ x=80 x=60 x=0 0869 6 0 0 =70 - = l cm : 80 =6p : l l=p(cm) p cm 8

0870 μ :μ= : : = : = x = x x= x+ x= x=7 7 : = : 0% 60% 087 μ : μ : μ=:: : : =:: + + =80 =80 _ =60 ++ =80 _ =80 ++ =80 _ =0 ++ 087 μ =60 =80 =0 =80 _ =0 9 μ =80 _ =6 x=0 +6 =6 9 6 0% 0% x 0% 087 + =80 _ =60 60 +++ 087 μ 6 =80 _ =0 6 μ : μ= : : = : =0 =0 +0 =70 087 0 =80 -(0 +60 +0 )=0 = =0 = = = =90 =0-80 =0 = =0 0 70 0876 = = = + =86 =80 -(70 +0 )=60,,, x= =60 0877 = = = + =7 x= +7 =79 0878 = x = x 86 60 79 = x-0 Q x+( x-0 )=00 x=0 x=7 7 0879 = = = =0 = +0 =6 x=80-6 = 0 x y 0 8

RM y= =_6 =0 y- x=0 - = 0880 = = = (80-0 )=70 x=80-70 =0 =90 =80 -(90 +0 )=60 x=80-60 =0 088 E= E=6 F x=0 +6 =8 E y=80-6 =8 x+ y=8 +8 =00 088 0 0 = μ=μ = = = 80 0 + =80 = _80 =0 =0-0 =80 x=80 -(80 +80 )=0 y= =80 y- x=80-0 =60 088 x= =00 =80-00 =80 y= =_80 =60 00 = E=70 x+0 =70 x=0 =90 =80 -(0 +90 )=60 y+60 =80 y=0 y x 60 x=00, y=60 x=0, y=0 088 = = = + =00 E= =00 088 E E=00 - =6 = E=6 0886 =80 _ =0 =80 - =80-0 =60 ` =80 _ =08 E= =08 + E=60 +08 =68 00 6 68 0% E 0% E 0% 0887 =80 -( + )=0 + =80 E+ = E=00 + =80 0888 = = x=80 -( +96 )=0 0889 = E=80-0 =0 F E=0 + =8 E x=80 -(8 +0 )= 0 8

0% E 0% x 0% +0 =80 =0 F E=0 + =8 E 0 = x+8 x= + + F =( E+ E)+ + F =( E+ F)+( E+ ) =80 +80 =60 60 0% 80 0% + + F 0% 0890 80 80 089 E + E=80 E=80-76 =0 =8-0 = = =_ =68 089 E =80-0 =78 = = _98 =9 =78 +9 =7 089 76 7 8 E 0 98 68 E 7 F =80-0 =70 0 70 E F=0-70 =0 0 EF E=80-0 =0 0 089 Q= =6 Q=6 + =80 Q x=80 -(6 +80 )= 0896 Q= = x Q= x+ Q x+( x+ )+ =80 x=0 x= 0897 = Q= a = a+ Q x= a+0 ( a+ )+( a+0 )=80 a=98 a=9 x=9 +0 =89 89 0898 =80-0 =0 Q= x+0 Q ( x+0 )+ =0 x=8 8 089 E EF E+ F=80 E E+ =80 F E 0899 Q Q Q ' Q= Q=00 Q=80-00 =80 00 00 ' Q 8

RM 0900 = = _0 =7 Q Q Q ' Q= =7 =80-7 =0 7 0 ' 7 Q 0 0906 = = = (80-6 )=9 T = T=7 x=80 -(9 +7 )=9 9 090 Q Q= =8 QE E= Q=8 8 Q 0% E 0% 090 = =9 G FG= =9 GEF EF=80-9 =8 090 = T=8 =_8 =6 = 8 = (80-6 )= 090 = T=80 μ=μ : = : 80 : = : =0 = _0 =7 = T'=7 090 x=80 -(7 +7 )= =T T= T=6 T= T=6 T x=80 -(6 +6 +6 )=7 0 7 0% 0% x 0% 0907 =80 -( +8 )=88 y=80 - =80-88 =9 T = T=6 x=80 -(6 +9 )= y- x=9 - =0 0908 = = =80 - =80 -(6 + )=0 T= =0 = =6 =80 -( +6 )=0 T= =0 0909 μ=μ = = = =7 T= =7 090 (80-06 )=7 =80-0 =70 70 = +6 = = = 0 0 7 86

09 T T=90 T T= T=68 T x=80 -(90 +68 )= T 68 = + y y=6 y- x=6 - = 09 x 68 68 y T T T=90 T T=80 -(90 + ) =6 6 T T T= T= T 6 = T+ T=0 0 09 T T=90 T= T= T x T=80 -( +90 )= T T= T= T = x+ x=0 0 09 T T= x T =T x T= T= x x T x x T T= x+ x= x T= T= x T=90 T x+ x+90 =80 x=90 x=0 T= x=_0 =60 60 T= T= x 0% T= T= x 0% T 0% 09 E= E =E (80-0 )=6 FE= E=6 EF EF=80 -(6 +8 )=67 096 = = (80 - )=6 = =7 E=80 -(6 +7 )= 097 E= E =E (80 - )=6 x= E=6 EF= EF=6 FE F =E FE= EF=6 y=80 -(6 +6 )=6 x+ y=6 +6 =9 098 Q=8 + =6 Q Q =Q Q= Q=6 x=80 -(6 +6 )=6 = = =80 -( +6 ) =9 y+9 =80 y=86 x+ y=6 +86 = 099 T T= =6 T= =70 y 6 8 6 6 6 70 67 9 x Q =80 -(6 +70 ) = T 70 87

RM 090 x= QT= T= T=70 T y=80 -( +70 )=6 x- y=70-6 = = T= T Q T Q x 0% y 0% x- y 0% T= TQ= T T Q 09 T= T T= =66 T=66 09 Q 66 T ' 7 66 y= T=70 x= y=70 x+ y=70 +70 =0 0 09 T= QT= T= T= TT T= T T Tª T ( ) T :T = : 09 T=80-00 =80 T= T=80 TQ= T=70 x=80 -(70 +80 )=0 0 096 y= =_70 =0 x+70 =80 x=0 x+ y=0 +0 =0 097 =90 +0 =80 =70 x=80 -(90 +70 )=0 098 = =_0 =60 =0-60 =0 Q= = _0 Q 0 0 = 09 = Q = E T= TQ= T = T Q= Q= Q Q T Q Q E 099 μ =80 _ =0 6 μ=μ = =0 x=0 +0 =60 090 6 = =60 =80 -(70 +60 )=0 =90 x=90-0 =0 60 0 88

09 = = = =0-80 =0 = 09 μ=μ : = : x : = : = x+0 = x x=0 09 x=0 μ : μ : μ=:: : : = :: =80 _ =60 ++ =80 _ =90 ++ =80 _ =0 ++ x μ : μ= : 6p : μ= : μ=9p(cm) 09 E E+ =80 E=6 = = x+ =6 x=0 0 0 096 = = = = = + =80 = =_80 =60 60 =p_ _ =p 60 097 E= 6 = x+0 x= =90 = x= y= +90 = 098 T= T=0 T=90 T =8 cm T =8 sin 0 =8_ T =8 cos 0 =8_ ' =(cm) ='(cm) E 6 y 0 x x= y= T= '=8'(cm ) 8' cm 099 QQ Q= =00 Q + Q=80 +00 =80 =80 + =00 +80 =80 = Q Q+ =80 + =80 09 E E+ E=80 = E=0 x+ y = + E+ E =0 +80 =0 x 0 E 0 y 0 090 =90 =80 -(66 +90 ) = = =_ =8 66 89

RM 09 = = (80 - )=6 = =6 μ : μ= : : = : = 6 + + =80 =7 =78 78 097 098 = Q= = _76 =88 TT' x= ' = =70 x=70 T T' x x 70 ' 6 70 09 Q= x Q= x+ Q x+( x+ )+ =80 x=06 x= 09 =80 -(6 + )=60 E =E E= (80-60 )=60 FE= E=60 09 TQ= T= TQ= T=7 x=80 -( +7 )=0 09 Q T= TQ= T ( ) T= T= T ( ) Tª T( ) ( ) ( ) 096 G G GEF = G= GE =80-8 =9 G 60 T Q F 8 88 E 9 099 = x+6 x x+6 = x+6 = = x μ=μ=μ = = 6 x+6 x ( x+6 )+( x+ x+6 )+( x+6 )=80 x=7 x=8 8 090 T T= = 00 T= =00 T T=80 -( +00 ) = T T 0% T 0% T 0% 09 = = x + = x = x- Q x+( x- )=7 x=0 x= 90

= x 0% x 0% x 0% 09 x =90 6 = T=6 x=80 -(90 +6 )=8 T 6 6 =8 + y y= y- x= -8 =6 y 6 0% x 0% y 0% y- x 0% 09 = x x = = x 0 = + x x μ=μ = =0 =80 -(0 +0 )=00 ( + x)+00 =80 x=7 7 = x x 0% 0% 0% T=80 -(6 +90 ) = T= T= T 6 = x+ x= 09 = = x E = x+0 yy =90 μ=μ = = x =90 - x yy x+0 =90 - x x=0 x= y= x+( x+0 ) = x+0 =_ +0 =90 x= y=90 096 =90 =80 -( +90 ) = Q x = Q= = + x x=0 0 097 Q. Q= = a, 0 Q Q= = b = a+ b ' ( a+ b)+(0 + a)+( b+ )=80 ( a+ b)=88 a+ b= = a+ b= 09 T T=90 T= T=6 T x 6 6 T 9

098 08 6_=x_ x=0 x=0 0 099 _x=_6 x= x=8 8 0960 x_x=8_ x =6 x= ( x>0) 096 x(-x)=9_ x -x+6=0 (x-6) =0 x=6 6 096 x(x+)=_(+6) x +x-0=0 (x+8)(x-)=0 x= ( x>0) 096 _(+7)=_(+x) x= x= 096 = =6 9_x=6_6 9x=6 x= 0970 6_(6+)=(+x) 8x= x= 097 x_x=_(+) x = x =8 x='( x>0) ' 097 = _=6_x 6x= x= 097 = _8=_x x= x=6 6 097 = _(+x)=_(+) x= x=7 7 097 = _(+6)=_(+x) x= x= 6 x 096 = =x =-= _(+)=x_x x = x='( x>0) ' 0976 = _9=x_ x=8 x=6 6 0966 =9-x (9-x)(9+x)=_8 x =9 x=7 ( x>0) 7 0967 =x- _{(x-)+x}=_7 x= x=8 8 0968 =0-x (0-x)(0+x)=7_(7+) x =6 x= ( x>0) 0969 6_(6+)=_(+x) 6x= x= 0977 = _x=8_ x= x=6 6 0978 = _(+x)=_(+) x=0 x=0 0 0979 = x(x+)=_(+9) x +x-6=0 (x+9)(x-)=0 x= ( x>0) 9

0980 x =_(+6) x =6 x= ( x>0) 098 =x(x+0) x +0x-=0 (x-8)(x+8)=0 x=8 ( x>0) 8 098 x= 098 6 =_(+x) 6x=7 x =_(+6) x =0 x='ß0 ( x>0) 098 6 =_(+) (') =_(+8) 8 =_(+) +_(+) 'ß0 T,, T 098 T = T' x= ' =_(+y) y= y=6 x= y=6 0986 T = T' x=8 ' 8 =_(+y) y=8 y= x=8 y= 0987 T =_(+) ' T =x(x+) _(+)=x(x+) x +x-=0 (x+6)(x-)=0 x= ( x>0) 0988 T =_(+x) ' T =_(+7) _(+x)=_(+7) 8x= x= 0989 9 Q Q 0 'ß0 9 099 099 Q 9 '6 =x =7-x (7-x)_x=6_7 x -7x+=0 (x-)(x-)=0 x=( > ) 099 _6=_0 6 =0 = 099 = = =_ =6 =x =-x 6_6=x(-x) x -x+6=0 (x-)(x-)=0 x= x= > x= 099 : =: =k =k(k>0) 6_6=k_k 6k =96 k =6 k=( k>0) =_=8 =_= = + =8+=0 0 0996 _(+9)=_(+x) x=0 x= 0997 =x =x _(+0)=x_x x =6 x =8 x='7( x>0) '7 0998 =x =x- (x-)_x=0_(0+6) x -x-60=0 (x-0)(x+8)=0 x=0( x>0) 0 0990 Q Q Q 7 0999 6_Q =_9 Q =6 =x 9

RM x_(x+6+6)=_(+) x +x-=0 (x+)(x-)=0 x= ( x>0) 9_=x_x x =6 x=6 ( x>0) =x=_6= Q 0% =x x 0% 0% 000 x 6 = =x =-=9 9_=x x =7 x='( x>0) ' 00 =6+x =6-x (6+x)(6-x)=_ x =6 x=( x>0) =x- (x-)_=8_ x=6 x=9 9 00 x =x- =x+ (x-)(x+)=(') x =8 x='7( x>0) p_('7) =8p 8p 0% 0% 0% 00 E 9 x = =x E =x x E 00 x x =-x =+x 8 (-x)(+x)=_(+8) x = x=( x>0) 00 =+x _(+)=_(+x) 6x=6 x=6 =x+6 _(+)=x(x+6) x +6x-80=0 (x+0)(x-)=0 x=( x>0) 6 006 Q _=_6 Q = E =x =x _(++)=x_x x =6 x=( x>0) 007 E E =(6+r) cm 7_(+7)=6_(6+r) r=8 r=(cm) _p_ =8p(cm ) 008 = (6+)_=_(+ ) =0 =0 009 = cm 7cm E r cm 6cm 8p cm _ =_6 = = 9

00 0 = _(+)=_(+ ) =6 = 0 =x =6-x = (+x)(6-x)=x(6-x+) x=7 x= =x x 0% 0% 0% 6_(6+)+_(+6) _(+)=(6-)_6 _+_ _+_6 _7+_6 0 = E,, E,. =E cm cm _9=(+E ) E =7 E =9(cm) 06 T = x =_(+9)=6 x=6( x>0) = _(+9)=_(+y) y=0 y= x+y=6+= 07 M MÚ =" - ='9= cm E 9cm = =9 T = T =_9=7 T ='( T >0) ' 0 = 6_(6+)=x(x+7) x +7x-60=0 (x+)(x-)=0 x=( x>0) 08 = =6_(6+8)=8 ='å(cm)( >0) = _6_'å_sin 0 =" 0-8 ='ß6=6 =" 7-8 =' = = _6_'å_ ='å(cm ) 'å cm = 6_=x_8 x= 09 Q =T = cm =x cm =x_(+6), 8x= x=8(cm) 8cm 0 =6 = =8 : =: =x =x x_x=8_8 x =6 x= ( x>0) =_=6 = = + =6+=0 0 00 x T = 8 =(0-x)(0+x) x =6 x=6( x>0) 0 8 T x 9

RM 0 T = T =_(+6)=7 T ='( T >0) T=90 T =" +(') ='ß='ß = + =+'ß 0 T = 9 T = _=9 T = ( T >0) T=90 T T =" - ='ß6= +'ß = T = _= p_ =p p T 0% 0% 0% 0 T= TQ=60 T=90 T=80 -(90 +60 )=0 μt : T= T : T =0 : 60 = : 0 Q Q =Q QT Q _=_6 Q = T = =x (7') =x_(x+7) x +7x-98=0 (x-7)(x+)=0 x=7 ( x>0) 7 0 Q Q =Q Q _=_Q Q =0, T = Q =x 8 =(x-0)(x+), x -8x-8=0 (x-)(x+6)=0 x= ( x>0) 06 x- E E T = 6 =_(++ ) x = = x E = (x+)(x-)=_ T 6 x =6 x=6 ( x>0) 6 07 Q Q =Q QT =Q =Q =x cm x_x=_9, x =7 x='(cm)( x>0), T = T ='_9', T =8 T =9(cm)( T >0) 9 cm 08 =x T = 6 =x(x+9) x +9x-6=0 (x+)(x-)=0 x=( x>0) TT T= T Tª T( ) :T =T :T : 6= T :0 6 T =0 T = 09 T = T =_(+9)=6 T =6( T >0) TT T= T Tª T( ) :T =T :T : 6= : x x= x=8 =a T = 8 =a(a+), a +a-6=0 (a+6)(a-)=0 a=( a>0) 96

TT T= T, Tª T ( ) T : =T :T 8 : (+)=x :, 6x=96 x=6 8 6 0 = = 8 = _6, 6 =6 8 6 = 00 T= T T =T =6 T= T T= T T =T = T = 6 =_(+ ) =0 = 06 T = T' =6 =x T = 6 =x(x+9) x +9x-6=0 (x+)(x-)=0 x= ( x>0) 0 T = (') =_(+ ) = =8(cm) T= T=0 T=90 T T =8 sin 0 =8_ T =8 cos 0 =8_ ' =(cm) ='(cm) T 8++'=+'(cm) 0 8 =_(+) T = T T T= T=0 0 (+') cm 8 0 T T T T = 6 = =6 = 0 T = T T T= T=6 T T=80 -(0 +6 +6 ) =8 8 0 6 6 T 07 T = T' =8 x=8 T = 8 =_(+y) y=8 y= x=8 y= 08 T = ' = T = T =_(+9)=6 T =6( T >0) 6 09 T = T =_(+7)=8 T ='( T >0) ' T' = T' =T =' T T' =T + T' ='+' =6' 6' T 0% T' 0% T T' 0% 97

RM 00 = =x x(x+8)=7_(7+) x +8x-8=0 (x-6)(x+)=0 x=6( x>0) =x :Q = : 0 : (x+7)=x : x(x+7)=0_ x +7x-0=0 (x-8)(x+)=0 x=8 ( x>0) 8 0 = =x _(+6)=x(x+) x +x-0=0 (x-)(x+8)=0 x=( x>0) 0 = =x _(+7)=(6-x)_6 6x=8 x= 06 Q= Q Q= Q μq Q= Q 6 Q Q =Q Q =_(+6)=7 Q Q ='( Q >0) ' Q 60% Q 0% 0 =x = 6_(6+)=x(x+7) x +7x-60=0 (x-)(x+)=0 6 T 7 x ' x= ( x>0) 07 Q= Q Q= Q μq Q= Q Q Q Q =Q Q =_(+)= Q ='( Q >0) ' 0 Q Q = Q = Q μ ª Q ( ) =x :Q = : 8 : (6+)=6 : x 8_x=6_8 x=6 8 x 6 Q 08 = = Q Q= μ Q= Q Q = Q =_(+)= ='6 ( >0) '6 0 Q Q = Q = Q μ ª Q ( ) 0 x 7 Q 09 = = Q Q= μ = Q 6 Q 9 98

Q = Q =x 6 =x(x+9) x +9x-6=0 (x+)(x-)=0 x=( x>0) 00 μ=μ = = =_(+)= ='6( >0) '6 0 μ=μ " = Q = Q μ = Q Q = Q =x (') =x(x+) x +x-8=0 (x-6)(x+8)=0 x=6( x>0) Q 6 0 = μ = =90 ª ( ) : = : 0: =8: 8 =0 = 0 8 =" - ='ß8=9 9 0 = μ = =90 ª ( ) : = : : 6= : 6 = = 0 =" 8 -('7) ='ß6=6 = μ = =90 ª ( ) : = : 8: =6:0 6 =80 0 = 0 0 = μ = =90 ª ( ) : = : x :=0: x=0 x=8 y=øπ - =" 0-8 ='ß6=6 x+y=8+6= y 8 "7 x 0 ª 0% x 0% y 0% x+y 0% 06 = =6 =x =8+x, =8-x 6_6=(8+x)(8-x) x =8 x='7( x>0) 07 Q _6=_ Q = T = =_(++6)=0 T ='( T >0) 99

RM 08 x =x =x 06 = = x_x=6_(6+) x =60 x =0 x='( x>0) ' (') =_(+ ) =8 =6 " 09 F = =x F =x E = F 9_=x_x, x = x='( x>0) 9 E _'=' ' F 06 x(x+9)= yy ' =_(+y) yy x(x+9)=_(+y) y=x+ x(x+9)=(x+6) x +x-=0 (x+8)(x-)=0 x=( x>0) y=+= x+y=+=8 8 060 _=_8 = =6 =E F 066 T = T' = T T' = _0=0 =x T = 0 =x(x+) x +x-00=0 (x+0)(x-)=0 x= ( x>0) 06 =x =0-x = = x(0-x)=_ x -0x+6=0 (x-)(x-8)=0 x=8 ( > ) 8 067 =E F ' E F = = EEF μe E= EF 06 _6=_6 _(+)+_(+) _(+)=_(+7) 6_6=8_ _(+6)+_(+) 068 _(+ )=_(+8) =9 = T =_(+8)=8 T ='( T >0) = 06 E= E=90 E _(+)=_(+E ) E = E =7 7 069 R R R =øπ(') -(') ='9= R =R = T = T =_(+6)=0 T ='å0( T >0) 'å0 00

070 = Q E = Q = E 6_= _(+8) 0 = 6 = 6 07 T =_(+6)=7 T ='( T >0) TT T= T, Tª T( ) :T =T :T :'=:T T =' T =' 07 = E 9_(9+ )=8_(8+0) 9 =6 =7 =E F 6_(6+ )=8_(8+6) 6 =76 = 07 T=90 T =" 6 +(6') =' = =x T = (6') =x(x+) x +x-08=0 (x+8)(x-6)=0 x=6( x>0) 6 07 07 6 =_(+ ) =0 = Q =T =6 Q =6-= Q = -Q =-= Q M= M M= M QM= M M M= QM M Q M =MÚ MÚQ =_(+8)=8 M ='( M >0) Q 8 M 076 = = E 6 E= (μ ) = E E, E, = E =(-)_=0 ='å0( >0) 'å0 077 Q= Q Q= Q μq 7 Q= Q Q Q Q =Q Q =_(+7)= Q ='ß( Q >0) 'ß 078 T T T 0 T=90 0 0 T = sin 0 =_ =6 T= T=0 T=80 -(90 +0 )=60 T 60 =0 + T T=0 T= T=0 =T =6 T = =6_(6+)=08 T =6'( T >0) : T = : ' : T = : ' T =6' T T= T=0 T = T =6' 079 =x x(x+)=6_(6+0) x +x-96=0 (x+)(x-8)=0 0 x=8( x>0) =" -6 =' 08=6' =" 0 +(6') =' 08='ß x 6 0

RM 'ß p_('ß) =p 080 E x E =+x = E _(+8)=_(+x) 6x=9 x= 8 x x E p = ª ( ) : = : :.=(+) : =0 = 0% ª 0% 0% x, E x 0% 0% 0% 08 = 7_(7+)=6_(6+ ) 6 =8 6 =8 7 = = = _8= r r = + =0 r=' ( r>0) p_(') =0p 0p 08 : = : 8 : 6= : =7 = = Q Q= Q= μ Qª ( ) : =Q : 8: =Q :6 Q =8 _( +Q )= + Q =8 yy Q = =_= +=8 =6 =6( >0) 6 0% Q 0% 60% 0% 0% 0% 08 =x = _(+6)=x(x+) x +x-0=0 (x+8)(x-)=0 x=( x>0) 08 ' Q ' = =_(+)= ='( >0) 'Q '= Q=90 'ª Q ( ) Q ' 0

:Q = ' : ' :Q =6:8 6Q =' 6' Q = 6' 08 086 = μ = =90 ª ( ) : = : : 6= :8 6 =96 =6 = = _6=8 8 = = =x _(+x)=8_(8+8) 8x= x= T = = 6 8 ' T = =8_(8+8)=8 T =8'( T >0) T=90 T T =" 6 -(8') =' 8=8' T ' = T = _8'=' ' = T +T ' =+' +' 087 = 0 8 = =90 ª ( ) : = : 0: = :8 =80 ='( >0) =" (') -8 ='ß6= = = _8 8 =6 = 0

RM 0 x 6 x +x =6 +x=9 x=7 0+7++++0 0 = 6 = = 6 = {(0-) +(7-) +(-) 6 +(-) +(-) +(0-) } 7 7 = = 6 0 a b c d 7 9 (a-7) +(b-7) +(c-7) +(d-7) =9 (a-7) +(b-7) +(c-7) +(d-7) =6 _+_+7_+9_ 0 0 = = = 0 0 = {(-) _+(-) _ 0 +(7-) _+(9-) _} = =. 0 ='. 0 06 07 08 0 -+++x+=0 x=- (-) + + +(-) + = = =8. =' 8. 0_6=60 _9= 60+=9 9 = = ='ß +a+b = = 0 a+b=6 yy = {(-) +(-) +(a-) +(-) + 0 + +(b-) +(-) + +0 } = {(a-) +(b-) +6} 0 =9 (a-) +(b-) = yy b=6-a (a-) +(6-a-) = a -6a-7=0 (a+)(a-7)=0 a=- a=7 a<b a=- b=7 0 0 ++a+b+=0 a+b=8 yy 80. 60_+70_+80_a+90_b+00_ =80. 0 80a+90b+90=60 8a+9b=70 yy a= b=6 90 09 a b c d e 70 a+b+c+d+e =70 a+8 b- c+7 d+ e- (a+8)+(b-)+(c+7)+(d+)+(e-) a+b+c+d+e+ = a+b+c+d+e = + =70+=7 0

0 =69_7=8 _ _ =7_=00 ~ 6 (-) _ ~ 0 (-) _ = - ~ 7 6 8 (-) _ =8-00=8 7 ~ 9 8 8 6 _8 8 = =6 9 ~ 0 7 70 _7 6 ~ 6 _ 0 80 80 a b c 80 a+b+c = =7 = 0 a+b+c= yy 80 = =7 0 a b c (a-) +(b-) +(c-) = (9+x) 8 (a-) +(b-) +(c-) =6 _7+_8+_x+_ a +b +c -8(a+b+c)+8=6 =8 9+x a +b +c =8(a+b+c)- yy +x =8 +x=+8x 9+x a +b +c =8_-= 7x=77 x= = {(-8) _7+(-8) _8 0 +(-8) _+(-8) _} 00 = =76 0 a +b +c ='ß9 7 8 8 9 0 0 = +=6 + = 6 = (_+_+_6+_+_) = = = {(-) _+(-) _+0 _6+ _+ _} 8 6 = = = (_+_+_+_+_+6_) 60 = = = {(-) _+(-) _+(-) _+0 _ + _+ _} = 0

RM 07 Q = = Q Q =øπ -Q =" - ='8=' 6 Q ='- QRS=('-) =9-' 08 x+ (x+) =(x-7) +x x -6x+8=0 (x-)(x-)=0 x= x= yy x-7>0 x>7 yy x= 0 0 =" - =' = =" 9 + =' = 09 -<a<+ 7<a<7 a a> 0 E =" + =' EFG EFG=(') = <a<7 yy a > + a >69 0 9 +0 = 9 +0 <(') a> yy <a<7 +(') >9 (') +6 <7 + =('ß9) 0 x=" - ='9= = _ =(+ ) =9 0 = 9 + = + = +8 =89 9 y=æ{ } + =Æ = 6 0 =" (') +(') ='= =" +(') ='6 7 x+y=+ = =" ('6) +(') ='8=' E =" (') +(') ='ß0 F =" ('ß0) +(') ='ß=' + = + (') + =(') + = =' ( >0) 06 =-6=6 0 6 =" 0-6 ='ß6=8 = =8 =" 8 + =' 08='ß x =" (x) +x ="çx ='x=' 'ß0 x= 'ß0 06

=" - ='ß6=(cm) F= E= = _ =8(cm ) 8cm ' ' = = cm = ' = _(-)=(cm) =" - ='ß6=(cm) cm cm cm = _(+)_=(cm ) cm 6 = = cm =" - ='ß8=9(cm) Q =x cm Q =Q =(-x) cm =-9=6(cm) Q (-x) =x +6 x=08 9 x= (cm) ' 9 cm ' Q =x cm Q x Q cm 0 0 0 0 0 06 07 a cm ' a =6' a = a=(cm) ( a>0) cm _=(cm ) : = : ' : x= : ' x=6' : = : ' y:6'= : ' y='6 xy=6'_'6=' (- ) ( -) =" {-(-)} + (--) ='ß6 '6 " (a) +a +a ='6 '6a='6 a= a cm ' G = _ a= a='(cm) ' = _(') ='(cm ) : = : ' :6'= : ' 0 =6(cm) : = : ' : 6= : ' ='(cm) =" {-(-)} + (-7) ='ß= =" (--) + (-) ='ß0=' =" {--(-)} + (7-) ='ß= = = + =90 60 6" cm 07

RM 08 y=x +x-=(x+) -9 (- -9) y Q(0 -) Q =" {0-(-)} +{ --(-9)} ='ß0=' 09 ' + cm ' cm ' ' ' ' =" + =' 69=(cm) + cm 0 a '6 = a='6 a= ' = _ =' " 6 +6 =6' h=" 6 -(') ='ß8=' = _6 _'=6' 6 6 h cm 6 =(6') -(-x) -x =(6') -(-x) x=0 x=(cm) =" - =' =(cm) = =66(cm ) 66 cm " (') + ='ß6=6(cm) x x p_6_ =p_ 60 x =80 6cm x cm 80 '6 V = _6='6 ' M = _6=' MÚ = M = _'=' VM= _MÚ _V = _'_'6=' ' =" + =' G = = _'=6' G V MÚ VM G =øπ -G =" -(6') G='ß7=6' G = 'G ' =G =_6'=' =x cm =(-x) cm = -x cm 6" cm x cm (-x) cm 6 x p_8_ x =90 x 60 =p_ M M =" 8 + ='ß80=' 8 x M ' 08

07 ' ' ' ' ={ + }{ - } = - = 08 cos 60 = x+8 =60 x= 0 09 8 ' = =8 =8' tan 0 0 =" - ='ß6= 7 sin +cos = + = 8 = =8 =8 tan = - =8'-8=8('-) 0 0 0 0 tan 60 = = =' =' ' ' sin = = = ='6 =80 -(90 + )=6 sin = = = =0.697 sin 6 = = = =0.79 sin +sin 6 =0.697+0.79 =. =_+_0= ' cos = =" -(') ='= ' tan = = = ' ' 0 y=x+ x=0 y= (0 ) y=0 x=- (- 0) = = =" + =' ' cos a= = = ' tan a= a= ( 0 <a<90 ) ' cos = sin 0 =0 cos 0 = sin 60 = cos 60 = < < < < tan 60 =' =80 -(90 +0 )=0 sin 0 = =0.68 00 =6.8 ' 06 =" + ='ß= ª ª x= y= 9 sin x+tan y= + = =" + =' 69= ª E( ) = x cos x=cos = = 09

RM 6 tan = = = =6 6 tan 60 = = =' =' 0 ' = sin 60 =_ 60 =' 6 = _(6+')_6 = cos 60 =_ = =6-= =6(+') 6(+') =" (') + ='ß8='7 EG =" + =' G =" + + =' EGEG=90 E " x " G 0 _ _sin 60 = _ _ ' ='(cm) = ' = E ' sin x= = = G ' EG ' '6 cos x= = = G ' ' '6 ' sin x_cos x= _ = EG G sin x cos x sin x_cos x ' 0 =0 = =6' sin ' =6'_ =6 ' =6' cos =6'_ =6 6 ' = =6 =' cos 0 =6 tan 0 =6_ ' =' 6' 0 60 6 0 << sin >0 sin -cos <0 " sin +" (sin -cos ) =sin -(sin -cos )=cos cos = +( + )+ =6'+6+'+' =6(+'+') 0 << 0 x 0 cos 6 = =0.697 x=.89 0 y sin 6 = =0.79 y=.86 0 x+y=.89+.86=8.8 0 06 =x = =x tan =x =60 =x tan 60 ='x + = (+')x=8 8 x= =('-) +' =h = =h tan =h 0

=0 ' =h tan 0 = h ' -' - = {- }h= h= h= =(+') -' Q = sin 60 ' =_ ='(cm) = cos 60 =_ =(cm) cm 60 cm Q cm 07 = 0'= =8(cm) _ _ _sin(80-0 ) _0_ _ ' Q = = cm Q = = cm =++=7(cm) = _(+7)_' =0'(cm ) 08 = + 0 = sin 60 " 60 + '_sin(80-0 ) ' = + '_ ' 7' ='+ = =80-0 _ =0 0 0 0 =p_ _ =8p 60 = sin(80-0 ) ' = =6' = - =8p-6' 09 8 cm cm G F E a S S= sin a =8 =8_{ sin } ' =8_{ } =0'(cm ) 0<sin a a=90 S= =0(cm ) 0 cm 0 =80 -(0 +70 )=60 = _8_9_sin 60 ' = _8_9_ =90-0 =60 =6 cos 60 =6_ =(m) ' =6 sin 60 =6_ ='(m) = tan 60 ='_'=9(m) =8'(cm ) 8' cm = + =9+=(m) m

RM 0 = =90 ' =60 -(90 +60 +90 ) =600 cos =600_ =00'(m) =0 0 =p_6 _ =00' tan 60 =00'_'=00'6(m) 60 00'6 m =p(cm ) 6 cm = cm = sin ='(cm) = ( ), = ( ) = = ='(cm) = _'_'_sin ' = _'_'_ =8'(cm ) 0 0 F F =F = E =F = =_=8 M = N = 8' cm 06 = = (80 - )=6 0 0 06 07 08 + = + +=8+ =7(cm) M M =" 0-8 ='ß6=6 MÚ = - M =0-6= M =" 8 + ='ß80=' M N = M = N M M =MÚ M MÚ =0_ = M =" 7 - ='ß='6 MÚN = M =_'6='6 M M M = = _8=9 M = = _0= = M - M =9-= =90 r = + (8+r) = +r 6r=80 r= 0 8 0 0 M 7 N 0 M M

09 =E =F E =F + + =F 8++7=F = - 6cm F =0 =6-=(cm) 0 F =x E =F =x =" 9 - ='ß7=6'(cm) =F =0-x =E =-x = _(6+)_6' = + =7'(cm ) =(0-x)+(-x) x= x=6 =Q =(-r) cm = + 7=(8-r)+(-r) r=6 r=(cm) Q R 7 cm r cm 8cm R QR r cm Q =R =(8-r) cm =" 7-8 =' =(cm) T T T T =T =6 cm r cm r' T -T = T r -r' =6 =6 =pr -pr' =p(r -r' ) =6p(cm ) 6cm E cm cm 7' cm r r' T 6p cm E =x cm E +E = +E 6+E =8+x E =x+(cm) E = -E =8-x(cm) E E =E + (x+) =(8-x) +6 0x=96 x= (cm) = = _8= =" - ='9= = - =-= E = =6 cm E = = cm =E +E =6+=9(cm) T T =T =6 cm 6 = = (SSS ) =90 =" 0-6 ='ß6=8 = _8_6= = =_=8 8

RM 0 07 = =_6 = x= (80 - )= x+ =00 x= = x= F y= + =80 x+ y= +80 = 0 0 = =0 E =80-0 =0 =90 =80 -( +90 )= + =80 =80 - = 09 QQ ' = Q = E =80 - =6 x= =_6 =0 y= = x+ y=0 + = E 6 x ' y Q 0 0 06 =80 -(0 +0 )=00 = E =80-70 =0 = E x+ y= + = ( + ) = x 0 y = _0 =60 E= + E E 0 μ T= 0 70 T= T = _0 =70 EF E =F EF= (80-60 )=60 EF= EF=60 EF FE=80 -(0 +60 )=70 T= T=7 T=80 -( +7 )= T= T= =0 +0 =0 0 = =80 -(0 +80 )=70 07 =90 =70 70 =80 -(90 +0 )=60 = = = _60 =0 = T=60 E E=0 +0 =60 + =80 +0 =80 08 = = = E =7 =80 -(60 +7 )=

T=90 T= T=0 0 T T T T T = T =6 sin 0 =6_ =8(cm) x =x(x+8) ' T =6 cos 0 =6_ =8'(cm) x +8x-=0 (x-6)(x+)=0 x=6 ( x>0) T= _8_8'='(cm ) ' cm T T T T T 0 T =, T' = T = T' T = T' T =_(+6)=0 T ='ß0 ( T >0) T T' =T =_'ß0='ß0 8 6 = x =90 E= = (90 - ) 0 =x = _(x+)=._ 6x=9 x=. = (90 - x) E E+ E= E (90 - x)+ x=80 - x=0 x=0 0 06 E E = =0 = E (r-)_=0_0 0r= r=. 0 r r- E = x E= ;!; (90 - x) x 07 E EQ =E E ' E EQ =E E E E =E E _=_E E =6 08 =x cm T = 6 =_(+x) x= 08 x=8(cm) =p_8 =6p(cm ) 0 =x = _(+x)=6_(6+) 8x= x= 09 Q Q =Q Q Q _8=6_ 8Q = Q = 0 =x = _x=0_6 x=60 x= T = T =_(++8)=80 T ='( T >0)

RM 0 Q T = =_(+)=6 cm Q cm T =6(cm) ( T >0) = Q = Q cm Q μ ª Q ( ) =x :Q = : :(x+)=x : x +x-0=0 (x+)(x-)=0 x=(cm) ( x>0) = = Q = Q μ = Q Q = Q =_(+)= =' (cm) ( >0) = = =90 μ ª ( ) : = : : = : =0 =0 =p_ =p Q = cm cm TT T= T Tª T ( ) T : =T :T 6:9=:T 6T =7 T = E= E E= E μe E= E E E =x E =E E 6 =x(x+9) x +9x-6=0 (x-)(x+)=0 x= ( x>0) (cm) 9 cm T 6 Tª T T 9 9 6 x E E= E E E = 0 = 0 =_(+ ) =7 = = =_(+) =88 ='(cm) ( >0) cm Q ' 6cm6cm Q 'ª Q( ) ' : = :Q 8 : =' :Q 8Q =88' Q =6'(cm) 6' cm 6

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