. 09~ cm 7 0 8 9 8'-p 0 cm x=, y=8 cm 0' 7 cm 8 cm 9 'åcm 90 'åcm T T=90 T T =" 8 - =' (cm) T= T= _T _T _'_ T=8' (cm ) 7 = == =80 -_ =0 = = _=(cm) M = = _0= (cm) M M =" - = (cm) r cm rcm (r-)cm H 8cm cm H H = = _=8 (cm) H = -H =r- (cm) H r =8 +(r-) 9 r=8 r= (cm) N = = = _8= (cm) N =" + = (cm) M =N =L = = =0 M M=0 M = = _'=' (cm) M = ='_ =(cm) cos 0 ' 9 =p_ =p (cm ) _=9 (cm) 'cm 0 M L N =90 =" - = (cm) = = cm 8 9 0 == = _0=0 =90 =80 -(90 +0 )=0 = tan 0 =_ = == =' '=' +- =('+')-p_(') _ =8'-p EF =E =x cm F = =0 cm E = -E =0-x (cm) E =F +EF =0+x (cm) E ' (0+x) =0 +(0-x) 0x=00 x= (cm) E =0+ = (cm) 0 0
0 cm (++x)=0 x= R QR Q =R =Q = cm =Q =-=(cm) =R =x cm (x+) = +(x+) x= x= (cm) =+=0 (cm) =+=8 (cm) + =0+_8= (cm) cm + = + = _= (cm) 7+x= x= +y= y=8,, QRS QR R =Q = cm S =R =-=7 (cm) =S =-7= (cm) E =x E E + =E + E +=x+ E =x- E =-E =-(x-)=-x E x = +(-x) 8x=0 x= E E FRHS F= = _0 =0 F F = cos 0 =0_ = + + =' = +( + )+ =( +E )+(F + ) =E +F =F =_' =0' Q cm ' cm cm R cm S 7cm 7 Q = _= (cm) 8 9 x cm Q =(+x) cm, =(-x) cm Q Q (+x) =(-x) + 8x= x= (cm) M =x cm M = = x(cm) M = = _'='(cm) M x ={ x}+(') 7cm x =7, x = x>0 x= (cm) cm M M M = = cm = = cm = + =+=8 (cm) = = H RHS = _'å ='ßå (cm) RHS = = = = _80 =90 = _ _ = _8_' ='ß (cm ) cm H H =-= (cm) H cm H H =" 8 - ='ß (cm) M 'cm % %
=" ("ç) + =' (cm) =" ("ç) + ='å0(cm) = _ _ = _'_'å0='å (cm ) x=0, y= x=80, y=0 x==0 y== Q Q== Q=R= x=q+q= + =80 x= y y=x=_80 =0. cm, cm, M, N N N =" - = (cm) =N =_= (cm) = M =N = cm cm cm cm 0 = x= 0 = = 80 x= 0 80 0 _0 =0 x x=80 x x=0 _0 =70 y= _(0-0 )= _0 =0 x+y=70 +0 =80 cmn. M. 78 0 Q==0 QR x=0 +8 =78 Q Q== Q= = _70 = x=q+q= + =0 x= =90 x==- E =90 - = E==7 E=90 x=e-e=90-7 = =90 =80 -( +90 )=8 === 88 = + = =+=8 + =, Q 0 8 x=0 x=_=.
0 =x0 x=8 μ=μ == == =80 -( + + )= =0, =80, =0 μ : μ : μ=:: =:: ++=80 =80 _ =80 _ ++ ++ =0 =80 =80 _ =0 ++, == + =80 -(0 +0 )=70 ==70,,, 00 0 ==0 E x=0 +0 =00 ==70 E 70 =0 +x x=0 0 ==0. 7 0 ==0 E 70 =0 +x x=0 E +0 =70 =0 x==0 0 pcm 70 0 80. 7~8 7 7 8 0 cm 9 0 0 0 x= x= _0 = _(0-0 ) = _00 =0 0 _=0 0 =p_ _ =p (cm ) 0 ==90 =0 -(0 +90 +90 )=0 x= = _0 =70 ==_ =0 =Q=_0 =0 =+ =0 +0 =0
==0 0 7 8 9 0 x+0 =8 x= =90 =90-0 =0 x==0 == = + =80 = = _ = =90 x+ =90 x=7 =90 =90-0 =0 =0 0 = μμ=, μ= μ=0 (cm) μ= μ`=μ =80 _ = ==_ = = + =0 =0 =0 =0 =0 + = =0 =0-80 =0 =0 =0-0 =90 =80 -(0 +80 )=0, =0 = = = =90 x=80 -(90 +0 )=0 x, y, y, 80 x=00, y=70 x=8, y=9 x=, y=0 80 x+80 =80 x=00 y+0 =80 y=70 x=80 -( +0 )=8 x+y=80 y=80-8 =9 x=80 -=E= y=x=_ =0 x=, y=8 x=0, y=0 x=80, y=80 x== +y=80 y=80 -(0 + )=8 =90 +=80 =80 -=0 x=- =0-90 =0 =80 -(90 +0 )=70 70 +y=80 y=0 E x+00 =80 x=80 =x=80 y=80 -(0 +80 )=80 0 +=9 = =80 - = +=80 =80 - =80 - = E=80 - =80 - =. 9
+9 =80 =80-9 =8 E=0 +8 = 80 80-70 =0 80 80 =80 -E=0 80 = =80 - = Z Z Z Z Z Y +=+Q=80 +Q=80 =Q Q+=80 Q=E =E =E //. 0 x=80-80 =00 y=80-90 =90 ==0 =80 -=E=00 x+0 =00 x=0 +=80 0 +y+ =80 y= =9-0 = x=80 -== 9 +y=80 y=8 9 +y=80 y=8 0 +x+8 =80 x= == _(80-0 )= = 80 = _0 =0 +=80 +E=80 +0 =80 =+ =0 +7 =0 =7 Q=80 -==x Q=x+0 Q x+(x+0 )+0 =80 x=0 x= x=00, y=90 x=0, y= x=, y=8 0 8 7. =7 - =0 80 +=80 (x+0 )+9 =80 x=
Q Q=80 -Q==9 70 70 70 x=0, y=0 Q x=t=0 x=80 -Q y=t=0 =80-9 =8 Q Q=80 -Q==7 x=q=7 =80 -=F =80 -EF=FEH =80 -FGH=HGJ =80 -HIJ=JIL =FEH=JIL // EF // I J EF IJ 0 90, 90, 90 x=0, y= x=, y= x=, y= =x x==t= y=80 -( + )= x=80 - = y=x= = = _8 = x== =T=7 =80 -=80-9 =8 =80 -(7 +8 )=0. =T=8 =90 =80 -(90 +8 )= x=8 - = T=80 -==0 TQ=T=0 T=80 -(0 + )= x 8.. ~ T 0 =T=70 =90 =80 -(70 +90 )=0 0 7 7 8 0 9 0 0 0 TQ, T TQ, T. =_0 =00 = = _(80-00 )=0 7
= x- = x=80 x=0 _(0 -) _{0 -(x+0 )} ' ' ' ' =90 ' =8 cm ' =_=0 (cm) ' =" 0-8 = (cm) =' ' 8 sin =sin '= =, 0 cos =cos '= = 0 7 sin +cos = + = 0cm cm 8cm 8cm ' ' cm 8 9 0 =x= y= + =80 x+y= +80 = Q=80 -Q==00 Q+=80 =80-00 =80 '= =_80 =0 T==80 _ =0 ++ T =T T=T=80 -x T T=(80 -x)-0 =0 -x T=T=0 -x T (80 -x)+(0 -x)=80 x=0 x=0 7 = = _0 = =90 =90 - = =80 _ = =80 _ =0 9 = +0 = =80 -(0 +0 )=90 +=90 +00 =90 +80 == =80 -( +00 )= +=80 +x+ + =80 0 x= =x =x+ μ=μ=μ ===x+ y +=(x+ +x) x+9 =80 +(x+ +x+ ) =80 x=8 x= y =x+ = + = y =80 -(70 +0 )=0 y =E E E= _(80-0 )=0 y x=e=0 y E x % % 8
0,, 0 _x=_ x= _x=_ x= _x=_(+) x=0 cm. 7 0cm x cm _=_(x-), x=0 x=0 (cm) 0 cm x cm x =(x-) +, x=0 x= (cm) _=0 (cm) =x cm x =_8=. 9 x>0 x= (cm) _(+)=_(+x) x= x= _= 8+ =_(+) _(+)+_(+),,,,, ' 7 8 = =x = + =(-)+= _=x_x x = x>0 x=' =9-x =9+x _8=(9-x)(9+x) =8-x, x =9 x>0 x=7 =0-x =0+x _(+9)=(0-x)(0+x) =00-x, x = x>0 x=8 9 7. 8 _=_x, x=8 x=9 _(+x)=_(+) x= x=7 _=_8 _(+8)+_(+) 7 7 r _8=(r-)(r+) 0=r -9, r =9 r>0 r=7 r _=(-r)(+r) 7=-r, r =9 r>0 r=7. 0 F, E = _x=9_, x=8 x= = (8+)_=_(+x), x=8 x= 9
8 9 _ =_(+9) =8 _ =_(+9) =9 = -=8-= = -=9-= + =+= _=_8 _+ (+)+_(+7) _(+)+_(+) _=(9-)_9 = _=_(+) =9 = - =9-=. 0 '7 7 cm 8' x_=_ x=0 (x-)_=(7-)_ x= x =_9= x>0 x= _(+x)=_(+7) x= x= _=(x+)(x-), x =8 x>0 x='7 x =_= x>0 x= =" +(+) = (cm) = `(+)_=_ = 7 (cm) = = + =+= = = _(+)=, =7 >0 =' = _ _ = '=8' 0 T, T, T, 8 x =_(+) x = x>0 x=8 =_(+x) x=0 x= =x(x+) x +x-=0 (x+8)(x-)=0 x>0 x= r = + =r+r=r T = 9 =_(+r), r=7 r= 0 =_(+), T = T T T=T=0. r 9 r T 0
,, _(+)=_(+x) x=8 x= T =T' x= T =T' = _= T = =x =x(x+), x +x-=0 (x+9)(x-)=0 x>0 x=. Q = Q x =_(+)=7 x>0 x=' 0 cm = H==90 Hª : =H : = H 8_= _ =0 (cm) 8cm H cm cm. ' Q=Q=Q Q Q =Q Q =_(+x) x=0 x= ==Q Q = Q x =_(+8)=8 x>0 x=' ' Q =Q ªQ = Q _=_(+x) x= x= = Q =Q =Q x Q x 8 Q x Q Q x. 'å0 0 ' ' x =_(+9)=90 x>0 x='å0 =8_(8+x), 8x=80 x=0 x =_(++)=8 x>0 x=' = T _=_9 = T = =x_(x++) x +9x-=0 (x+)(x-)=0 x>0 x= +_ +_0 +_ +_7 =_8 T T
T = T =_(+)= T >0 T = T = =_(+ ) =7 =9 = T = Q =Q =Q,, Q = Q =9_(9+)=08 >0 =' Q 9 =" - = (cm) = = cm _ = = (cm) E = =_0 =0 =E = =0 =x E = _(+0+0)=x_(x+0) x +0x-9=0 (x+)(x-)=0 x>0 x= 8_9= + = 0+_8 x 0 0 0 E. ~7 0 'cm 7 8 9cm 9 0 0 8'cm p cm _x=_8 x=0 _(+)=_(+x) x= x= =_8= (cm) = =_ + = - =-=(cm) = = (cm) = =_=8 >0 =' (cm) 7 8 =E F ' =E = F = _ =_ = Q Q =Q Q Q _=_ Q = (cm) T = =x cm =x(x++) x +7x-=0 (x+)(x-9)=0 x>0 x=9 (cm) F 8' ' y y
9 0 T =_(+9)= T >0 T = T T T=T TªT T =T T =T T =0 T =_(+)= T >0 T = (cm) T T =" 8 - =' (cm) T= + T _T = ' =8' (cm ) (') +_ =_8 (') +_ =_9 T,, T = Q =Q =Q Q y = Q (') =x(x+) y x +x-=0, (x+)(x-)=0 ' x>0 x= y,, Q = Q x 0 m, ==_0 =0 = = _0=0 (m) 0 m 0 x Q % %. 8 0 T = = =_(+)= T >0 T = = _ =_ =8 (cm) y y = _(+8)=(cm) y ( )=p_ =p (cm ) y 0% 0% (9'-p)cm cm 7 8 9 0 0 7 8 9 0 ' 8 'cm 7 ' 8 'å0 9 cm =r cm M =(r-)cm M r = +(r-) r= r= (cm). 9~
r r r + =r, r -r = = =pr -pr =p(r -r ) =p RHS = = _0 =0 =80 -(90 +0 )=0 = tan 0 ='_ =- = (cm) 0 =_ { '}-{p_ _ } 0 =9'-p (cm ) = T +T = + =+=9 (cm) H H =-= (cm) H H =" 9 - =' (cm) = H ='cm = _'=' (cm) =x cm F = =x cm E = =(-x)cm E =F =(-x)cm =E +E =(-x)+(-x)= x= x=7 (cm) =, =Q, =Q y =90 =" - = (cm) y = + + = +( + )+ = +( +Q )+ =( + )+(Q + ) cm = +Q = =_= (cm) y ' =, =Q, =Q T r r cm H 0 ==90 =0 -(0 +90 +90 )=0 = _(0-0 )= =Q=_0 =00 =00-0 =0 = = _0 =0 ==0 =90 =90-0 =0 =x =x = +x E 8 =( +x)+x x= 7 8 9 μ`=μ ==_0 =0 =0 +0 =90 + =80 _ =0 ++7+ Q=80 -==0 y Q= +0 =8 y Q Q=80 -(0 +8 )= y Q Q Q =80 -(0 +0 )=0 +=80 +0 =90 +80 + =80-70 =0 =80-0 =0 +=0 +0 =70 +80 _= +0_ x+ Q 0 0 0 x E 8 x % %
=T 80 T=T=x x 7 8 9 0 T=T =x T x+0 +x+x=80 x=0 x=0 =x μμ= =: ==x = ==x x+x+x=80, x=80 x= T==x= =QE=E E ==0 =80 -( +0 ) =7 =80 -==70 T==70 _(+x)=_(+7), x=9 x= = =8 cm =x cm =(x-)cm (x-)_=8_8, 8x=80 x=0 (cm) 0 cm =x cm x =(x-) +8, 8x=80 x=y y x=0 (cm) (+)_(x+)=(0+)_(y+0) x-y=- y x= y=0 y-x=0-= _8= _ = = _ _ _sin 0 ' = _(+8)_(+)_ = ' 0 T 0 x T x x x x x = _8=_ 8_(8+)=_(+0) = (cm) = E E y E==8 y FE FE=0-8 =8 y FE M M =" - = (cm) 0 0 =M =_=8 (cm) E 0 T =_(+8)=0 Q T >0 T =' (cm) 7 8 9 ' x =_(+)= x>0 x=' x =(+y), =9+y y= xy='_=' μ=μ = = =,, = = =x x =8_(8+)=0 x>0 x='å0 = =_(+)= >0 =' (cm) ' Q '=90 ' Q=90 'ªQ Q =' ' :Q =(+) : (+), Q =' Q = ' (cm) cm,,, E E cm 8 F 8cm 0 x 8 0cm % % E
I.. ~7 8' 0' 8 = +++++0+++x 9 +x = = 9 +x= x=,,,,,,,, 0 = 0 a+(-)++b+=0 a+b=- y. a +(-) + +b + a +b +8=8 =. a +b =0 y (a+b) =a +ab+b (-) =0+ab, ab= ab=8 a+b a +b ab 0% % % x 7+0+8++9 0 = = =8 (-) + +0 +(-) + 0 = = = =' = = 0_+70_+80_+90_+00_ 0 800 = =80 0 (-0) _+(-0) _+0 _+0 _+0 _ 0 00 = =0 0 =' 0=' 0%. 8~0.8... '. ' 0.8 7 '. 8 7, 0 9 0,. 0 x=, y= 7'7,. = ++++++++0+ 0 8 = =.8 0 0,,,,,,,,, + = =
= _+_+_+_+_ 9 = =. 7 8 + = =. = 90 = =9 0 ++a+b+0++ = 7 a+b+= + +0 +(-) +0 + +0 +(-) +0 +0 = 0 a+b=9 8 a, b = =0.8 0 a<b a=, b= =' 0.8,,,,,, 0 a+b a, b % % x, y = 90 = =9 0 = = =. 0 ='. = 9+0+0+9+9+7+0+9+0+7 0 0 + + +0 +0 +(-) + +0 + +(-) 0 0+0+9+8+9+0+9+7+9+9 0 (-)+++(-)+++(-)+(-)+x+y = 0 x+y+=0 x+y=7 x-y= x=, y= y -, -, -, -,,,,,, + = =. = 0 +(x-)++x+(-)=0 x= x= = - =0- =8(kg) -=y-8 y= =z-8 z=0 x-y+z=-+0= x 0% 0% y, z x-y+z 0%
7 0 x, y, z +9+x++y=0 (x-0) +(y-0) +(z-0) = x+y= y (x-0) +(y-0) +(z-0) = _+_9+_x+7_+9_y = 0 x+y+z+7+ 0 = = =0 x+9y=9 y x=, y= (x-0) +(y-0) +(z-0) +(-) + = 8 9 (-) _+(-) _9+ _+ _+ _ = 0 9 = =. 0 ='. x, y 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-) =0 (a+)+(b+)+(c+)+(d+)+(e+) = = +0 = =7 = = =0 x, y, z 0 x+y+z a+b+c+d+e+0 (a+-7) +(b+-7) +(c+-7) +(d+-7) +(e+-7) (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% 0% =0 x+y+z=0 0 0% 0% = =. x, y,,, 7 x+y+++7 =, x+y+8= x+y=7 y x, y,,, 7.8 (x-) +(y-) +0 + + =.8 (x-) +(y-) =9 y y=7-x (x-) +(7-x-) =9 x -7x+0=0, (x-)(x-)=0 x<y x=, y= 8 7 0 7 { }= _8= { }= _=8 0 ='7 x, y, z x, y, z x, y, z, 7, x, y, z, 7, x, y,,, 7 x, y,,, 7 x, y 0 0 +8 0 0% 0% =7 0% 0%
+=8+8 0 (-)_+(-)_+(-)_x+0_y+_=0 -x+=0 x= 8 +(8-) +(8-) 0 +=80 =8 = =8 +(-) +(-) 0 = =. 0 8. brix. brix. brix. brix brix. brix. brix. brix. brix. brix. brix 0% 0%. = brix, 0 ml, E, 7, 8, 9, 9, 9, 0, 0, 0 =9 7 8 9 0+80+70+0+0=70(mL) 70 = =0(mL) æ { } 0 ml, -70 ml, 0 ml, -0 ml, 70 ml E. brix. brix - brix -=- =(brix). brix. brix -=-(brix). brix. brix -=0(brix) x, y 0 0% 0% = _(7+0+7+0+0+++0+9+0 0 +0+++0+++9+0+0+) = _70=8.(g) 0,,,, 7, 7, 9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0,,, 0 = 0+0 =0(g). ~
0 g 9 =0 g 8. g 0 g 0 g 0 g II.. ~7 '-' 7 = 0 = =0 = 0 = =0 0 + + +(-) +(-) + = = 8 = =77. y + + +(-) +(-) +8 = = 0++7+78+0+8 7+++0+08+8 00+9+0+8++7 9++++0+ 8 = =9,, % % % % = - =0 >0 =' =(') -(') = >0 = = - =-= =" + =' E = =' EF F =" (') + =' G =F =' EG =G -E ='-' E G EG x+ x +8 =(x+) x +=x +x+ x=88 x= = + + =0++8=7 x x = = _8= E =x E =E =8-x E x + =(8-x) 0% 0% x=8 x=
채점 기준 배점 ⑴ E =EG =G = =c 의 길이 구하기 0% + E= + =90 이므로 E 의 길이를 x에 대한 식으로 나타내기 0% E=90 x의 값 구하기 0% 마찬가지 방법으로 EG= EG= G=90 따라서 EG는 네 변의 길이가 같고, 네 내각의 크기 가 같으므로 정사각형이다.. 8~0 단계 cm ' ⑴ 풀이 참조 ⑵ 풀이 참조 x=', ' m 8 cm ', ' 7 7 9 ' cm 8 ⑵ FH=(a+b) = ab EG=c 따라서 0 ⑴ 풀이 참조 ⑵ 0 ⑴ bc ⑵ FH= + (a+b) =_ 0 cm 정 답 과 해 설 EG이므로 ab+c a +ab+b =ab+c = cm 이므로 a +b =c =' =(cm) 채점 기준 EFG= cm 이므로 E =EF =' =(cm) 따라서 FE에서 채점 기준 배점 정사각형 EFG의 한 변의 길이 구하기 FH,, EG의 넓이 구하기 E이므로 이때 E의 넓이가 0 cm 이므로 =0, =0 그런데 >0이므로 ='(cm) 에서 =" + =' 9 따라서 에서 =" (' 9 ) - =' 채점 기준 0% 의 길이 구하기 0% E = = cm, = = cm E= _(+)_(+)=8(cm ) 채점 기준 m xm 에서 =" (') - =(cm) 배점 의 길이 구하기 m E는 E=90 인 직각이등변삼각형이다. 를 그으면 EG가 정사각형임을 설명하기 정사각형 의 한 변의 길이 구하기 F 의 길이 구하기 배점 피타고라스 정리가 성립함을 설명하기 F =" (+) + ='ƒ=(cm) 배점 의 길이 구하기 의 길이 구하기 E, 의 길이 구하기 0% 사다리꼴 E의 넓이 구하기 0% H m m m a가 가장 긴 변의 길이일 때, +7 =a, a =7 위의 그림과 같이 천막 지붕의 꼭짓점 에서 담벼락에 내린 수선의 발을 H라 하면 a + =7, a = 따라서 천막 지붕의 넓이는 그런데 a>0이므로 a=' 따라서, 에서 a의 값은 ', ' 7이다. 채점 기준 배점 배점 가장 긴 변의 길이가 a일 때, a의 값 구하기 x의 값 구하기 0% 가장 긴 변의 길이가 7일 때, a의 값 구하기 천막 지붕의 넓이 구하기 0% a의 값 구하기 0% 채점 기준 Ⅱ. 피타고라스 정리 _'=' (m ) 7이 가장 긴 변의 길이일 때, H =-=(m), H = m, =x m이므로 H에서 x=" + =' 그런데 a>0이므로 a=' 7 7 답지 블로그
7 a=" + =0 0 =a, =b, =c, =d =a +b =, = _ =b b=9 c=" +9 = a+b+c=0+9+= a b c a+b+c 0% =c +d =a +d =b +c + =(a +b )+(c +d ) =(a +d )+(b +c ) = + + = + =00 >0 =0 8 9, E, = =x, E =E =y E E =(x) +y =x +y =x +(y) =x +y (x) +(y) =0 x +y =00 x +y = E + =(x +y )+(x +y ) N =x cm =(x +y ) =_= M, N, M M = = _=(cm) MN = M = = _=(cm) M N N =M MN x= =x(cm) =(x) - N =x - = (x) - =x - x =, x = y` y` x>0 x=n ='(cm) N N N E E + 0% 0%,,, + = + =90 a =b +c = + + - c b =[ p_{ }]+[ p_{ }]+ bc a -[ p_{ }] = p(c +b -a )+ bc 8 = bc bc F= =F F=F F F =F F =x cm F =x cm F =(-x) cm F (-x) +8 =x x=0 x=f =0(cm) 0% 0% 8
F F F. (-x) (x+9) x -x+8=0 8 7.7 S+U=T x =-x 9 =x+9 + = x +(-x) =(x+9) x -x+8=0 x -x+8=0 (x-8)(x-)=0 x=8 x= 0<x< x=8 8-8= 8+9=7, H H =x = =(x+0.) H x + =(x+0.) x=.7 x x x +ax+b=0 a, b x.7 0. H x 0% 0% x+0. 0% =90 =c, =a, =b +R=Q b +c =a,, cab STU=c a b S=kc, T=ka, U=kb (k>0) S+U=kc +kb =k(c +b ) b +c =a k(c +b )=ka =T S+U=T STU +R=Q S+U=T ' cm x=', y=' =90 0 00p cm 0%. ~ H = ' _='(cm) G G = H = _'='(cm) ' G= _(') ='(cm ) G G =' =' =' =' ' x'=' x= =' ' = 0% 'y= y=' 9
x y, Q Q 0% 0% =" (--) +(-) =' =" {--(-)} + (--) =' =" (--) + (--) =' 8 = + =90 = _'_'=0,, =++ = _ _ + _ _E + _ _F = _0_ + _0_E + _0_F =( +E +F ) 0 ' = _0 =' ( +E +F )=' +E +F =' 70 =" - =(cm) _p_ _=00p(cm ) 7 cm ' 9 '7 '7 {, } ' cm ('-) cm 7 =90 8' cm 8 ' cm 9 ' cm 00' 0 ' cm, cm 9 p cm '7. ~ =" + =(cm) = _ 9 = _ = (cm) (x, y) 0% x>0, y>0 x 9 Q = (cm) 9 9 7 Q =-{ + }= (cm) H H =x, H =-x, H =y H y = -x H y = -(-x) -x = -(-x) y` y` 9 x=7 x= 8 y =- = y>0 y= 9 '7 {, } = _ _H '7 7 H '7 '7 = = x y =( +E +F ) 0 +E +F y 0% x
H= _90 =, H= H=90 H ' H = _8='(cm) H H H =' ' 'H =' H = ='(cm) ' ' cm Q x cm H=90 H E x cm == = =' x=' x ' = = x(cm) ' ' Q = x cm Q = + +Q ' ' = x+x+ x ('+)x= S G cm F R 0 8 x= =('-)(cm) '+, Q =" {(t+)-} + (-t) =' (t-) +(-t) =0, t -0t+0=0 H 8cm t -t+=0, (t-) =0 t= cm =' cm cm =' cm 8 cm, cm =" 8 + ='(cm) = + =90 = _'='_H _ _ = _'_'=8'(cm ) 8 HF HF ='(cm), F ='(cm) H _HF =F _H 0% 7 9 t t ' H = ='(cm) ' M cm ' M = _='(cm) H H = M = _'='(cm) H H =" -(') ='(cm) H= HF, F H M H H _H _H 0% 0% 0% 0% = _'_'=' (cm ) H % % % % 7
0 =0'(cm) H = = _0' ='(cm) H 0 cm H 0 cm 0 cm M M 0% H =" 0 -(') ='(cm) 00' _0 _'= (cm ) H H = = cm H =H - =7-=(cm) H H =" - ='7(cm) % % 9 _p_('7) _7= p(cm ). 7 0' ' 0 ' 7p cm " 0 +0 ='ƒ800=0' (cm) 0' cm a 0' a 0% 0% H 0% H M M M 0 H M H 8 MH HM =80 -(0 +0 ) =0 M = = _8= H =, MH =' MH H =8+=0 M =" 0 +(') ='7 =p_9_ =p(cm) p = =(cm) p =" 9 - ='(cm) VÅ= _p_ _'='p(cm ) =p_9_ =p(cm) p = =(cm) p 0 0 0 0 =" 9 - ='(cm) Vı= _p_ _'=8'p(cm ) VÅ 'p = =' 0 y`fi Vı 8'p 7
VÅ fi p cm ' p cm " " VÅ Vı Vı ' p cm ' =p_=p(cm) "" " " =" (p+p) +(p) =' 7p(cm) 0% 0% 0% 0% 0% ` 0% b =cx y` =, ac=ya a =cy y` a +b =cx+cy=c(x+y) x+y=c c =a +b b =cx a =cy c =a +b Q Q E=+FGH c =_ c =a +b ab+(a-b), c =ab+a -ab+b E=++E (a+b)(a+b)= ab+ c + ab (a+b)(a+b)=ab+c +ab, a +ab+b =ab+c +ab c =a +b E=+FGH c =a +b E=++E c =a +b =, bc=xb. 8~9 0% 0% Q =(+)+==' 0(cm) Q =" (++) + (+) =' 000(cm) Q =" (+) + (+8+) =' 00(cm) ' 000=0' 0(cm) Q Q 7
III.. ~ ' ' sin =, cos =, tan = '7 x=', y='. tan = = = =0.9 + =0.8+0.9=., + 0% 0% 0% 7 =" + =' ' sin = = =, ' ' cos = = =, ' tan = = 9 sin = = = = =" -9 ='7 '7 '7 cos = = = cos tan 0 = x=' =' y ' sin = = y=' x y =0.7 cos =0.7 = x sin = = = =0.8 % 7% 0% 0%. ~ ' 0 '7 0 +'7 ' 7 8 9 0 ('+) 0.0 =" - =' =" ('+') + =' 7 ' ' 0 cos = = = ' cos, H, H' 8 x H = _(-9)= H H =" 8 - ='7 H 9 H H '7 '7 tan x= = = H H H tan x H' % %
E E==x =" + =, E =" + = E =" - = cos x= = E E sin x= =, cos x= = sin x-cos x= - = E==x E =k, =k k>0 =" (k) -(k) =' k ' k ' k sin = = =, k ' k ' tan = = = k ' ' sin _tan = _ = 0 x-y+=0 x y, x-y+=0 sin x, cos x sin x-cos x sin, tan sin _tan y=0 x=-8 =8 x=0 y= = =" 8 + =0 sin a= = =, 0 8 cos a= = = 0 7 sin a+cos a= + = x y x y sin a, cos a sin a+cos a k 0% 0% 0% 7 8 GEF=EF EF=GFE GEF=GFE GEF GF =GE =E = cm GH = = cm FHG FH =" - ='7(cm) F EG 0% 0% 0% 0% cos x F =HG = cm, E =EG -G =EG -FH =-'7(cm) EF F +'7 tan x= = = y`fi E -'7 cm sin x= = = =9(cm) E E =, E =9 E =(cm) cm F '7cm GF, GH FH E E =" - ='(cm) E x cm G cm H cm F, E fi tan x 0% 0% 0% 0% 7
9 E E E ' ' tan y= = = = E +E 9+ E E tan y (sin -cos 0 )_(cos +sin 0 ) ' ' ={ - }_{ + } ' ={ }-{ } = - 0% 0% 0% = = =sin 8 =0.7 = =cos 8 =0.88 = =tan 8 =0. = _( + )_ = _(0.7+0.)_(-0.88) = 0.=0.0 % % % % 0% 7 0 = =80 _ =0 ++ ' sin _cos _tan = ' sin, cos, tan sin _cos _tan tan = = = x =x = 0% 0% 0% x ' tan 0 = = = +x x='+'x, (-')x=' ' x= =('+) -' =x x x. 7 sin =, cos =, tan = '- sin a=, cos a=, tan a= H H =x, H =h H h = -x H h = -(-x) y` y` -x = -(-x) 8x= x=9 h = -9 = h>0 h= H 9 sin = =, cos = =, tan = = 9 x H h
H H =90, =0 8= =a(a>0) = =a, ='a, = ='a = - =('-)a ('-)a tan x= = ='- a, tan x sin a= = =, cos a= = =, tan a= = = a 0 y, 0 sin a=, tan a= sin 0 =0, tan 0 =0 cos a= cos 0 = a sin 0, tan 0 cos 0 a 0% 0% 0% x 8 cos 7 = = y 8 8 y= = =0 cos 7 0.80 x y H H =' sin 0 ='_ =' H =' cos 0 ='_ H =0-= H =" (') + ='7 H H H H = ' H = sin =_ =' =80 -(0 + )=0 H ' ' = ='_=' sin 0 ' 0 H 0 0% 0% 0% 0 0 H 0% 0%. 8~9 x=, y=0 '7 ' ' cm x tan 7 = = 8 x=8 tan 7 =8_0.7= = sin (80-0 ) ' = ='(cm ) = _'_'_sin 0 ' = _'_'_ ='(cm ) =+ ='+'='(cm ) 77
0% H =80 cos 0 =80_ =0(m) H =" (00+0) + (0') =0' (m) H H 0%. 0~. m.7 m 0' m km.8 cm 0('-) m 0 7.9 m 8 0' 9 { p-} cm 0 ' m ' = tan 8 =_0.78=.9(m) = + =.9+.7=.(m) H H H =0 tan =0_.8 =.8(m) H H =0 tan 0 =0_0.89 =8.9(m) =H +H =.8+8.9=.7(m) H H H H H =80 sin 0 =80_ =0'(m) ' 00m 0 0 0m 0% 0 H H H H =0 sin 9 =0_0.7 =0(km) H H 0% 80m 0 0 = = =. (km) sin 7 0.9, km H, H H H =0 cos =0_0.8 =.(cm) H = -H =0-.=.8(cm).8 cm H H H =h m 9 H H 9 0km 0% 0% hm 0 H 80m 0cm 0% 0% 78
7 8 H H =h tan =h(m) H H =h tan 0 ='h(m) =H +H =h+'h, (+')h=80 80 h= =0('-)(m) +' 0('-) m H H H=90-7 = H H =0 tan =0_0.8=.(m) H=90-0 =70 H H =0 tan 70 =0_.78=.9(m) 0 =H -H =.9-.=9.(m) 9. m,.9 m 0 H H H H H 0 H cos = = H = H =" - =' = _ _H = _0_' =0' 0 0 7 H 0m 0% 0% 0% 0% = =80 -( + )=0 = 0% 0% 9 0 H H sin (80-0 ) = =(cm ) =p_ _ 0 = p(cm ) = - = cos 0 =_ 0 = p-(cm ) =8(m) ' = sin 0 =_ =8'(m) = _8_8'='(m ) = _8'_0_sin 0 = _8'_0_ =0'(m ) =+ ='+0'='(m ) E E =" + =' 0(cm) E FSS F =E =' 0 cm, 0 0 0% 0% 0% 0% 0% 79
80 EF=-E-FE EF= =_-_{ }- =--8=(cm ) y` _E _F _sin x = _' 0_' 0_sin x =0 sin x y` = =0 sin x sin x= = 0 = E, F EF EF sin x _8 sin 0 ' = _8 =' Q H h m, Q 0, H=90-0 =0, QH=90 - = H H =h tan 0 ='h(m) QH QH =h tan =h(m) Q =H -QH ='h-h ('-)h=00 00 h= =0('+)(m) '- 0('+) m = _8_ _sin 0 0 8= = _8 = _8_ _ = =( sin )_8 ='(cm ) = _ sin 0 = _ = += + =' ' =' = 0('+) m ' cm 0' += 0% 0% % % % %. E 0 0 F,,,, E, F, G, H EFGH EF = =0, EH = =, E==0 EFGH=HEF =_{ _0 sin 0 } =0' H G 0 00m, Q H QH Q H 0% 0% 0% 0% hm
= a 0 b tan tan =0.087 =0.08y <tan EFGH = _0' =0' d c =a, =b, =c, =d =+++ = ab sin 0 + bc sin (80-0 ) + cd sin 0 + ad sin (80-0 ) ' ' ' ' = ab+ bc+ cd+ ad ' ' ' ' ={ ab+ bc}+{ cd+ ad} ' ' = b(a+c)+ d(a+c) ' = (a+c)(b+d) ' = _0_ =0' EFGH EFGH,,,,,, 0% 0%,, 0. tan = 0. 0. = = =.87 (m) tan 0.087.87 m 0% 0%. ~ ' 0. = ' =7.(m) ' ' - =7.-.87 =0.8 (m) 0. m 0. m x km cos 87 = 8000 8000 x= = =707. (km) cos 87 0.0 70000 km m 8000 x xkm 0.m 0% 0% 8000km 87 0% 0% 8
IV.. 8~9 0 cm = = _8= =x =x- x =(x-) + x= x=, = = =90 =" - = = = =_(+)=,, E =x =E =x, F = =9-x, F =E =-x =F +F 0=(9-x)+(-x) 0=0-x, x=0 x=e = F, F E E 0% 0% 0% 0% =_=0(cm) + = + 0+= +7 =7(cm) = _(7+7)_0 =0(cm ) 0 cm 8' cm 8' cm 0 cm 8cm 7 8cm 8 9p cm 9 cm cm 9 cm 0 0 7 0. 0~ N =N = = _'='(cm) N N =" 7 -(') =(cm) M =N = cm M +N =+=0(cm) N N M M +N M, M = = _8=(cm) M M =" 8 - ='(cm) =M =_'=8'(cm) M 0% 0% 8
M M =E =F = = E =E=90, =E ERHS E= = _0 =0 E = cos 0 =_ E =E =E =_'='(cm) = =_'=8'(cm) M ' E ='(cm) x cm M =(x-)cm M x =(x-) + x=0 x=0(cm) cm cm M cm x cm x- cm 0 cm % % 0% 0% =M T =M M =(cm) M M =" - =(cm) Q =M =_=8(cm) M T M M Q E = =x cm =E =(-x) cm = +x=7+(-x) x= x= E x x x x 7 =90 =G = cm, =0- =0-E =0-8=(cm) =" + =(cm) G = -G =-=8(cm) G % % % % % % 0% 0% 0% M % % QÍ M T Q T M cm cm cm M T M =T =90 M T 8, F F x cm =F=90 cm E cm x cm =F =x cm F =F =x(cm) =E = cm, F =E = cm (+) =(x+) +(x+) x +x-0=0, x +7x-0=0 (x+0)(x-)=0 x>0 x=(cm) 8
9 =p_ =9p(cm ), F E = = cm E = =9 cm =E +E =+9=(cm) H H =9-=(cm) H H =" - =(cm) =H =(cm) E E = _ _E = =9(cm ) 9cmH cm = _=(cm) E 0% 0% 0 G E =G =x F =E = =-x H =E =G =0-x F =H =-(0-x)=x- =F +F =(-x)+(x-)=0 a+b=8+8= y b+c=+7= y c+d=+7= y a+b+c+d=9 a++d=9 a+d=7 H F F F 0% 0% 0% a+b b+c c+d a+d 0% 0% 0% 0 =8 cm S =R =0-=(cm) ES =E =0-x-=-x(cm) _8=(cm) E =S +ES =+(-x)=-x(cm) E (-x) =8 +x 0 x=80 x= E x x x. ' cm, 8
,, M = M = _=(cm) = M _0=(cm) M =" - =' (cm) =M =_' =' (cm) _' =' (cm) M M =S, =Q, Q =R, R =S + = + +R +R =S +Q +S +Q =S +S +Q +Q = +,, M 0% 0% 0% 0% 0% 0%. ~ 70 8 x=, y=0 x=', y=, ==90 ==_ =0 =0 -(0 +90 +90 )=70, E E=90 μ E== E=90 - =8 E E E x=q= =80 - =80-00 =80 0 +y=80 y=0 x y % % 0% =S, =Q, Q =R, R =S, Q, R, S S,, Q, R 0% 0% T = x =_(+)= x>0 x=' ' T = (') =y_(y+) y +y-=0, (y+)(y-)=0 y>0 y= 8
8 x x y y. ~8 8cm 8 8 7 8 8 9 cm 9 0 x=, y= cm cm =- =8-0 = 0% 0% 7 E E= = _0 =0 E=9 -E =9-0 = E =80 -E =80 - = μ=x cm 0 =9x =90 x=μ=8(cm) =90 - = =80 - = E μ 0% E=80 -E=80 - = =90 =80 -(90 +8 ) = = =_ =8 Q Q=80-0 =7 Q=80-7 =0 ' Q =80-0 =7 '==_7 =8 8 % % Q ' E E E E=80 -==x F E=x+ E +x+(x+ )=80, x=0 x= E=x E=x+ x TQ=T= TQ=T=0 0 % % 9 0% % % E
8 9 T=80 -(TQ+TQ) EF =80 -( +0 )=8 TQ TQ T FE=80 -( + )=8 FE=FE=8 E =F EF=FE=8 FE x=80 -_8 = FE FE EF x T T=90 T =" 8 +(+) =0(cm) T = 8 = _0 = (cm) T=90 0% % % % % 0% T = _= _ =(cm) =x cm T = (') =x_(x++) x +7x-8=0 (x+9)(x-)=0 x>0 x= =(cm) μ = E=E,, E E =x cm =E 8 =x_(x+) x +x-=0, (x+)(x-)=0 x>0 x=e =(cm),, E E cm 0% 0% E x cm 8cm % % 0 T = x =_(+)= x>0 x= T T T=T TT x=y, y=x 9 y= x= _= x % T T y %. 9 ' = = ==a, ==b a+b=80 a+b=90 =a+b=90 90 a a b b 87
=, = 90 0% 0% k T =T T= T = μ=μ jk k k k 88 = μ=μ H =QH H QH =H H H =_= H >0 H =' H = _'=' =p_(') =p H, H = _p_ -{ _p_ + _p_ } =p H H Q 0% 0% r 0% 0% 0%. 0~ l r, l l Q, R Q<, R< Q r R 0% 0% 0% 0% l