Article View: fj.education.math
Article #304Re: 昔の、ある入試問題
From: Yuzuru Hiraga
Date: Tue, 08 May 2001 15:43
Date: Tue, 08 May 2001 15:43
50 lines
3150 bytes
3150 bytes
In article <9d75ku$qrr$1@nw031.infoweb.ne.jp> =?iso-2022-jp?B?GyRCJFckaSRIJHMbKEI=?= <ZAP14260@nifty.ne.jp> writes:
>$B!!1_<~N($r#p$GI=$9$3$H$K$9$k!#!V(Ja=b$B$^$?$O(Ja<b$B!W$r!V(Ja=<b$B!W$GI=$9$3$H$K$9$k!#(J
JIS $B%3!<%I$,;H$($k$N$@$+$i!"&P!"!e(J $B$G$$$$$N$G$O!)(J
# $B;d$OJQ49<-=q$KEPO?$7$F$"$k!#(J
> 0 =< a < p, 0 < b < 1/2, 0 =< x =< 1, y =< cos(p*b)$B!!$G$"$k$H$-!"ITEy<0(J
>
> sin(p*b) =< y*sin(a*b) + x*sin{(p-a)*b}
>
>$B!!$,@.$jN)$D$J$i$P!"(Jx = 1 $B$G$"$k$3$H$r<($;!#(J
>
>$B!!(Ja,$B!!(Jb,$B!!(Jx,$B!!(Jy $B$K$D$$$F$ODj?t!"JQ?t!"L$CN?t$J$I$H$$$&8+J}$h$j$b!"<+M3JQ?t!"(J
>$B!!B+G{JQ?t$H$$$&8+J}$GE}0l$9$k$[$&$,M-8z$J$N$@$m$&!#(J
$B!)!)!)(J
$B>e$NITEy<0$r(J (A) $B$H$7$^$9!'(J
(A) sin($B&P(Jb) $B!e(J y sin(ab) + x sin{($B&P(J-a)b}
$BLdBj$N>r7o$h$j(J 0 < cos(ab) $B!e(J 1$B!"(J0 < sin($B&P(Jb) < 1 $B$@$+$i!'(J
(B) cos(ab) sin($B&P(Jb) $B!e(J sin($B&P(Jb)
$B$?$@$7Ey9f$O(J a=0 $B$N$H$-$N$_@.$jN)$D!#(J
$BF1MM$K(J y $B!e(J cos($B&P(Jb) $B$H(J 0 $B!e(J sin(ab) < 1 $B$h$j!'(J
(C) y sin(ab) + x sin{($B&P(J-a)b} $B!e(J cos($B&P(Jb) sin(ab) + x sin{($B&P(J-a)b}
$BEy9f$O(J y = cos($B&P(Jb) $B$+!"(Jsin(ab)=0$B!"$D$^$j(J a=0 $B$N$H$-@.$jN)$D!#(J
(A), (B), (C) $B$rAH$_9g$o$;$k$H!"(J(A) $B$,??$J$i!'(J
(D) cos(ab) sin($B&P(Jb) $B!e(J cos($B&P(Jb) sin(ab) + x sin{($B&P(J-a)b}
$B$b??!"$D$^$j(J (A)=>(D)$B!#(J
(D) $B$N1&JU$NBh#19`$r0\9`$7$F!'(J
cos(ab) sin($B&P(Jb) - cos($B&P(Jb)sin(ab) $B!e(J x sin{($B&P(J-a)b}
$B$9$J$o$A!'(J
sin{($B&P(J-a)b} $B!e(J x sin{($B&P(J-a)b}
$BLdBj$N>r7o$h$j(J 0 < sin{($B&P(J-a)b} < 1 $B$@$+$iN>JU$r3d$C$F!'(J
(E) 1 $B!e(J x
$B$?$@$7Ey9f$,@.$jN)$D$N$O(J a=0 $B$N>l9g$@$1!#(J
(E) $B$HLdBj$N>r7o$N(J 0 $B!e(J x $B!e(J 1 $B$rAH$_9g$o$;$k$H!'(J
(F) x = 1 $B!J$?$@$7(J a=0$B!K(J
$B$D$^$j(J (A) $B$,@.$jN)$D$J$i<B$O(J a=0 $B$G$"$j!"$=$N$H$-(J x=1 $B$G$9!#(J
>$B!!!t$3$NLdBj$K!"IaDL$N?t3X20$5$s$,LLGr$,$k$h$&$JGX7J$J$I$,$"$k$N$@$m(J
>$B!!!!(J $B$&$+!#(J
$B$5$"!)(J
# (A) $B$r(J xy $BJ?LL$ND>@~$K$h$kNN0hJ,3d$H9M$($F$N(J
# $B4v2?E*%"%W%m!<%A$b$"$j$=$&!#(J
$B!JJ?2l!w?^=q4[>pJsBg3X!K(J
Technical Details
Message-ID:
<9d946e$1501@goat.ipc.ulis.ac.jp>Path:
arc1-ca.pugleaf.net!newsfeed.google.com!newsfeed.stanford.edu!canoe.uoregon.edu!logbridge.uoregon.edu!nntp-relay.ihug.net!ihug.co.nz!newsfeed.media.kyoto-u.ac.jp!itakura-news!news.cs.ritsumei.ac.jp!igakukei!nadesico.cc.tsukuba.ac.jp!nntp.ipc.ulis.ac.jp!hiragaReferences:
<9d75ku$qrr$1@nw031.infoweb.ne.jp>Show Full Headers
Complete Article Headers
X-Google-Language: Japanese,JIS X-Google-Thread: f4956,6caaaf06631047f3 X-Google-Attributes: gidf4956,public X-Google-Thread: 1065a2,6caaaf06631047f3 X-Google-Attributes: gid1065a2,public X-Google-ArrivalTime: 2001-05-08 09:05:09 PST Path: arc1-ca.pugleaf.net!newsfeed.google.com!newsfeed.stanford.edu!canoe.uoregon.edu!logbridge.uoregon.edu!nntp-relay.ihug.net!ihug.co.nz!newsfeed.media.kyoto-u.ac.jp!itakura-news!news.cs.ritsumei.ac.jp!igakukei!nadesico.cc.tsukuba.ac.jp!nntp.ipc.ulis.ac.jp!hiraga From: hiraga@ulis.ac.jp (Yuzuru Hiraga) Newsgroups: fj.education.math,fj.sci.math Subject: Re: 昔の、ある入試問題 Date: 8 May 2001 15:43:10 GMT Organization: Univ. of Lib. & Info. Sci., Tsukuba, Japan Lines: 52 Message-ID: <9d946e$1501@goat.ipc.ulis.ac.jp> References: <9d75ku$qrr$1@nw031.infoweb.ne.jp> NNTP-Posting-Host: hiraga-lab.ulis.ac.jp