̤ꤹ1
ǽ˴ְ㤨ƳABCФƤޤޤ()
ɺ̤ʤ餺
񡡡 915ڡ 0:08:02 45200
٥륯åĥ
45ΤϤǤǼĤʤΤǤ⤦ĤβõƤߤȤ112.5٤⤢ޤ
ҤȤнʬȻפΤ45٤Ƥޤ
915ڡ 0:19:52 45201
٥륯åĥ
45٤ϡġ£äξͤ餹˽ФƤޤ
112.5٤ϣ£äФƣоΤФȤꡢˣäФƣФоΤѤȤäơѷѣĤȻѷãѣǤȤͤޤ
915ڡ 0:29:42 45202
鯤ο
AB=a,AD=2a,AC=b,ACBȡADCXȤȡ
ˤꡢ

b/1=a/sin
b/sinX2a=sin2

ꡢcosȡsinXcos(/2-X)
/2-Xަ
X/2-ަ
X+3ȡ
äơ
(,X)(/4/4)or(/8,5/8)

X=45or112.5
915ڡ 0:38:41 45203
ǯ
ABCAC򼴤ˤȿžAEC롣
ˡAECEC򼴤ˤȿžECFĤ롣
AF=ADȤʤΤǡADFջѷ
ACB=ȤȡCAB=90-DAC=ACB=ʺѡˤʤΤǡFAD=90-
Τˡջѷ AFD=45+
줬CAB=90-ƱʤΤǡ=45ΤˡADC=180-=180-3*45/2=225/2

915ڡ 10:06:30 45204
⡼ޥ
äȤ ^^;...
ޤǡ
ACǾޤäơ⤦BCޤȤȡD̤礭ջѷ
ADջѷǤƤ...礭ջѷBCˤʤΤǡ
=90
so
180-3=180-(3/4)*90=450/4=112.5

45뤬Фʤ^^;
915ڡ 0:48:00 45205
Mr.ǥ
CDαĹˡCA=CEȤʤEȤ
CAEϢCAB򣲤Ĺ碌ΤȤʤꡡAE=AD
CAB=AED=ADE
ADE=Ȥ
DCB=CAB=ACB=/3
CABܢACB=90
ܦ/390
67.5
ADC=180-67.5=112.5
ʾΤ褦˵ޤ
915ڡ 0:56:15 45206
ǯ
#45201 45٤餷ϻפ⤷ޤǤ

915ڡ 9:51:50 45207
Ȥ
ɸA(0,1),B(0,0),C(a,0),D(2,1)Ȥ
tan(ִ)=1/a,tan(3*ִ)=1/(a-2)Ԥμ3ܳѤθԤͤ
aǤ롡XMaxima Ǥ

trigexpand(tan(3*a))$
solve(ev(%,tan(a)=1/a)=1/(a-2),a)$
part(%,3)$part(%o2,2)$%th(2);%th(2);a=1,a=sqrt(2)+1 ޤͤ
a=1ΤȤADC=45롦(1Ĥ)
a=sqrt(2)+1ΤȤϡ(BC-AD)/AB=sqrt(2)-1=tan(22.5*%pi/180)
ADC=90+22.5=112.5롦(2Ĥ)
˭ԡ 915ڡ 1:14:51 45208
鯤ο
#45202˸ʤäΤǼ­ʤ顢䴰Ƥߤޤ

ACBȡADCX

QCPCAC顢CAQϡCA=CQջѷ
ޤADAPAQ顢ADQϡAD=AQջѷ
CAQȢADQϡѤΰĤͭƤ뤫顢
äơDAQACD2

AD//BC顢CAD
ꡢAQDQDA3
顢2ȡ3ȡ3ȡ180
ȡ22.5롢ȡ67.5롢X180-3ȡ112.5
915ڡ 1:07:47 45209
ȤޤԤ
2³ޤ֤ޤ
ܡBC򼴤˭CBAAưA
ܡCA򼴤˭CAA' AǤưA"

ȡCA'A" ջѷǡѤ¤֡8ʬȤʤ
äơ֡180/822.5

Ѥϡ180-3֡180-322.5112.5
915ڡ 9:41:26 45210
ˤ
ϥܥǭ̿ˤʤޤ
915ڡ 11:23:27 MAIL:nikotan@fat.coara.or.jp 45211
uchinyan
Ϥˤϡơϡ
־οޤΤ褦ʡפȤΤ¿ʬ𤷤ϾʤȻפޤAD < BCĤޤꡤADC > 90롤ȻפäƲ򤭤ޤ
Ǥǽ龯ͤޤդ饹륹Ȳ򤱤ޤȤƤɸŪʡ
ʴǡ

ABC AC ˴ؤޤ֤ B ΰư E Ȥ ACE CE ˴ؤޤ֤ A ΰư FȤޤ
CEF = CEA = CBA = 90ꡤAEF Ʊľˤꡤ
ACF = ACE + FCE = ACE * 2 = ACB * 2 = ACD ꡤCDF Ʊľˤꡤ
AF = AE + FE = AE * 2 = AB * 2 = AD ꡤADF AD = AF ջѷǤ
ǡλѷˤơ
DAF = BAF - BAD = BAC * 2 - BAD = (90- ACB) * 2 - 90= 90- ACB * 2
AFD = ADF = BCD = ACB + ACD = ACB + ACB * 2 = ACB * 3
DAF + ADF + AFD = 180롤(90- ACB * 2) + ACB * 3 + ACB * 3 = 180롤
ACB * 4 = 90롤ACB = (45/2)롤DCB = ACB * 3 = (135/2)롤ADC = 180- DCB = (225/2)롤
ˤʤޤ

٤μդϡȤƤϿޤ򸫤ʤ򤯡Ȥˤʤޤ
ޤ¿ʬʲˡǤ礦

ʤAD < BCADC > 90롤ȤƲ򤤤ƤΤǡ
DCB < 90롤ACB < 30롤BAC > 60롤CAD = ACB < 30롤ǡEF ABCD γˤޤ
⤷ʳξͤȤȡ
AD = BC ξϡACB = 30롤AC = AB * 2 = ADǤABCD ĹʤΤǡ餫Բġ
AD > BC ξϡACB > 30롤ǤACB = 45뤬ݥȤǤ
30< ACB < 45ΤȤϡAD < BC ξƱ EF ABCD γˤꡤƱ٤μΤǡ
ACB = (45/2)< 30ȤʤäơԲġ
ACB = 45ΤȤϡE AD F = DADF ϤĤ֤ơ餫˲ˤʤꡤADC = 45롤Ǥ
45< ACB ΤȤϡAD < BC ξȰۤʤ EF ABCD ˤޤƱ褦ˤƳ٤μϡ
DAF + ADF + AFD = 180롤(ACB * 2 - 90) + (180- ACB * 3) + (180- ACB * 3) = 180롤
ȤʤޤϡACB * 4 = 90롤ACB = (45/2) < 30ȤʤäơԲġ
ɤΤȤACD (225/2) 45롤Ǥ͡

45Ȥ򤬤ʾ塤AD < BCȤξդΤΤޤ
915ڡ 13:03:44 45212
uchinyan
ǼĤɤߤޤ


ʲεҤϡ⤽ϻ伫ȤٶΥ˲᤮ʤΤǤ
޳ѤʤΤǤͤޤǤˤȻפäƸΤǤ
Ȥ⤢äơˡʬϻ F.A.Q. ΡֻϰϡפεҤ򻲹ͤˡ
ĿͤǤиǼŪ˹ԤäƤΤǤäơҴŪʤΤǤϤޤ
ޤǤ⤴ͤǤ餺

Ϥꡤ#45212ʳˤ 45򵤤ˤʤäƤ#45201#45203#45208ޤ͡
äȤ⡤ؤDz򤱤мȸޤ

ʲϡ(225/2) = 112.5ˡʬǤ
ǽ㤤ޤ¼ϤɤۤƱǤ͡

#45202#45210
BC ˴ؤ A оΤȤꤵ AC ˴ؤƤоΤȤäջѷäƲ򤯲ˡ

#45204#45205#45212
ABC AC ˴ؤޤ֤˰ư BC ˴ؤޤ֤ջѷäƲ򤯲ˡ
ɤջѷܤɤȤǼ㴳ΥХꥨ󤬤ޤ

#45206
CD αĹ CA = CE Ȥʤ E ȤäջѷäƲ򤯲ˡ

#45215
ABC BC 򼴤ޤ֤ ACD AC 򼴤ޤ֤ջѷäƲ򤯲ˡ

#45225#45226
ο޷򣸸Ľ˰դ AD Ťʤ褦¤ٰդ CD ȬѷäƲ򤯲ˡ
¤ϻФƤȬѷǤʤȤϻפäΤǤˡȤƤޤǤϹͤޤǤ
ȤΤϡȬѷΤΤǤ D ȤϤʤȥåȤʤäΤǡ
ŪˤϡߤäƤ濴濴Ȥĺ߼ˤʤäơ
դ˿ľľ¤üΤդؤθ٤ȡ
ľ¤ʿԤƱβդФƱθ٤ϡפʤȻפΤǡ
¿ʬˡȤƤΤȻפޤ׻ǤϤޤ͡
ϤȬѷդ꤫餫ʡ
ʤߤˡ45βˤʤꤽǤ͡

#45203#45208#45216#45219#45223
ؤˤˡ

ʤ#45212Ͼؤݤäʤȿʡ
ADFCAF ջѷ ACB * 8 = 180ȤǤ
916ʶ 16:19:45 45213

10ˤʤä ϲδۤȤȤ Ф뤫
915ڡ 16:07:12 45214
2N.K.
windows10ѤäȤȤˡ23ʹPCȤʤʤäorz

ʤۤɡ45Ȥ⤢Ǥ
ͤޤǤ

ͤϡ
ѷABCBC򼴤ޤ֤ΤȤAΰưEȤ롣
ѷACDAC򼴤ޤ֤ΤȤDΰưFȤ롣
ȡѷAEFջѷȤʤ
ĤȤˤƳ٤򤪤äƤޤ

915ڡ 17:57:37 45215
ˤ狼
Dz򤱤Ƥޤ¤Ǥ
ʬ鲿ǥꥴ򤤤ΤǤ
Ȥ̤βˡǤäƤ
sin^2-sin=cos^2-cos
ȤФƤΤǤѤʤ龯ͤǤϲ򤱤ޤǤ
ï˲򤤤Ƥޤ
ߤ˦ִʬγ٤Ǥ
915ڡ 18:09:28 45216
ˤ狼
Dz򤱤Ƥޤ¤Ǥ
ʬ鲿ǥꥴ򤤤ΤǤ
Ȥ̤βˡǤäƤ
sin^2-sin=cos^2-cos
ȤФƤΤǤѤʤ龯ͤǤϲ򤱤ޤǤ
ï˲򤤤Ƥޤ
ߤ˦ִʬγ٤Ǥ
915ڡ 18:09:38 45217
ˤ狼
ХϢꤹߤޤ󡦡
ʤäޤ
915ڡ 18:16:00 45218
ǯ
#45127
(cosA)^2-(sinA)^2=(cosA-sinA)*(cosA+sinA)=cosA-sinA
(1) cosA-sinA=0 or (2)cosA+sinA=1
(1)ꡢA=45,or A=225
(2)ϡξդ2褷ơ(cosA)^2+(sinA)^2+2*cosA*sinA=1
2*cosA*sinA=sin2A=0ʤΤǡ2A=180 or 360
ǡŬڤʤΡ03A/2180)ʤɤǤ礦A=45ʢADC=225/2)2A=180(ADC=45)Ǥ
ष(sinA)^2-sinA=(cosA)^2-cosAɤäƽФƤΤꤿǤ͡
915ڡ 21:22:44 45219
tera
Dz򤱤
915ڡ 22:35:41 45221
ޥ
ߤޤ󡢤45Ȥ򤬤ޤΤǡ򰷤ȤơƤޤ
MacbookPro 915ڡ 22:41:51 45222
ˤ狼
#45219
꤬Ȥޤ
ʬⵤŤʤäΤ

ƳǤDAC˿򤪤EȤޤִݤγ٤Ϧ лͳѤĹ1Ȥޤ
AEĹ2cos
CEĹDE=2sinȤ2sin/tan2
ιפABC1/sinȤ
2cos +2sin/tan2 = 1/sin
2cossin +2(sin)^2/tan2 = 1
2(sin)^2/tan2 = 1-sin2
(1-cos2)/tan2 = 1-sin2
2=ȤΤμǤ
915ڡ 23:52:18 45223
ϥ饮㡼ƥ
äȽޤ
ꤨޤ׻⡪
916ʶ 4:17:02 HomePage:湩ؤ˥45224

ְäƤʤСο޷8ŤͤȬѷǤȻפޤ
ʬACг1ܤǤ͡
Ȭѷ1ĤγѤ135
Ȭѷ2ĤդդȤĺ135ջѷѤ22.5
äơ135롼22.5112.5
ʡ
ޤäƤ鴪ǤääƤȤǡ
916ʶ 9:00:58 HomePage:45225

8ŤͤȤDCȬѷ1դȤʤ褦ˡ¤٤ƤȤäǤ͡
916ʶ 9:05:35 HomePage:45226
uchinyan
#45225
¿ʬǤȻפޤ#45213
916ʶ 13:05:19 45228

uchinyan
꤬Ȥޤǧޤ
917ڡ 1:04:36 HomePage:45229

ʬϡΤգ£äޤ֤Τ򤯤äĤ5ѷꡢ
բĺѡλѷĤʬǤ뤳Ȥ顢
߼Ѥιͤ顢5ѷߤܤ롢ȹͤƲ򤭤ޤ
ľŪʲǡϰϤǤʤǤ
917ڡ 1:15:55 45230

uchinyan
꤬Ȥޤǧޤ
917ڡ 7:17:22 HomePage:45231

Ĥ͡
ͤ£ä˰­š
Ĥ£ä˰­ơ
äȣͣŤθǡäȣģƤθȤȤޤ

ȣĤȢã¤Ǥ
ģãƤ⤳ä餤ʤȻפ
δ˾Ūͽ¬ǤʤȤͤƲ򤭤ޤ

//£äꡢܣã¡ܣͣǡ

͡ģ͡ᢣͣǤ϶̡ܣͣǡܣģͣǡ90ꡢ
ǣ͢ᢤģǣ
ܣǣ͡ܣǣģ͡

ܣģǣáܣǣ͡ܢܣǣģ͡
äƢģǣäϡܣģǣáܣģãǡջѷȤʤΤǡ
ģǡģ

ģǡģáģ͡ģơᢣܣģͣǡܣģƣá90ꡢ
ģǣ͢ᢤģã
ܣǣģ͡ܣãģơ

ģãƤˤơ
ܣãģơܣģãơܣģƣá90ȤʤΤǡ
ܣãģơܢܣģãơ90롡
22.5

ܣģáܣģơܢܣãģơ9022.5112.5
918 23:30:47 45232
Ф
ܣã¡ȤȤƣȤɽ̤Ȥʤꡢʤ3ˤʤä
920ʲС 6:47:31 45233
cocogoo
3ʬ1Ĥγ٤ȤơDCsin2=ADsinñ˵ޤ롣ѴؿǺǽĩ路ʣ롣ܤƤߤäƤ롣
920ʲС 10:28:19 45234