Coordenadas Polares
August 23, 2022 | Author: Anonymous | Category: N/A
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JB_KPZKEBLZF JB EKZBEËZMIK Ektbeëtmik MM Ea.3 Emaubh Ëlabh Zkrkzflk Amrkhjf emtkamOaekmh.ife - emtkamOdftekmh.ife emtkamOdftekmh.ife B-ekmh3 emtkamOaekmh.ife B-ekmh3 dttp3//emaubhtkrkzflkamrkhjf.ife/ dttp3//emaubhtkrkzflkamrkhjf.ife/ Cuhmf jbh 0?0? Iffrjblkjks pfhkrbs
Jbgmlmimùl jb iffrjblkjks pfhkrbs Bh smstbek jb iffrjblkjks pfhkrbs bephbk jmstklimks y jmrbiimflbs pkrk bspbimgmikr hk u`mikimùl jb ul pultf bl bh phklf. _krk prbpkrkr bh smstbek, sb bhmab ul pultf gmcf F bl bh phklf hhkekjf bh pfhf (u F
y sb jbsjbbl hkulgmaurk rkyf (sbemrrbitk) frmabl hhkekjf) bh bcb jm`uck pfhkr ifef Bltflibs k ikjk pultf _ sb hb pubjbl ksmalkr iffrjblkjks pfhkrbs jfljb r bs hk jmstklimk jb Fk_
,
bs bh ëlauhf bltrb bh bcb pfhkr y bh sbaebltf Yb usk hk iflvblimùl jb qub bs pfsmtmvf sm sb emjb bl jmrbiimùl ifltrkrmk k hks eklbimhhks jbh rbhfc jbsjb bh bcb pfhkr f lbaktmvf sm sb emjb bl jmrbiimùl jb hks eklbimhhks jbh rbhfc. Ym r bs lbaktmvk, bltflibs sb jbgmlb ifef bh pultf qub sb bliubltrk k ulmjkjbs jbh pfhf bl hk jmrbiimùl fpubstk k hk qub jk vbr hk gmaurk.
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Arkgmikr pultfs bl iffrjblkjks pfhkrbs Arkgmqub hfs pultfs iuyks iffrjblkjks sb jkl. k)
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_ëamlk ; jb ;2
i)
9,9
j) sb hfikhmzk k : ulmjkjbs jbh frmabl k hf hkraf jbh ëlauhf , pfrqub bh vkhfr jkjf jb r bs lbaktmvf.
`) Ftrks rbprbsbltkimflbs ifl r < ? sfl
:,/: 2/:
050, 19 0 0, 9 05 050,0, 29 0 0, 9 05 50, :9 0, 9 5
Ftrks rbprbsbltkimflbs ifl r8? sfl
,, ,
Yb f`sbrvk qub rbprbsbltkl bh emsef pultf, ifef sb eubstrk bl hk gmaurk. Kjbeës, tmblbl jb`mjf k qub tfjfs hfs ëlauhfs bh emsef hkjf tbremlkh qub bh ëlauhf ikjk pultf bl bh phklf tmblb ul lóebrf mlgmlmtf jb rbprbsbltkimflbs bl iffrjblkjks pfhkrbs. Jb dbidf, iukhqumbr pultf sb pubjb rbprbsbltkr pfr y pkrk iukhqumbr bltbrf l.
0,, , ,0 , 0;
0, 0, 50, 09 9 5
Hks arëgmiks jb hk gmaurk bxphmikl pfr quí bstks iffrjblkjks rbprbsbltkl bh emsef pultf.
Iffrjblkjks pfhkrbs jmgbrbltbs pkrk bh emsef pultf k) Arkgmqub bh pultf ifl iffrjblkjks pfhkrbs
0,/9
`) Bliubltrb ftrks jfs rbprbsbltkimflbs jb _ bl iffrjblkjks pfhkrbs ifl r < ? y jfs ifl r 8 ?. Yfhuimùl k) Hk arëgmik sb eubstrk bl hk gmaurk. _ëamlk 0 jb ;2
Pbhkimùl bltrb rbitklauhkrbs
iffrjblkjks
pfhkrbs
y
;. _krk ike`mkr jb iffrjblkjks pfhkrbs k rbitklauhkrbs, usb hks gùreuhks
{5 5 5 5 ≯?
0. _krk ike`mkr jb iffrjblkjks rbitklauhkrbs k pfhkrbs, usb hks gùreuhks
Iflvbrtmr iffrjblkjks pfhkrbs k iffrjblkjks rbitklauhkrbs
Pbhkimùl bltrb rbitklauhkrbs
iffrjblkjks
pfhkrbs
y
Bliubltrb iffrjblkjks rbitklauhkrbs pkrk bh pultf qub tmblb iffrjblkjks pfhkrbs
:, . 5 : 50/9, 55:09 5 : ;0 5 0 55: 55:09 5 : ∓ 09 5 0∓ 9 55:
Yfhuimùl
_ubstf qub Ifl grbiublimk surabl smtukimflbs bl hks qub bs lbibskrmf iflsmjbrkr kh emsef tmbepf iffrjblkjks pfhkrbs y rbitklauhkrbs. Hk iflbxmùl bltrb hfs jfs smstbeks sb mhustrk bl hk gmaurk, jfljb bh bcb pfhkr ifmlimjb ifl bh bcb x pfsmtmvf.
y
Iflvbrtmr iffrjblkjks iffrjblkjks pfhkrbs
Hks gùreuhks bl bh smaumbltb iukjrf i ukjrf sb f`tmblbl jb hk gmaurk pfr ebjmf jb hks jbgmlmimflbs jb gulimflbs trmaflfeítrmiks y bh tbfrbek jb _mtëafrks. (Kulqub sb dk mhustrkjf bh iksf jfljb r < ? y bs kaujf, hks gùreuhks sb iuephbl pkrk iukhqumbr ëlauhf y pkrk iukhqumbr vkhfr jb r .) .)
sb tmblb sb
rbitklauhkrbs
k
Bliubltrb iffrjblkjks pfhkrbs pkrk bh pultf qub tmblb iffrjblkjks rbitklauhkrbs Yfhuimùl Ifl , sb f`tmblb _fr hf tkltf f Zke`míl Zke`míl
0,0 50 550 0 5 4 5 0 0 50 50∓ ∓ 00.. ∓ 50
∐ 5 5 5 ;
_ëamlk 9 jb ;2
5 5
Kså qub . _ubstf qub bh pultf sb bliubltrk bl bh MW iukjrkltb víksb hk gmaurk, sb pubjb rbprbsbltkr bl iffrjblkjks pfhkrbs
0,0 00∓ ∓ 00>> 00∓ ∓ 00>>
ifef
.
5 : 5:∝
Jmvmjk pfr
Ymephmgmqub
Iflvbrtmr biukimflbs jb iffrjblkjks pfhkrbs k rbitklauhkrbs Bxprbsb hk biukimùl pfhkr bl iffrjblkjks rbitklauhkrbs. Ym bs pfsm`hb, jbtbremlb hk arëgmik jb hk biukimùl k pkrtmr jb su gfrek rbitklauhkr. k)
52
5 . 52 52 52 5 52
pubstf qub
, sb euhtmphmik ke`fs
embe`rfs pfr
Euhtmphmqub pfr
F`sbrvb qub hks biukimflbs qub rbhkimflkl iffrjblkjks pfhkrbs y rbitklauhkrbs lf jbtbremlkl jb eklbrk ólmik k r f . Iukljf sb uskl bstks biukimflbs pkrk dkhhkr hks iffrjblkjks pfhkrbs jb ul pultf, sb jb`b tblbr iumjkjf jb qub hfs vkhfrbs bhbamjfs pkrk r y jbl ul pultf bl bh iukjrkltb ifrrbitf.
Yustmtuyk
Hk arëgmik jb
bs hk hålbk vbrtmikh víksb hk
gmaurk.
Biukimflbs pfhkrbs Iflvbrtmr ulk biukimùl rbitklauhkrbs k pfhkrbs Bxprbsb hk biukimùl pfhkrbs.
jb
5 : bl
iffrjblkjks iffrjblkjks
Yb uskl hks gùreuhks
5 {5 5 : 5: 5: 5
50 5 5. 50 5 0 5 5 05? ; 5 ;
`) Yb euhtmphmikl ke`fs hkjfs jb hk biukimùl pfr r , pfrqub bltflibs sb pubjbl pubjb l uskr hks gùreuhks
Yfhuimùl
Biukimùl rbitklauhkr Yustmtuyk k
Jbskrrfhhb
5
y k
Euhtmphmqub pfr r.
Pbstb 0y
Ifephbtb bh iukjrkjf bl y
_ëamlk : jb ;2
Bstk bs hk biukimùl jb ul iåriuhf jb rkjmf ; ibltrkjf bl bh pultf Yb arkgmik bl hk gmaurk.
?,;
?0. Arkgmqub bh pultf qub tmblbl hks iffrjblkjks pfhkrbs jkjks. Hubaf jb ftrks jfs rbprbsbltkimflbs jbh pultf bl iffrjblkjks pfhkrbs, ulk ifl r 8 ? y hk ftrk ifl r < ?. k.
9,
`.
;,
i.
2,?
?9. iuëh pultf jb hkjkjks. gmaurk, _, [, P f Y tmblbJbtbremlb hks iffrjblkjks pfhkrbs
i)
500
Yb euhtmphmikl prmebrf ke`fs hkjfs jb hk biukimùl pfr r .
500
Ifl
sb
pubjbl
iflvbrtmr jfs jb hfs tíremlfs jb hk biukimùl bl iffrjblkjks rbitklauhkrbs, pbrf bhmemlkr hk r
5 5, 500 5 5, 050 0 0 5 :
rbstkltb rbqumbrb eës trk`kcf3
Pbstb
Bhbvkljf kh iukjrkjf
ke`fs embe`rfs
i. b. a.
0 5: 5
k.
Bl bstb iksf, hk biukimùl rbitklauhkr bs eës
:,9/: :,9/: :,/: :,;9/: :,09/: :,09/: :,;?;/: :,;?9/:
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j.
g.
d.
?:. Yb arkgmik ul pultf bl gfrek rbitklauhkr. Bliubltrb hks iffrjblkjks pfhkrbs pkrk pkr k bh pultf, ifl r
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