
versin

aadyakaala chilathil (samskritham "aaryabhathiya") kaanapedunna oru trikonamitheeya pravarthanamaanu versign allengil versed saine.
vibhaagam i) trikonamitheeya pattikakal. oru konile varsain 1 mainus athinte kosain aanu.
niravadhi anubandha pravartthanangal undu, prathyekichu coversign, haversign. randaamathethu, pakuthi versin, naavigeshante haversin formula prathyeka praadhaanyamullathaanu.
avalokanam.
aadyakaala trikonamithika pattikakalil chilathil ithinakam prathyakshappedunna oru trikonamithika pravarthanamaanu versign allengil versed saine. churukkapperukal,,,, allengil upayogichu soothravaakyangalil ithu pratheekappeduthunnu. laattin bhashayil ithu "sainas vezhsas" (flip cheytha saine), "versinus", "vezhsas", allengil "sagitha" (ambu) ennariyappedunnu.
saadhaarana trikonamitheeya functionukalaaya saine, kosain, taanjant ennivayude adisthaanathil prakadippikkunna versign thulyamaanu
soothravaakyam _ 1
versine anuyojyamaaya niravadhi anubandha pravartthanangal undu
mukalil soochippicha naalu functionukalumaayi poornnamaaya saamyam nalkikkond naalu "pakuthi moolyamulla" functionukalude mattoru koottavum nilavilunda
charithravum prayogangalum.
versin, coversin.
saadhaarana "saine" functione (vyuthpathiyekkurichu kuripp kaanuka) chilappol charitraparamaayi "sainas rectus" ("strait saine") ennu vilikkapettu, ithu versed saine ("sainas vezhsas") ennathumaayi thaarathamyappeduthunnu. eee padangalude ardham vyakthamaan, avayude nirvachanathinaayi yadhaartha pashchaathalatthil oraal pravartthanangal nokkukayaanenkil, oru yoonit sarkkil
yoonit sarkkilinte lambamaya oru coord "abb"-nuu, "θ" konile saine (subtended angle "δ"-nte pakuthiye prathinidheekarikkunnu) ennathu dooram "essy" (cordinte pakuthi) aanu. maruvashathu, "θ" yude vars saine ennathu cordinte kendratthil ninnu aarkkinte madhyabhaagathekkulla "cd" dooramaanu. athinaal, koos ("θ") (variyude neelam "oc" nuu thulyamaanu), versin ("θ") (variyude neelam "cd" nuu thulyamaanu) ennivayude aakethuka "od" (neelam 1) aanu. eee reethiyil chithreekarichirikkunna saine lambamaan ("rectus", aksharaarthatthil "nere") athesamayam versign thirascheenamaanu ("vezhsas", aksharaarthatthil "nere thirinjathu, sthalathinu purathu"); randum "sii" yill ninnu vrithathilekkulla dooramaanu.
athe ardhamulla arabi upayogamaaya "sahem" ennathil ninnu ambinu laattin bhashayil chilappol "sagitha" ennu vilikkappedunnathinte kaaranavum eee chithram vyakthamaakkunnu. utkarsha-jya" yeei soochippikkaan saadhaaranayaayi upayogichirunna indian padamaaya "saara" (ambu) yill ninnaan ithu vannath. eratta-angle "δ" = 2 "θ" yude arck "adb" oru "boow" aayum coord "ab" athinte "string" aayum kaanukayaanengil, versign "cd" vyakthamaayi "ambu shaaft" aanu.
sainine "lambam" ennum vyaasaarthamaaya saine "thirascheenam" ennum vyaakhyaanikkunnathinal, "sagitha" ennathu absissayude (oru graafinte thirashcheena achuthandu) kaalaharanapetta paryaayapadamaanu.
1821-ll, kauchi versine "sainas vezhsas" ("sivu"), coversine "cosinus vezhsas" ("cossive") ennee padangal upayogichu.
charitraparamaayi, vivechanaadhikaaramulla saine ettavum pradhanappetta trikonamitheeya pravarthanangalilonnaayi kanakkaakkappettirunnu.
θ" poojyathilekku pookumbool, versin ("θ") ennathu ekadesham thulyamaaya rund alavukal thammilulla vyathyaasamaan, athinaal kosaininu vendi maathram oru trikonamithika pattikayude upayokthaavin vinashakaramaaya radhaakkal ozhivakkaan versin labhikkunnathin valare uyarnna krithyatha aavasyamaanu, ithu randaamathethinu prathyeka pattikakal soukaryapradamaakkunnu. oru calculatoro computero undengilum, raundu-oof pishakukal cheria "θ"-nuu sin2 formula upayogikkunnathu uchithamaakkunnu.
versaininte mattoru charitraparamaaya nettam athu ellaayppozhum negatteevu allah ennathaanu, athinaal single angle ("θ" = 0,2, ozhike ellaayidathum athinte logaritham nirvachikkappedunnu...) poojyamaayirikkumbol-athinaal, versign ulppedunna soothravaakyangalile gunanangalkkayi logarithamik tableukal upayogikkaam.
vaasthavathil, bii. sii. moonnaam noottaandile indiayile sooryasidhanthayil ninnu kanakkakkiya saine (pakuthi-coord) moolyangalude (tolamy mattu greak rachayithaakkalum pattikappedutthiya cordukalkku vipareethamaayi) nilanilkkunna aadyakaala pattika, saine, versed saine ennivayude moolyangalude oru pattikayayirunnu (0 muthal 90 digri vare 3.75 digri vardhanavil).
atharam pattikakal nirmmikkaan upayogichirunna tolami uruthirinja sin2 = verin ("θ") enna ardha-koona soothravaakyathinte prayogatthile oru idatharam ghattamayi versin kaanapedunnu.
havsign.
oru jyotishaasthra golatthile doorangal nyayamaayum krithyamaayi kanakkakkaan upayogikkunna haversin formula prathyakshappedunnathinaal naavigeshanil haversin prathyekichum pradhanamaayirunnu (bhoomiyude aaram vezhsas thammilulla prasnangal kaanuka. golam) koneeya sthaanangal nalkiyirikkunnu (udha.jii., rekhaamshavum akshaamshavum). oraalkk nerittu sin2 upayogikkaam, pakshe havsign table undaayirikkunnathu squareukalum square roottukalum kanakkaakkendathinte aavasyakatha illaathaakki.
pinneedu havsigns ennu vilikkappedunnavayude aadyakaala upayogam 1801 ll rekhappeduthiyittundu.
1805ll jaims andrew "squares oof naachural semi-coords" enna peril oru table oof havsignsinu thulyamaaya aadyathe engleesh prasidheekarichu.
1835-ll "havsign" enna padam (swaabhaavikamaayi "haav" ennu ariyappedunnu."allengil bays-10 logarithamik aayi" logue ". haversin allengil logue. harver.") jaims inman thante kruthiyaaya" "naavigeshan aandu nottikkal astronomy phoor dhaa yoos oof britiish seamens" "enna kruthiyude moonnaam pathippil bhoomi uparithalathile rund pooyintukal thammilulla dooram kanakkukoottunnath lalithamaakkunnathin naavigeshanile prayogangalkkaayi golaakrithiyilulla trikonamithiye upayogichu roopappeduthi". inman "naatt" enna padavum upayogichu. versin "," naatt ". nere marichu."versinsinu.
1856-ll richard farleyudeyum 1876-ll joonn coalfield hanningtoninteyum meshakalaan mattu uyarnna bahumatiyullah haavezhsainukal.
naavigeshanil haversin upayogikkunnathu thudarunnu, koodaathe broose dii pole sameepa dashakangalil puthiya prayogangal kandethi. 1995 muthal gausiyan logaritham upayogicho 2014 muthal kazhcha kuraykkunnathinaayi kooduthal othukkamulla reethiyilo chandradooram neekkamcheyyunnathinulla staarkks reethi.
aadhunika upayogangal.
versin, coversin, haversin ennivayude upayogavum avayude vipareeta pravartthanangalum noottaandukalkku munbu kandethaamenkilum, mattu anchu kofangshanukalude perukal valare cheruppamaanennu thonnunnu.
oru versinte oru kaalayalav (0 <θ "<2" π ") allengil, kooduthal saadhaaranayaayi, oru haversin (allengil havercosin) tharamgaroopam signal prosessingilum niyanthrana sidhaanthathilum pulsinteyo vindo functionteo (hahn, hahn-poyson, tukki vindokal ulppede) aakruthiyaayi saadhaaranayaayi upayogikkunnu, kaaranam ithu sugamamayi (moolyathilum charivilum thudarchayaayi) poojyathil ninnu onnilekku (haversin)" oonaakkunnu ". eee prayogangalil ithine hahn function allengil rised-cosine filter ennu vilikkunnu. athupole, probability sidhaanthathilum sthithivivarakkanakkukalim uyarnna-cosine vitharanagalil havercosin upayogikkunnu.
2005 muthal norman joonn wilde berger nirddeshicha alavilulla samatalam, khara jyaamithikal ennivayude parishkaranam, eratta konaaya 'δ' yude haversign, eratta konaaya 'sin2' (θ) roopathil, yukthisahamaya trikonamithiyile spreadukalum konukalum thammilulla bandhathe vivarikkunnu.
ganithashaasthraparamaaya vyakthithvangal.
vrithaakrithiyilulla bhramanagal.
parasparam vrithaakrithiyilulla bhramanangalaan functionukal.
vipareeta pravartthanangal.
aarkkaversin (aarkkaversin, arcover, avars, avar), archavercosin (archavercosin, archavercos, avarcos, avc), arcoversin (arcoversin, arcouver, acover, eiii. sii. vii. ezz), arcovercosin (arcovercosin, arcovercos, acovercos, eiii. sii. vii. sii), archaversin (archaversin, arcovercos, acovercos, arcovercos, arcovercos, arcovercos, arcovercos, arcovercos, arcovercos, arcovercos, arcovercos, arcovercos, arcovercos, arca
mattu swathukkal.
eee pravartthanangal sankeernamaaya thalatthilekku vyaapippikkaan kazhiyum.
maclorin seereesa
ekadesha kanakk.
r" enna vyaasavumaayi thaarathamyappeduthumbol "v" enna varshanthyam cheruthaanenkil, athu "l" (mukalil kaanichirikkunna dooram "ac") enna soothravaakyam upayogichu pakuthi-coord neelatthil ninnu ekadeshamaayi kanakkakkaam.
soothravaakyam _ 6
pakaramaayi, versign cheruthum versign, aaram, pakuthi-coord neelam enniva ariyaamenkil, aarkkinte neelam "s" (mukalilulla chithratthile "ad") formula upayogichu kanakkakkaan avaa upayogikkaam.
soothravaakyam _ 7
chainees ganithashaasthranjanaaya shhein kuvoik eee soothravaakyam ariyamaayirunnu, koodaathe sagitta ulppedunna kooduthal krithyamaaya oru soothravaakyam rund noottaandukalkku sesham guwo shoujing vikasippichu.
enchineeyaringil upayogikkunna kooduthal krithyamaaya ekadesha kanakk
soothravaakyam _ 8
ekapaksheeyamaaya valavukalum cordukalum.
melpparanja vritham oru prathyeka kesaaya ekapaksheeyamaaya planner vakrathile nertthathayil ninnulla vyathiyaanangale vivarikkaanum "versin" enna padam chilappol upayogikkunnu. oru vakrathile rund pooyintukal thammilulla oru coord nalkiyaal, cordil ninnu vakrathilekkulla (saadhaaranayaayi coord madhyabinduvil) lambamaya dooram "vii" yeei "versign" alakkal ennu vilikkunnu. oru nerrekhaykku, eathu cordinteyum versign poojyamaanu, athinaal eee alavu vakrathinte nertthathaye savisheshamaakkunnu. coord neelam "l" poojyathilekku pookumbool, anupatham thalkshana vakrathayilekku pookunnu. reyil gathaagathathil eee upayogam prathyekichum saadhaaranamaanu, avide ithu reyil tracukalude nerttha alavu vivarikkunnu, ithu reyil sarveykkulla halled reethiyude adisthaanamaanu.
lensukaludeyum kannaadikaludeyum uparithalangale vivarikkunnathin "sagitha" (palappozhum "sag" ennu churukkipparayunnu) enna padam opttiksil samaanamaayi upayogikkunnu.

