Trigonometry: Mehopolo, Histori, le Ts'ebeliso Bophelong ba Letsatsi le Letsatsi
Pendahuluan
Trigonometry, lekala le lecha la lipalo, le bapala karolo ea bohlokoa mafapheng a fapaneng a saense le boenjiniere. E ithuta likamano pakeng tsa likhutlo le bolelele ba mahlakoreng ka likhutlotharo. Karolo ea bohlokoa ea lipalo, trigonometry e na le mefuta e mengata ea lits'ebetso, ho tloha bolepi ba linaleli le boenjiniere ba sechaba ho ea ho tsamaiso ea likepe le theknoloji ea tlhahisoleseling. Sengoloa sena se hlalosa likhopolo tsa motheo tsa trigonometry, nts'etsopele ea eona ea nalane, le ts'ebeliso ea eona bophelong ba letsatsi le letsatsi.
Mehopolo ea Motheo ea Trigonometry
Ho ya ka setso, trigonometry e tswa mantswe a mabedi a Segerike: "trigonon," e bolelang dikhutlo tse tharo, le "metron," e bolelang tekanyo. Kahoo, trigonometry e bolela 'tekanyo ya dikhutlo tse tharo.'
Mesebetsi ea Trigonometric
Motheong oa trigonometry ho na le mesebetsi ea motheo ea trigonometry: sine (sin), cosine (cos), le tangent (tan). Mesebetsi ena e hlalosoa moelelong oa khutlotharo e nepahetseng, moo:
– Sine (sin) ea angle θ ke karolelano pakeng tsa bolelele ba lehlakore le fapaneng la angle le bolelele ba hypotenuse.
– Cosine (cos) ea angle θ ke karolelano pakeng tsa bolelele ba lehlakore le haufi la angle (e haufi) le bolelele ba hypotenuse.
– Tangent (tan) ea angle θ ke karolelano pakeng tsa bolelele ba lehlakore le fapaneng la angle le bolelele ba lehlakore le haufi la angle.
Bakeng sa dikhutlo tse fetang di-degree tse 90 kapa tse ka tlase ho di-degree tse 0, boleng ba sin, cos, le tan bo ka balwa ho sebediswa mohopolo wa sedikadikwe sa yuniti moo sedikadikwe se nang le radius ya yuniti se sebediswang ho hlalosa mesebetsi ya trigonometric.
Boitsebiso ba Trigonometric
Boitsebahatso ba trigonometric ke equation e kenyeletsang mesebetsi ya trigonometric e leng nnete bakeng sa sekhutlo se seng le se seng. Boitsebahatso ba motheo bo tsebahalang haholo ke boitsebiso ba Pythagorean:
\[ \sin^2\theta + \cos^2\theta = 1 \]
Boitsebiso bo bong bo kenyelletsa boitsebiso bo eketsehileng ba likhutlo le liphetoho tse peli:
\[ \sebe(\alpha \pm \beta) = \ sebe\alpha \cos\beta \pm \cos\alpha \sin\beta \]
\[ \cos(\alpha \pm \beta) = \cos\alpha \cos\beta \mp \sin\alpha \sin\beta \]
Histori ea Nts'etsopele ea Trigonometry
Nts'etsopele ea trigonometry e qalile ka tsoelo-pele ea boholo-holo, haholo-holo meetlo ea Baegepeta, Bababylona le Bagerike.
Babylona le Egepeta
Bababylona ba boholo-holo le Baegepeta ba ile ba hlahisa mekhoa e meng ea motheo ea ho lekanya le ho bala eo hona joale e nkoang e le li-precursor tsa trigonometry. Ba sebelisitse litafole tsa chord ho bala bolelele ba mahlakore a likhutlotharo.
Mehla ea Boholo-holo ea Bagerike
Monehelo o moholo o tsoa ho setsebi sa lipalo sa Mogerike Hipparchus (hoo e ka bang ka 190-120 BC), ea tsejoang e le "Ntate oa Trigonometry." Hipparchus o ile a bokella litafole tsa pele tsa trigonometry, a lumella lipalo tse nepahetseng tsa likhutlo le bolelele ba mahlakoreng.
Lilemong tse mahareng
Nakong ea Boislamo, bo-rasaense ba kang Al-Battani le Al-Khwarizmi ba ile ba atolosa thuto ea trigonometry ka ho eketsa mesebetsi e mecha ea trigonometry le ho bala litafole tsa trigonometry tse nepahetseng haholoanyane. Nakong ena, mesebetsi ea trigonometry ea sine le cosine e ne e tsebahala hantle.
Nako ea Kajeno
Tsoelo-pele e kholo ho trigonometry ea sejoale-joale e fihletsoe ke litsebi tsa lipalo tse kang Leonhard Euler le ba bang. Ka mohlala, Euler o hlahisitse mosebetsi oa exponential mme a theha kamano e tebileng pakeng tsa trigonometry le tlhahlobo e rarahaneng.
Tšebeliso ea Trigonometry Bophelong ba Letsatsi le Letsatsi
Trigonometry ha se sesebelisoa sa thuto ea lipalo feela empa hape e na le lits'ebetso tse fapaneng tse sebetsang masimong a fapaneng.
Bolepi ba linaleli
Trigonometry ke sesebelisoa sa bohlokoa thutong ea linaleli, se thusang litsebi tsa linaleli ho lekanya sebaka se pakeng tsa linaleli, lipolanete le lihloliloeng tse ling tsa leholimo. Mohlala, mokhoa oa parallax oa linaleli o sebelisa trigonometry ea motheo ho bala sebaka sa naleli e haufi le Lefatše.
Boenjiniere ba Meaho le Meaho
Ho boenjiniere ba tsa kaho le meralo ea meaho, trigonometry e sebelisoa ho bala matsoapo, matla a sebopeho le moralo oa moaho. Mohlala, e ka sebelisoa ho fumana bolelele ba mahlakore le likhutlo tsa marokho kapa mehaho e melelele.
Navigation
Basesisi ba likepe le bafofisi ba lifofane ba sebelisa trigonometry ho fumana hore na ba hokae leoatleng kapa moeeng. Ba sebelisa lisebelisoa tse kang sextants le li-compass, ba ka bala likhokahano tsa jeokrafi ho latela sekhutlo se pakeng tsa horizon le lihloliloeng tse itseng tsa leholimo.
Theknoloji ea Tlhahisoleseling le Khokahano
Lefatšeng la theknoloji ea tlhahisoleseling le puisano ea mohala, matšoao a dijithale hangata a sebetsoa ho sebelisoa likhopolo tsa trigonometric. Tlhahlobo ea Fourier, mokhoa oa ho hakanya mesebetsi le matšoao a nako le nako, e itšetlehile haholo ka mesebetsi ea sine le cosine.
Bongaka
Li-scan tse kang li-CT scan le li-MRI li hloka trigonometry ho hapa litšoantšo tsa mahlakore a mararo. Sena se lumella lingaka ho fumana 'mapa o hlakileng le o nepahetseng oa karolo ea' mele e hlahlojoang.
Geodesy le Limmapa
Trigonometry e boetse e thusa ho hlahlobisiseng naha le ho etsa 'mapa. Geodesy e sebelisa mohopolo oa triangulation, moo libaka le sebaka holim'a Lefatše li baloang ho latela litekanyo tsa angular ho tloha ntlheng e tsitsitseng.
Ho koala
Trigonometry ke e 'ngoe ea makala a bohlokoa ka ho fetisisa a lipalo, e nang le boteng bo matla bophelong ba letsatsi le letsatsi le theknoloji ea sejoale-joale. Leha tšimoloho ea eona e le tekanyong e bonolo ea likhutlo le bolelele ba mahlakoreng ka likhutlotharo, ts'ebeliso ea eona e fetile meeli e sebetsang ho ba tšehetso ea bohlokoa lithutong tse fapaneng tsa mahlale. Ho tloha nts'etsopele ea meralo ea motheo ho ea ho lipatlisiso tsa sepakapaka, trigonometry e ntse e le motheo oa bohlokoa likarolong tsohle. Ka ho utloisisa likhopolo le lits'ebetso tsa eona tsa motheo, re ka bona hore na saense ena e bohlokoa hakae ho ntlafatseng bophelo ba batho.
Daftar Pustaka
1. Boyer, Carl B. (1991). Nalane ea Lipalo. Wiley.
2. Merzbach, Uta C.; Boyer, Carl B. (2011). Nalane ea Lipalo.
3. Katz, Victor J. (1998). Nalane ea Lipalo: Selelekela.
Ena ke selelekela se selelele haholo. Sengoloa sena se fana ka kakaretso e felletseng ea trigonometry, ho tloha metheong ho isa lits'ebetsong tsa eona bophelong ba letsatsi le letsatsi. U ka eketsa lintlha tse ling kapa mehlala ha ho hlokahala.
