Trigonometry: Pfungwa, Nhoroondo, uye Mashandisirwo Muhupenyu Hwezuva Nezuva
Pendauluan
Trigonometry, bazi idzva remasvomhu, rinoita basa rakakosha muzvikamu zvakasiyana-siyana zvesainzi neinjiniya. Rinodzidza hukama huripo pakati pemakona nehurefu hwemativi mumakona matatu. Chikamu chakakosha chemasvomhu, trigonometry ine mashandisirwo akasiyana-siyana, kubva kuongororo yenyeredzi neinjiniya yezvivakwa kusvika kuhunyanzvi hwekufamba neruzivo. Chinyorwa chino chinotsanangura pfungwa huru dzetrigonometry, kukura kwayo kwenhoroondo, uye mashandisirwo ayo muhupenyu hwezuva nezuva.
Pfungwa huru dzeTrigonometry
Muchidzidzo chekare, trigonometry inobva pamashoko maviri echiGiriki: "trigonon," zvichireva makona matatu, uye "metron," zvichireva chiyero. Saka, trigonometry zvinoreva "kuyera makona matatu."
Mabasa eTrigonometric
Pakati pe trigonometry pane mabasa ekutanga e trigonometry: sine (sin), cosine (cos), uye tangent (tan). Mabasa aya anotsanangurwa muchimiro chetriangle yekurudyi, apo:
– Sine (sin) yekona θ ndiyo chiyero chiri pakati pehurefu hwedivi rakapesana rekona nehurefu hwehypotenuse.
– Cosine (cos) yekona θ ndiyo chiyero chiri pakati pehurefu hwedivi riri pedyo rekona (riri pedyo) nehurefu hwehypotenuse.
– Tangent (tan) yekona θ ihuremu huri pakati pehurefu hwedivi rakapesana rekona nehurefu hwedivi riri pedyo rekona.
Kune maangles anopfuura madhigirii makumi mapfumbamwe kana pasi pemadhigirii makumi matatu, kukosha kwe sin, cos, uye tan kunogona kuverengerwa uchishandisa pfungwa yedenderedzwa reyuniti uko denderedzwa rine unit radius rinoshandiswa kutsanangura mabasa etrigonometric.
Kuzivikanwa kweTrigonometric
Kuzivikanwa kwetrigonometric iequation ine mabasa etrigonometric ayo anoshanda kune ese angle. Kuzivikanwa kwakakosha kunonyanya kuzivikanwa ndiko kuzivikanwa kwePythagorean:
\[ \chivi^2\theta + \cos^2\theta = 1 \]
Zvimwe zviratidzo zvinosanganisira mamwe makona ekuzivikanwa uye kushandurwa kaviri:
\[ \chivi(\ alpha \pm \beta) = \chivi\alpha \cos\beta \pm \cos\alpha \sin\beta \]
\[ \cos(\ alpha \pm \beta) = \cos\alpha \cos\beta \mp \sin\alpha \sin\beta \]
Nhoroondo yeKubudirira kweTrigonometry
Kukura kwetrigonometry kwakatanga netsika dzekare, kunyanya dzevaIjipita, veBhabhironi, nevechiGiriki.
Bhabhironi neIjipiti
VaBhabhironi vekare nevaIjipita vakagadzira nzira dzekutanga dzekuyera nekuverenga idzo dzava kunzi ndidzo dzinotangira trigonometry. Vakashandisa matafura echord kuverenga hurefu hwemativi ematriangles.
Nguva dzekare dzechiGiriki
Mupiro mukuru wakabva kunyanzvi yemasvomhu yechiGiriki Hipparchus (c. 190-120 BC), anozivikanwa sa "Baba veTrigonometry." Hipparchus akaunganidza matafura ekutanga etrigonometric, achibvumira kuverenga kwakanyatsojeka kwemakona nehurefu hwemativi.
Makore Epakati
Munguva yeIslam, masayendisiti akadai saAl-Battani naAl-Khwarizmi vakawedzera kudzidza kwetrigonometry nekuwedzera mabasa matsva etrigonometric uye kuverenga matafura etrigonometric akanyatsojeka. Munguva iyi, mabasa etrigonometric ane sine necosine aizivikanwa zvikuru.
Nguva Yemazuva Ano
Kufambira mberi kukuru mu trigonometry yemazuva ano kwakaitwa nenyanzvi dzemasvomhu dzakadai saLeonhard Euler nevamwe. Semuenzaniso, Euler akatanga basa re exponential uye akatanga hukama hwakakura pakati pe trigonometry nekuongorora kwakaoma.
Kushandiswa kweTrigonometry muhupenyu hwezuva nezuva
Trigonometry haisi chishandiso chedzidziso mumasvomhu chete asiwo ine mashandisirwo akasiyana-siyana mumabasa akasiyana-siyana.
Nyeredzi
Trigonometry chishandiso chakakosha mukuongorora nyeredzi, chinobatsira vaongorori venyeredzi kuyera daro riri pakati penyeredzi, mapuraneti, nezvimwe zvinhu zvemudenga. Semuenzaniso, nzira yekuongorora nyeredzi inonzi parallax inoshandisa trigonometry yekutanga kuverenga daro renyeredzi iri pedyo nePasi.
Uinjiniya hweZvekuvaka neMagadzirirwo ezvivakwa
Mukugadzira zvinhu zvekuvaka nekuvaka, trigonometry inoshandiswa kuverenga materu, simba rechivako, uye dhizaini yechivako. Semuenzaniso, inogona kushandiswa kuona hurefu hwemativi nemakona emabhiriji kana zvivakwa zvirefu.
Navigation
Vafambisi vechikepe nevatyairi vendege vanoshandisa trigonometry kuti vaone nzvimbo yavo mugungwa kana mumhepo. Vachishandisa maturusi akadai se sextants nemacompass, vanogona kuverenga nzvimbo dzinoenderana nedenderedzwa renyika zvichienderana nekona iri pakati pehorizon nedzimwe nyeredzi.
Tekinoroji yeRuzivo neKutaurirana
Munyika yeruzivo rwetekinoroji nekutaurirana, masaini edhijitari anowanzo gadziriswa uchishandisa pfungwa dzetrigonometric. Kuongororwa kweFourier, nzira yekuenzanisa mabasa enguva nenguva uye masaini, kunonyanya kushandiswa pamabasa esine necosine.
Medical
Kuongororwa kwemuviri kwakadai seCT scans neMRIs kunoda trigonometry kuti itore mifananidzo ine mativi matatu. Izvi zvinobvumira vanachiremba kuwana mepu yakajeka uye yakarurama yenhengo yemuviri iri kuongororwa.
Geodesy uye Cartography
Trigonometry inobatsirawo pakuongorora nyika uye kugadzira mapu. Geodesy inoshandisa pfungwa yetriangulation, uko nzvimbo nedaro riri pamusoro peNyika zvinoverengerwa zvichibva pakuyera kwemakona kubva panzvimbo yakatarwa.
Penutup
Trigonometry ndeimwe yenzvimbo dzakakosha zvikuru dzemasvomhu, ine kuvapo kwakasimba muhupenyu hwezuva nezuva uye tekinoroji yemazuva ano. Kunyange zvazvo yakatangira pakuyera makona nemativi ekureba mumatriangles, mashandisirwo ayo akadarika miganhu inoshanda kuti ave rutsigiro rwakakosha muzvidzidzo zvakasiyana-siyana zvesainzi. Kubva pakuvandudzwa kwezvivakwa kusvika pakuongorora muchadenga, trigonometry inoramba iri hwaro hwakakosha mune zvese. Nekunzwisisa pfungwa dzayo dzekutanga uye mashandisirwo ayo, tinogona kuona kukosha kwesainzi iyi mukupfumisa hupenyu hwevanhu.
Mabhuku
1. Boyer, Carl B. (1991). Nhoroondo yeMasvomhu. Wiley.
2. Merzbach, Uta C.; Boyer, Carl B. (2011). Nhoroondo yeMasvomhu.
3. Katz, Victor J. (1998). Nhoroondo yeMasvomhu: Nhanganyaya.
Iyi isumo refu. Chinyorwa chino chinopa ruzivo rwakakwana rwe trigonometry, kubva pazviri nyore kusvika pakushandiswa kwayo muhupenyu hwezuva nezuva. Unogona kuwedzera rumwe ruzivo kana mienzaniso sezvinodiwa.
