Isibali se-tangent esiphambene (esaziwa nangokuthi i-arcus tangent calculator) sihlanganisa arctanumenzeli (atan) wanoma iyiphi inombolo yangempela futhi sibuyisela i-engeli okuthanji kwayo okulingana nalelo nani. Kungakhathaliseki ukuthi uthola i-engeli yomthambeko ngokufaka i-engeli ekhuphukayo futhi ugijime ngokuphambene noma eduze, noma ngokumane uguqule isilinganiso se-tangent sibe amadigri noma ama-radians, lesi sitholi se-engeli sikunikeza umphumela ngokushesha. Faka idesimali noma isilinganiso sezinhlangothi ezibhekene / eziseduze ukusuka kunxantathu ongakwesokudla, khetha phakathi kwamadigri nama-radians, bese uthola imiphumela esheshayo. Lesi sibali se-arc tan siphinda sidwebe umdwebo ongunxantathu osebenzisanayo, sihlele igrafu arctan(x), futhi sibonise ithebula elicwebezelayo—yonke into edingekayo ukuze kube nezibalo ze-trigonometry, i-calculus, kanye nokuzulazula endaweni eyodwa.
I-Tangent ephambene Isibali
Ngemva kokubala ngakunye, unxantathu uyabuyekeza ukuze ubone ukuthi θ = arctan(okuphambene / okuseduze).
Igrafu imaka okokufaka kwamanje ukuze ukwazi ukuqhathanisa inombolo ne-engeli yayo.
Iyini i-Inverse Tangent?
I-tangent ephambene, ebhalwe ngokuthi tan⁻¹(x), arctan(x), noma atan(x), ibuyisela i-engeli okukhona kwayo okufana no-x. Ezincwadini zokufunda zaseYurophu naseJalimane lo msebenzi ofanayo uvela njenge-arcus tangens noma i-arkus tangens. Endingilizini yeyunithi, arctan ibuyisela i-engeli ehambelana nanoma yiliphi inani le-tangent eduze kombuthano.
Kunxantathu ongakwesokudla, u-tan(θ) = okuphambene / eduze, ngakho-ke arctan(okuphambene / okuseduze) unikeza i-engeli θ.
Isizinda saso siyizinombolo zangempela, futhi ububanzi baso obuyinhloko sithi (-π/2, π/2) noma (-90°, 90°).
Hambisa isilayidi ukuze ubone ukuthi noma yimaphi amamephu wokufaka wangempela aye engeli ephakathi kuka -90° no-90°.
Ungabala kanjani i-Inverse Tangent?
Sebenzisa i-θ = arctan(x) uma u-x eyinani ledesimali noma isilinganiso.
- Khomba inani x.
- Sebenzisa umshini wokubala wesayensi noma umsebenzi we-atan() ukuze ubale arctan(x).
- Guqula umphumela uma udinga amadigri esikhundleni sama-radians. Phindaphinda umphumela we-radian ngo-180/π ukuze uthole amadigri, noma phinda inani ledigri ngo-π/180 ukuze uguqule ubuyele kuma-radians. Noma iyiphi indlela ifomula ye-tan ephambene ihlala θ = arctan(x) yonke indawo.
Thayipha inani ukuze ubuyekeze isinyathelo ngasinye ngokushesha.
Ungasisebenzisa Kanjani Lesi Sibali Esiphambene Ne-Tangent?
Khetha okokufaka kwedesimali noma okuphambene/okuseduze, khetha amadigri noma ama-radians, bese ucindezela okuthi Bala.
Izindlela Zokufaka
Imodi yedesimali yamukela amanani anjengo-0.5, 1, noma -2.75.
Imodi ephikisanayo / Eseduze ihlukanisa izinhlangothi ezi-2 kuqala bese iyasebenza arctan.
Iphaneli yomphumela ibonisa amafomethi empendulo amaningi ukuze asetshenziswe ngokushesha.
Isetshenziswa Kanjani I-Inverse Tangent Kumshini wokubala?
Cindezela inkinobho ethi “2nd” noma “Shift” kusibali sesayensi (njenge-Casio noma TI-84), bese ucindezela inkinobho “tan” ukuze ufinyelele u-tan⁻¹.
- Vula isibali bese usetha imodi ye-engeli ibe amadigri (DEG) noma ama-radians (RAD).
- Cindezela okuthi “2nd” noma “Shift.” Lo khiye wenza kusebenze imisebenzi yesibili ephrintwe ngaphezu kwenkinobho ngayinye. Le nhlanganisela yokhiye we-shift tan itholakala kuwo wonke amamodeli we-Casio, TI-84, kanye ne-Sharp. Hlala usetha imodi yakho ye-engeli kokuthi DEG noma RAD ngaphambi kokuyicindezela, njengoba okokufaka okufanayo kubuyisela izinombolo ezihlukene kuye ngemodi.
- Cindezela inkinobho ethi "tan". Isibonisi sibonisa “tan⁻¹(” noma “atan(”.
- Thayipha inani bese ucindezela u-“=".
Isithombe esingezansi sibonisa izinkinobho eziqondile ongazicindezela kumshini wokubala wesayensi TI-84.
Ukuthola u-tan⁻¹(1) = 45° kumshini wokubala TI-84
Ungayibala Kanjani I-Inverse Tangent Ngaphandle Kokubala?
Sebenzisa arctanisandiso sochungechunge lwe-gent Taylor ukuze ulinganisele okuthi arctan(x) ngesandla: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + … Lolu chungechunge luhlangana lapho |x| ≤ 1.
- Taylor Series (Maclaurin series). Ithuluzi arctanlokulinganiswa kochungechunge lwe-gent lisebenzisa x − x³/3 + x⁵/5 − x⁷/7. Amagama amaningi anikeza ukunemba okuphezulu.
- I-Engle Values eyaziwayo. Ngekhanda imiphumela evamile: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- I-algorithm ye-CORDIC. Le ndlela yeleveli yehadiwe ibala arctani-gent ngokuzungezisa i-engeli okuphindaphindiwe.
Khetha ukuthi mangakhi amatemu ozowafaka. Buka ukuthi ukulinganiselwa kuhlangana kanjani kunani langempela.
Igrafu ye-Tangent ephambene
Igrafu arctan(x) iyijika elikhulayo elimise okuka-S elidlula kumsuka kanye nezindlela ±π/2.
- Inama-asymptote avundlile kokuthi y =-π/2 kanye no-y = π/2.
- Kuyaxaka, ngakho-ke arctan(-x) = -arctan(x).
- Ihlala ikhuphuka ukusuka kwesobunxele kuya kwesokudla.
Hambisa phezulu kwegrafu ukuze uhlole amanani aqondile.
Ithebula le-Tangent
Amanani aphambene ne-tan ku-0°, 30°, 45°, 60°, kanye no-90° avela cishe kuzo zonke izifundo ze-trigonometry futhi afanele ukuzibophezela ekhanda. Chofoza noma yimuphi umugqa wethebula ukuze ulayishe lelo nani elijwayelekile kusibali.
| x | arctan(x) Amadigri | arctan(x) AmaRadians | π Isiqephu |
|---|---|---|---|
| −∞ | −90° | −1.5708 rad | −π/2 |
| −√3 ≈ −1.7321 | −60° | −1.0472 rad | −π/3 |
| −1 | −45° | −0.7854 rad | −π/4 |
| −1/√3 ≈ −0.5774 | −30° | −0.5236 rad | −π/6 |
| 0 | 0° | 0 rad | 0 |
| 1/√3 ≈ 0.5774 | 30° | 0.5236 rad | π/6 |
| 1 | 45° | 0.7854 rad | π/4 |
| √3 ≈ 1.7321 | 60° | 1.0472 rad | π/3 |
| +∞ | 90° | 1.5708 rad | π/2 |
I-Notation for the Inverse of Tangent
I-notation yokuphambene kwe-tangent ithatha amafomu angu-3 ajwayelekile: tan⁻¹(x), arctan(x), kanye nokuthi atan(x).
- tan⁻¹(x) Okujwayelekile kuzibali ezibonakalayo.
- arctan(x) Okujwayelekile kuzibalo ezisemthethweni.
- atan(x) Uhlelo nesoftware notation.
Abanye abafundi bakubiza ngokungakahleleki ngokuthi i-anti tangent njengoba ihlehlisa okwenziwa yi-tangent, nakuba leli kungelona igama elijwayelekile lezibalo.
Chofoza inothi ngalinye ukuze ugqamise lapho livela khona ezibalweni, ezinhlelweni, nasezibalini.
tan⁻¹(x) iwuphawu oluvame kakhulu kuzibali eziphathekayo. Umbhalo omkhulu -1 ubonisa “umsebenzi ophambene,” hhayi “1 / tan(x)”.
Ukuthola i-tan⁻¹ yezinombolo ezingezinhle
I-tan⁻¹ yezinombolo ezinegethivu ibuyisela i-engeli eyinegethivu. Ngoba arctani-gent ingumsebenzi oyinqaba, arctan(-x) = -arctan(x).
- arctan(-1) = -45° noma π/4 ama-radians
- arctan(-√3) = -60° noma π/3 ama-radians
Iyini i-tan⁻¹ ye- -1?
I-tan⁻¹ ka -1 ingu -45° (-π/4 radians noma -0.7854 radians).
Faka noma iyiphi inombolo enegethivu ukuze ubone ukuthi i-arctan ibeka kanjani imephu okokufaka okunegethivu kuma-engeli anegethivu.
Imibuzo Evame Ukubuzwa
Izimpendulo zemibuzo evamile mayelana ne-tangent ephambene.
Yebo, i-tan⁻¹ iyinothi evamile yezibalo ye-tangent ephambene, ebizwa nangokuthi arctangent noma arctan. Umbhalo ongenhla ⁻¹ awusho u-1/tan (okuyi-cotangent). Kunalokho, tan⁻¹(x) uyabuza: 'Iyiphi i-engeli ene-tangent elingana no-x?' Isibonelo, tan⁻¹(1) = 45° ngoba tan(45°) = 1. Ungase futhi ukubone kubhalwe ngokuthi arctan(x) noma atan(x) ezilimini zokuhlela.
Umsebenzi we-tangent uthatha i-engeli futhi ubuyisela isilinganiso sohlangothi oluphambene ohlangothini oluseduze kunxantathu ongakwesokudla. I-tangent ephambene (arctan) yenza okuphambene: ithatha isilinganiso futhi ibuyisela i-engeli ehambisanayo. Ngokwesibonelo, tan(45°) = 1, ngakho arctan(1) = 45°. I-Tangent inesizinda sazo zonke izinombolo zangempela ngaphandle kokuphindaphinda okuyinqaba okungu-90°, kuyilapho i-tangent ephambene yamukela zonke izinombolo zangempela nama-engeli okukhiphayo phakathi kuka-−90° no-90° (−[2]] kuya ku-π/2 ama-radians).
Inkinobho ye-tangent ephambene ihlala ngaphezu kokhiye othi tan kuzibali eziningi zesayensi. Ukuze uyifinyelele, cindezela ukhiye wesi-2 noma u-Shift kuqala, bese ucindezela inkinobho ethi tan. Isibonisi sizobonisa i-tan⁻¹ noma i-arctan. Kuzibali zegraphing ezifana ne-TI-84, cindezela u-2nd bese u-TAN. Kuzibali ze-Casio, cindezela u-SHIFT bese u-tan.
Sebenzisa ukunwetshwa kochungechunge lwe-Taylor: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... kokuthi |x| ≤ 1. Ngamanani avamile, khumbula ngekhanda ama-engeli ayinhloko: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Ungasebenzisa futhi i-algorithm ye-CORDIC. Ngamanani angaphandle kokuthi [−1, 1], sebenzisa ubunikazi arctan(x) = π/2 − arctan(1/x) kokuthi x > 0.
I-tangent ephambene ka-1 ingu-45° (noma π/4 radians). Lokhu kungenxa yokuthi i-tan(45°) = 1. Kunxantathu ongakwesokudla lapho izinhlangothi eziphambene neziseduze zilingana, i-engeli ingu-45°.
I-Tan iguqula i-engeli ibe isilinganiso (okuphambene/eseduze), kuyilapho i-tan ephambene (arctan) iguqula isilinganiso sibuyele engeli. I-Tan ihamba ngezikhathi ezithile futhi ingakhiqiza noma iyiphi inombolo yangempela, kuyilapho i-arctan njalo ibuyisela i-engeli eyingqayizivele kububanzi (−90°, 90°).
Yebo, sebenzisa ifomula =ATAN(value) ku-Excel. Lokhu kubuyisela umphumela ngama-radians. Ukuze uguqulele kumadigri, sebenzisa i-=DEGREES(ATAN(value)). I-Excel iphinde isekele i-=[2]] yezingxabano ezimbili arctangent.
Zungezisa i-iPhone yakho ekumeni kwezwe ukuze uveze isibali sesayensi. Thepha inkinobho yesi-2 ukuze ushintshele emisebenzini ephambene. Inkinobho ye-tan izoshintsha ibe ngu-tan⁻¹. Faka inani lakho bese uthephe okuthi tan⁻¹.
Kunxantathu ongakwesokudla, i-tangent ephambene yesilinganiso esiphambene/eseduze ilingana ne-engeli kuleyo vertex. Uma okuphambene = 3 futhi eduze = 4, khona-ke arctan(3/4) ≈ 36.87°.
Kunezinhlelo ezingu-6 ezivamile ezisetshenziswayo: (1) Ukuzulazula kanye ne-GPS yokuthwala ama-engeli, (2) Ubunjiniyela bama-engeli emithambeka, (3) I-Physics yama-force vectors, (4) Imifanekiso yekhompyutha yokuzungezisa, (5) Ubunjiniyela bogesi wama-engeli ezigaba, (6) Isayensi yezinkanyezi yama-engeli okuphakama.
Nge-tan(θ) = sin(θ)/cos(θ). Uma θ = arctan(x), khona-ke sin(θ) = x/√(1+x²) kanye cos(θ) = 1/√(1+x²). Okuphuma kokunye kokuthi arctan(x) kuthi 1/(1+x²).
Yebo. I-slope ratio iyafana nokuphambene ngaphezu konxantathu ongakwesokudla. Faka ukuphakama kwakho njengohlangothi oluphambene nokugijima kwakho njengohlangothi oluseduze futhi ithuluzi libuyisela i-engeli yokuthambekela kuwo womabili amadigri nama-radians.
Leli thuluzi lakhelwe ngokuqondile i-arctangent. Uma udinga isibali esigcwele esiphambene esihlanganisa i-arcsin ne-arccos eduze kwe-arctan, uzodinga ithuluzi elibanzi eliphambene le-trigonometry.