Ekibalirizi kya tangent eky’enkyukakyuka (era ekimanyiddwa nga ekibalirizi kya tangent ya arcus) kibala arctangent (atan) ya namba yonna entuufu era n’ezzaayo enkoona nga tangent yaayo yenkana omuwendo ogwo. Ka obe ng’ozuula enkoona y’omusenyu ng’oyingiza okusituka n’okudduka nga ebikontana n’okumpi, oba ng’okyusa omugerageranyo gwa tangent okudda mu diguli oba radiyani, ekizuula enkoona eno ekuweereza ekivaamu mu kaseera ako. Yingiza decimal oba omugerageranyo gw’enjuyi ezikontana / eziriraanye okuva mu njuyi essatu entuufu, londa wakati wa diguli ne radians, era ofune ebivaamu eby’amangu. Ekibalirizi kino ekya arc tan era kikuba ekifaananyi ky’enjuyi essatu ezikwatagana, kikola grafulo ya arctan(x), era kiraga emmeeza ya tangent enzijuvu —buli kintu ekyetaagisa okubala trigonometry, calculus, n’okutambulira mu kifo kimu.
Tangent ey’ekifuulannenge Ekyuma ekibalirira
Oluvannyuma lwa buli kubala, enjuyi essatu zitereeza osobole okulaba nti θ = arctan(opposite / adjacent).
Grafu eraga ekiyingizibwa mu kiseera kino osobole okugeraageranya ennamba n’enkoona yaayo.
Inverse Tangent kye ki?
Tangent enzijuvu, ewandiikibwa nga tan⁻¹(x), arctan(x), oba atan(x), ezzaayo enkoona nga tangent yaayo yenkana x. Mu bitabo by’Abazungu n’Abagirimaani omulimu guno gwe gumu gulabika nga arcus tangens oba arcus tangens. Ku nkulungo ya yuniti, arctan ezzaayo enkoona ekwatagana n’omuwendo gwonna ogwa tangensi okumpi n’enkulungo.
Mu njuyi essatu entuufu, tan(θ) = ekikontana / ekiriraanye, kale arctan(ekikontana / ekiriraanye) kiwa enkoona θ.
Ekitundu kyayo kyonna namba ddala, era ekitundu kyayo ekikulu kiri (-π/2, π/2) oba (-90°, 90°).
Tambuza slider olabe engeri input yonna entuufu gy’ekola maapu ku angle wakati wa -90° ne 90°.
Obala Otya Okubala Inverse Tangent?
Kozesa θ = arctan(x) nga x muwendo gwa decimal oba omugerageranyo.
- Laba omuwendo x.
- Kozesa ekibalirizi kya ssaayansi oba omulimu atan() okubala arctan(x).
- Kyuusa ekivaamu bw’oba weetaaga diguli mu kifo kya radians. Kubisaamu ekiva mu radiyani 180/π okufuna diguli, oba kubisaamu omuwendo gwa diguli ne π/180 okukyusa okudda mu radiyani. Mu ngeri yonna ensengekera ya inverse tan esigala θ = arctan(x) wonna.
Wandiika omuwendo okulongoosa buli mutendera mu bwangu.
Okozesa Otya Ekibalirizi Kino Eky’enkyukakyuka (Inverse Tangent Calculator)?
Londa decimal oba opposite/adjacent input, londa diguli oba radians, era onyige Calculate.
Enkola z’Okuyingiza
Mode ya decimal ekkiriza emiwendo nga 0.5, 1, oba -2.75.
Opposite / Adjacent mode esooka kugabanya enjuyi 2 n’oluvannyuma n’ekola arctan.
Ekipande ky’ebivuddemu kiraga ensengeka z’okuddamu eziwera okukozesebwa amangu.
Okozesa Otya Inverse Tangent ku Calculator?
Nywa ekisumuluzo “2nd” oba “Shift” ku kalkulayiza ya ssaayansi (nga Casio oba TI-84), olwo onyige bbaatuuni ya “tan” okuyingira mu tan−1.
- Ggyako kalkulayiza era oteeke mode ya angle ku diguli (DEG) oba radians (RAD).
- Nywa ku “2nd” oba “Shift.” Ekisumuluzo kino kikola emirimu egy’okubiri egyakubibwa waggulu wa buli bbaatuuni. Omugatte guno ogw’ekisumuluzo kya shift tan gwa bonna mu Casio, TI-84, ne Sharp models. Bulijjo teeka mode yo eya angle ku DEG oba RAD nga tonnaginyiga, okuva input y’emu bweddiza ennamba ez’enjawulo okusinziira ku mode.
- Nywa ku kisumuluzo kya “tan”. Okwolesebwa kulaga “tan−1(” oba “atan(”.
- Wandiika omuwendo n’onyiga “=”.
Ekifaananyi wansi kiraga obutambi obutuufu bw’olina okunyiga ku TI-84 ekibalirizi kya ssaayansi.
Okuzuula tan−1(1) = 45° ku TI-84 ekibalirizi
Obala Otya Inverse Tangent nga Tolina Calculator?
Kozesa arctangent Taylor series expansion okugerageranya arctan(x) n’omukono: arctan(x) = x − x3/3 + x5/5 − x7/7 + ... Omulongooti guno gukwatagana nga |x| ≤ 1.
- Taylor Series (omusomo gwa Maclaurin). Ekintu eky’okugerageranya eky’omuddiring’anwa arctangent kikozesa x − x3/3 + x5/5 − x7/7. Ebigambo ebisingawo biwa obutuufu obw’oku ntikko.
- Emiwendo gy’Enkoona Egimanyiddwa. Mukwata mu mutwe ebivuddemu ebya bulijjo: arctan (0) = 0°, arctan (1) = 45°, arctan (√3) = 60°.
- Enkola ya CORDIC. Enkola eno ey’omutendera gwa hardware ebala arctangent okuyita mu kukyukakyuka kw’enkoona okuddiŋŋana.
Londa ebigambo bimeka by’olina okussaamu. Laba engeri okugerageranya gye kukwataganamu okutuuka ku muwendo omutuufu.
Grafu ya Tangent ey’ekifuulannenge
Grafu ya arctan(x) ye nkulungo eyeeyongera mu ngeri ya S eyita mu nsibuko n’esemberera ±π/2.
- Kirina obutafaanagana (horizontal asymptotes) ku y = -π/2 ne y = π/2.
- Kiba kya njawulo, kale arctan(-x) = -arctan(x).
- Bulijjo kyeyongera okuva ku kkono okudda ku ddyo.
Hover ku graph okwekenneenya emiwendo emituufu.
Omulongooti gwa Tangent
Emiwendo gya tan inverse ku 0°, 30°, 45°, 60°, ne 90° girabika kumpi mu buli kkoosi ya trigonometry era gisaana okwewaayo mu kujjukira. Nywa ku lunyiriri lwonna olw'emmeeza okutikka omuwendo ogwo ogwa mutindo mu kalkulayiza.
| x | arctan(x) Diguli | arctan(x) Aba Radians | π Ekitundu ekitono |
|---|---|---|---|
| −∞ | −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 |
Ennyiriri (notation) ku Inverse ya Tangent
Ennyiriri z’ekikyuusakyusa ekya tangent etwala engeri 3 eza mutindo: tan⁻¹(x), arctan(x), ne atan(x).
- tan⁻¹(x) Ya bulijjo ku kalkulayiza ezirabika.
- arctan(x) Omutindo mu kubala okutongole.
- atan(x) Okukola pulogulaamu n’okuwandiika pulogulaamu za kompyuta.
Abayizi abamu mu ngeri etali ntongole bakiyita anti tangent okuva bwe kiri nti kikyusa tangent ky’ekola, wadde nga kino si kigambo kya kubala kya mutindo.
Nywa ku buli nnyiriri okulaga we kirabika mu kubala, pulogulaamu, ne kalkulayiza.
tan⁻¹(x) ye nnyiriri esinga okukozesebwa ku bibalirizi eby’omubiri. Ennyiriri eziri waggulu -1 ziraga “omulimu ogw’ekifuulannenge,” so si “1 / tan(x)”.
Okuzuula tan−1 ya Namba Negative
Tan−1 ya namba negatiivu ezzaayo enkoona ya negatiivu. Kubanga arctangent mulimu gwa njawulo, arctan(-x) = -arctan(x).
- arctan (-1) = -45° oba -π/4 radiyani
- arctan (-√3) = -60° oba -π/3 radians
Tan−1 ya -1 kye ki?
Tan−1 ya -1 eri -45° (-π/4 radians oba -0.7854 radians).
Teeka ennamba yonna eya negatiivu olabe engeri arctan gy’akola maapu y’ebiyingizibwa negatiivu ku nkoona za negatiivu.
Ebibuuzo ebibuuzibwa
Eby’okuddamu mu bibuuzo ebya bulijjo ebikwata ku inverse tangent.
Yee, tan−1 ye nnyiriri y’okubala eya bulijjo eya tangent ey’ekifuulannenge, era eyitibwa arctangent oba arctan. Ennyiriri eziri waggulu −1 tekitegeeza 1/tan (ekibeera cotangent). Mu kifo ky’ekyo, tan⁻¹(x) abuuza nti: ‘Enkoona ki erina tangent eyenkana x?’. Okugeza, tan−1(1) = 45° kubanga tan(45°) = 1. Oyinza n’okukiraba nga kiwandiikiddwa nga arctan(x) oba atan(x) mu nnimi za pulogulaamu.
Omulimu gwa tangent gutwala enkoona ne guzzaayo omugerageranyo gw’oludda olulala n’oludda oluliraanye mu nkoona essatu entuufu. Tangent enzijuvu (arctan) ekola ekikyuusa: etwala omugerageranyo n’ezzaayo enkoona ekwatagana. Okugeza, tan(45°) = 1, kale arctan(1) = 45°. Tangent erina domain ya namba zonna entuufu okuggyako odd multiples eza 90°, ate inverse tangent ekkiriza namba zonna entuufu era efulumya enkoona wakati wa −90° ne 90° (−π/2 okutuuka ku π/2 radians).
Butaamu ya inverse tangent etuula waggulu w’ekisumuluzo kya tan ku kalkulayiza za ssaayansi ezisinga obungi. Okugifuna, sooka onyige ekisumuluzo kya 2nd oba Shift, olwo onyige button ya tan. Okwolesebwa kujja kulaga tan−1 oba arctan. Ku kalkulayiza z’okukola giraafu nga TI-84, nyweza 2nd olwo TAN. Ku Casio calculators, nyweza SHIFT olwo tan.
Kozesa okugaziya kw’omuddiring’anwa gwa Taylor: arctan(x) = x − x3/3 + x5/5 − x7/7 + ... ku |x| ≤ 1. Ku miwendo egya bulijjo, kwata mu mutwe enkoona z’ebisumuluzo: arctan (0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Osobola n’okukozesa enkola ya CORDIC algorithm. Ku miwendo egy’ebweru wa [−1, 1], kozesa endagamuntu arctan(x) = π/2 − arctan(1/x) ku x > 0.
Tangent enzijuvu eya 1 eri 45° (oba π/4 radians). Kino kiri bwe kityo kubanga tan(45°) = 1. Mu njuyi essatu entuufu ng’enjuyi ezikontana n’eziriraanye zenkanankana, enkoona eba 45°.
Tan ekyusa enkoona mu mugerageranyo (opposite/adjacent), ate inverse tan (arctan) ekyusa omugerageranyo okudda mu nkoona. Tan ya periodic era esobola okufulumya namba yonna entuufu, so nga arctan bulijjo ezzaayo enkoona ey’enjawulo mu bbanga (−90°, 90°).
Yee, kozesa ensengekera =ATAN(value) mu Excel. Kino kizzaayo ekivaamu mu radians. Okukyusa okudda mu diguli, kozesa =DEGREES(ATAN(value)). Excel era ewagira =ATAN2(x, y) ku nsonga bbiri arctangent.
Zingulula iPhone yo ku landscape orientation okulaga calculator ya ssaayansi. Koona ku 2nd button okukyusa okudda ku inverse functions. Butaamu ya tan ejja kukyuka efuuke tan−1. Yingiza omuwendo gwo onyige tan−1.
Mu nnyiriri essatu eza ddyo, tangensi enzijuvu (inverse tangent) y’omugerageranyo ogw’ekikontana/ekiriraanye yenkana enkoona eri ku ntikko eyo. Singa ekikontana = 3 ate ekiriraanye = 4, olwo arctan(3/4) ≈ 36.87°.
Waliwo enkozesa 6 eza bulijjo: (1) Okutambulira mu nnyanja ne GPS ku nkoona za bbeeri, (2) Yinginiya ku nkoona z’okusereba, (3) Fizikisi ku vekita z’amaanyi, (4) Ebifaananyi bya kompyuta okusobola okukyusakyusa, (5) Yinginiya w’amasannyalaze ku nkoona za phase, (6) Eby’emmunyeenye ku nkoona z’obugulumivu.
Okuyita mu tan(θ) = sin(θ)/cos(θ). Singa θ = arctan(x), olwo sin(θ) = x/√(1+x²) ne cos(θ) = 1/√(1+x²). Ekiva mu arctan(x) kiri 1/(1+x²).
Yee. Omugerageranyo gw’okusereba gwe gumu n’ogw’ekikontana ku kumpi mu njuyi essatu entuufu. Yingiza okusituka kwo ng’oludda olulala ate emisinde gyo ng’oludda oluli okumpi era ekintu ekikozesebwa kizzaawo enkoona y’okuserengeta mu diguli zombi ne radians.
Ekintu kino kizimbibwa nnyo ku arctangent. Bw’oba weetaaga ekibalirizi kya inverse trig ekijjuvu ekibikka arcsin ne arccos ku mabbali ga arctan, wandibadde weetaaga ekintu ekigazi ekya inverse trigonometry.