Chiverengero chetangent yakapesana, chinonziwo chiverengero chearcus tangent, chinoverenga arctangent (atan) yenhamba chaiyo ipi zvayo chichipa kona ine tangent yakaenzana nenhamba iyoyo. Kuti uwane kona yemateru, isa kukwira nekufamba kwakachinjika semativi akatarisana neakabatana nekona. Unogonawo kushandura reshiyo yetangent kuita madhigirii kana maradhiyani. Isa nhamba yedesimali kana reshiyo yerutivi rwakatarisana / rutivi rwakabatana mutriangle ine kona ye90°, wosarudza madhigirii kana maradhiyani kuti uwane mhinduro ipapo. Chishandiso ichi chinoratidzawo triangle inopindirana, girafu rearctan(x), netafura yetangent, zvichibatsira muzvidzidzo zvetriangle, calculus nekutsvaga nzira.
Tangent Yakapesana Chiverengero
Mhinduro
Zvaverengwa arctan(1)
45°
Madhigirii 45°
Maradhiyani 0.7854 rad
Magradhiyani 50 grad
Chikamu cheπ π/4
Triangle Ine Kona ye90° Inopindirana
Mushure mekuverenga, triangle inoshanduka ichiratidza kuti θ = arctan(rutivi rwakatarisana / rutivi rwakabatana).
Girafu reTangent Yakapesana
Girafu rinomaka nhamba yawaisa kuti uienzanise nekona yayo.
Tangent Yakapesana Chii?
Tangent yakapesana, inonyorwa ichinzi tan⁻¹(x), arctan(x) kana atan(x), inopa kona ine tangent yakaenzana nax. Mumabhuku eEurope neGermany, basa iri rinonziwo arcus tangens kana arkus tangens. Padenderedzwa rine radius ye1, arctan inopa kona inoenderana nechiyero chetangent.
Mutriangle ine kona ye90°, tan(θ) = rutivi rwakatarisana / rutivi rwakabatana. Saka arctan(rutivi rwakatarisana / rutivi rwakabatana) inopa kona θ.
Inobvuma nhamba chaiyo ipi zvayo, uye mhinduro yayo iri pakati pe(-π/2, π/2) kana (-90°, 90°), isingasviki kumagumo aya.
Edza: Nhamba Dzinobvumirwa neMhinduro dze arctan(x)
Fambisa chinotsvedza kuti uone kona iri pakati pe-90° ne90° inoenderana nenhamba yawaisa.
Tangent Yakapesana Inoverengwa Sei?
Shandisa θ = arctan(x) kana x iri nhamba yedesimali kana reshiyo.
- Tsvaga nhamba x.
- Shandisa chiverengero chesainzi kana basa re atan() kuverenga arctan(x).
- Kuti uwane madhigirii, wedzera mhinduro yemaradhiyani ka180/π. Kuti ushandure madhigirii kuva maradhiyani, wedzera kaπ/180. Fomula inoramba iri θ = arctan(x).
Edza: Kuverenga Nhanho neNhanho
Isa nhamba kuti nhanho imwe neimwe ivandudzwe ipapo.
1Nhamba Yaiswa: x = 1
2arctan(1) = 0.7854 rad
3Shandura: 0.7854 × 180/π = 45°
Chiverengero Ichi Chinoshandiswa Sei?
Sarudza nhamba yedesimali kana rutivi rwakatarisana/rwakabatana, wosarudza madhigirii kana maradhiyani, wodzvanya Verenga.
Nzira dzeKuisa Nhamba
1
Nhamba yeDesimali
Nzira yedesimali inobvuma nhamba dzakaita se0.5, 1 kana -2.75.
2
Rutivi Rwakatarisana / Rwakabatana
Nzira yeRutivi Rwakatarisana / Rwakabatana inotanga yagovanisa mativi maviri, yozoshandisa arctan.
Chikamu chemhinduro chinoratidza mhinduro nenzira dzakasiyana kuti ishandiswe zviri nyore.
Tangent Yakapesana Inoshandiswa Sei paChiverengero?
Dzvanya “2nd” kana “Shift” pachiverengero chesainzi chakaita seCasio kana TI-84, wozodzvanya “tan” kuti uwane tan⁻¹.
- Batidza chiverengero, wosarudza madhigirii (DEG) kana maradhiyani (RAD).
- Dzvanya “2nd” kana “Shift” kuti uvhure mamwe mabasa akanyorwa pamusoro pemabhatani. Nzira iyi inoshandiswa pamhando dzeCasio, TI-84 neSharp. Sarudza DEG kana RAD usati watanga, nokuti nhamba imwe chete inopa mhinduro dzakasiyana zvichienderana nechiyero.
- Dzvanya “tan”. Chiratidziro chinobva charatidza “tan⁻¹(” kana “atan(”.
- Isa nhamba, wodzvanya “=”.
Gwaro reMifananidzo: Kutsvaga tan⁻¹ paChiverengero
Mufananidzo uri pazasi unoratidza mabhatani ekudzvanya pachiverengero chesainzi cheTI-84.
Kutsvaga tan⁻¹(1) = 45° pachiverengero cheTI-84
Tangent Yakapesana Inoverengwa Sei Pasina Chiverengero?
Shandisa nhevedzano yaTaylor kuwana mhinduro yepedyo nearctan(x) neruoko: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + … Nhevedzano iyi inosvika pamhinduro kana |x| ≤ 1.
- Nhevedzano yaTaylor (yaMaclaurin). Chishandiso ichi chinoshandisa x − x³/3 + x⁵/5 − x⁷/7. Kuwedzera zvikamu kunoita kuti mhinduro iswedere pachiyero chaicho.
- Zviyero zveMakona Zvinozivikanwa. Yeuka mhinduro dzinowanzoonekwa: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- Nzira yeCORDIC. Nzira iyi inoshandiswa mumidziyo kuverenga arctangent nekudzokorora kutenderedza makona.
Edza: Mhinduro Yepedyo neNhevedzano yaTaylor
Sarudza huwandu hwezvikamu. Ona kuti mhinduro inoswedera sei pachiyero chaicho.
Girafu reTangent Yakapesana
Girafu rearctan(x) rine chimiro cheS, rinokwira richipfuura pa(0, 0) uye richiswedera ku±π/2.
- Rine mitsetse yakachinjika yarinoswedera kwairi asi risingasviki, pa y = -π/2 ne y = π/2.
- Basa iri rine symmetry yepakati: arctan(-x) = -arctan(x).
- Rinogara richikwira kubva kuruboshwe kuenda kurudyi.
Edza: Girafu re arctan(x)
Isa chinongedzo pamusoro pegirafu kuti uone zviyero chaizvo.
Tafura yeTangent
Zviyero zvetangent nemakona e0°, 30°, 45°, 60° ne90° zvinowanikwa kazhinji muzvidzidzo zvetriangle, saka zvakanaka kuzviyeuka. Dzvanya mutsara wetafura kuti uise chiyero ichocho muchiverengero.
| x | arctan(x) Madhigirii | arctan(x) Maradhiyani | Chikamu cheπ |
|---|---|---|---|
| −∞ | −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 |
Manyorerwo eTangent Yakapesana
Tangent yakapesana inonyorwa nenzira nhatu dzakajairika: tan⁻¹(x), arctan(x), neatan(x).
- tan⁻¹(x) Inowanzoonekwa pazviverengero.
- arctan(x) Manyorerwo anowanzoshandiswa mumasvomhu.
- atan(x) Inoshandiswa mumapurogiramu emakombiyuta.
Vamwe vadzidzi vanoidana kuti anti tangent nokuti inodzosera zvinoitwa netangent, asi iri harisi zita repamutemo remasvomhu.
Edza: Kuenzanisa Manyorerwo
Dzvanya manyorerwo ega ega kuti uone paanoshandiswa mumasvomhu, mumapurogiramu nemuzviverengero.
tan⁻¹(x) inowanzoonekwa pazviverengero. -1 iri pamusoro inoreva basa rakapesana, kwete 1 / tan(x).
Kutsvaga tan⁻¹ yeNhamba dziri Pasi peZero
tan⁻¹ yenhamba iri pasi pezero inopa kona iri pasi pezero. Basa rearctangent rine symmetry yepakati: arctan(-x) = -arctan(x).
- arctan(-1) = -45° kana -π/4 maradhiyani
- arctan(-√3) = -60° kana -π/3 maradhiyani
tan⁻¹ ye-1 Inoita Sei?
tan⁻¹ ye-1 i-45° (-π/4 maradhiyani kana -0.7854 maradhiyani).
Edza: Nhamba dziri Pasi peZero
Isa nhamba iri pasi pezero kuti uone kuti arctan inopa sei kona iri pasi pezero.
arctan(-1) = -45° = -π/4 rad
arctan(1) = 45° ↔ arctan(-1) = -45°
Mibvunzo Inowanzobvunzwa
Mhinduro dzemibvunzo inowanzobvunzwa nezvetangent yakapesana.
Hongu. tan⁻¹ ndiwo manyorerwo etangent yakapesana, inonziwo arctangent kana arctan. ⁻¹ iri pamusoro hairevi 1/tan, inova cotangent. tan⁻¹(x) inobvunza kuti: ndeipi kona ine tangent yakaenzana nax? Somuenzaniso, tan⁻¹(1) = 45° nokuti tan(45°) = 1. Mumapurogiramu, unogonawo kuona arctan(x) kana atan(x).
Tangent inotora kona ichipa reshiyo yerutivi rwakatarisana nerutivi rwakabatana mutriangle ine kona ye90°. Tangent yakapesana (arctan) inotora reshiyo ichipa kona inoenderana nayo. Somuenzaniso, tan(45°) = 1, saka arctan(1) = 45°. Tangent inobvuma makona ose kunze kwe90° yakawedzerwa kanhamba isingagovaniki na2. Arctan inobvuma nhamba chaiyo ipi zvayo ichipa kona iri pakati pe−90° ne90° (−π/2 kusvika π/2 maradhiyani), isingasviki kumagumo aya.
Pazviverengero zvesainzi zvakawanda, tan⁻¹ yakanyorwa pamusoro pebhatani retan. Dzvanya 2nd kana Shift, wozodzvanya tan. Chiratidziro chinoratidza tan⁻¹ kana arctan. PaTI-84, dzvanya 2nd wozoti TAN. PaCasio, dzvanya SHIFT wozoti tan.
Shandisa nhevedzano yaTaylor: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... kana |x| ≤ 1. Yeuka makona akajairika: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Unogonawo kushandisa nzira yeCORDIC. Kune nhamba dziri kunze kwe[−1, 1], shandisa arctan(x) = π/2 − arctan(1/x) kana x > 0.
Tangent yakapesana ye1 i45° kana π/4 maradhiyani, nokuti tan(45°) = 1. Mutriangle ine kona ye90°, kana rutivi rwakatarisana nerwakabatana akaenzana, kona yacho i45°.
Tan inoshandura kona kuva reshiyo yerutivi rwakatarisana/rwakabatana. Inverse tan (arctan) inoshandura reshiyo kuva kona. Tan inodzokorora zviyero zvayo uye inogona kupa nhamba chaiyo ipi zvayo. Arctan inogara ichipa kona imwe chete iri mu(−90°, 90°).
Hongu. Shandisa =ATAN(value) muExcel kuti uwane mhinduro mumaradhiyani. Kuti uwane madhigirii, shandisa =DEGREES(ATAN(value)). Excel inewo =ATAN2(x, y) yearctangent inotora nhamba mbiri.
Tenderedza iPhone yako kuti ive yakachinjika, kuti chiverengero chesainzi chionekwe. Bata 2nd kuti uvhure mabasa akapesana. Bhatani retan rinobva rava tan⁻¹. Isa nhamba yako, wobata tan⁻¹.
Mutriangle ine kona ye90°, tangent yakapesana yereshiyo yerutivi rwakatarisana/rwakabatana inopa kona yacho. Kana rutivi rwakatarisana = 3 uye rwakabatana = 4, arctan(3/4) ≈ 36.87°.
Inowanzoshandiswa munzira 6: (1) kutsvaga nzira neGPS kuwana makona enzira, (2) engineering kuwana makona emateru, (3) physics kuongorora mafambiro emasimba, (4) mifananidzo yekombiyuta pakutenderedza, (5) engineering yemagetsi pakutsvaga phase angles, uye (6) kudzidza nyeredzi pakuwana makona ekukwirira.
Hukama hwacho ndi tan(θ) = sin(θ)/cos(θ). Kana θ = arctan(x), sin(θ) = x/√(1+x²) uye cos(θ) = 1/√(1+x²). Derivative ye arctan(x) ndi 1/(1+x²).
Hongu. Reshiyo yemateru yakafanana nerutivi rwakatarisana rwakagovaniswa nerwakabatana mutriangle ine kona ye90°. Isa kukwira serutivi rwakatarisana, nekufamba kwakachinjika serwakabatana. Chishandiso chinopa kona mumadhigirii nemaradhiyani.
Chishandiso ichi chakagadzirirwa arctangent. Kana uchida arcsin nearccos pamwe nearctan, unoda chiverengero chemabasa akapesana etrigonometry chinobatanidza mabasa iwayo.