Wanpela 'inverse tangent calculator' (ol i save kolim tu olsem 'arcus tangent calculator') i save kompiutim arctangent (atan) bilong wanpela ril namba na i save givim bek angle we tangent bilong en i wankain olsem dispela veliu. Maski yu painim angle bilong wanpela 'slope' long rot bilong putim 'rise' na 'run' olsem oposit na 'adjacent', o senisim tasol 'tangent ratio' i go long 'degrees' o 'radians', dispela 'angle finder' i givim yu risal hariap tru. Putim wanpela desimal o reshio bilong ol sait i stap klostu / klostu long wanpela rait traiengol, makim namel long ol digri na ol radian, na kisim ol risal hariap. Dispela arc tan kalkuleta i save droim tu wanpela 'interactive triangle diagram', droim arctan(x) graf, na soim wanpela ful tangent tebol - olgeta samting we i nidim long trigonometri, kalkulas, na nevigesen kalkulesen long wanpela ples tasol.
Inves Tangent Kalkuleita
Bihain long olgeta kalkulesen, traiengol i save kamap nupela na bai yu ken lukim olsem θ = arctan(oposit / klostu).
Graf i makim input bilong nau bai yu ken skelim namba wantaim angle bilong en.
Wanem Em Inverse Tangent?
Inverse tangent, ol i raitim olsem tan⁻¹(x), arctan(x), o atan(x), i save givim bek angle we tangent bilong en i wankain olsem x. Insait long ol teksbuk bilong Yurop na Jemani dispela wankain wok i kamap olsem 'arcus tangens' o 'arkus tangens'. Long yunit sekol, arctan i givim bek angle we i stret long wanem 'tangent' veliu i stap long sekel.
Insait long wanpela rait traiengol, tan(θ) = oposit / klostu, olsem na arctan(oposit / klostu) i givim angle θ.
Domen bilong en em olgeta namba tru, na bikpela mak bilong en em (-π/2, π/2) o (-90°, 90°).
Muvim 'slider' long lukim olsem wanem wanpela 'real input' i go long wanpela 'angle' namel long -90° na 90°.
Hausait Long Kalkulim Inverse Tangent?
Yusim θ = arctan(x) taim x em i wanpela desimal veliu o wanpela resio.
- Luksave long veliu x.
- Yusim wanpela saientifik kalkuleta o wanpela atan() fanksen long kompiutim arctan(x).
- Senisim risal sapos yu nidim ol digri na i no ol radian. Multiplaim 'radian result' long 180/π long kisim ol digri, o multiplaim wanpela digri veliu long π/180 long senisim i go bek long 'radian'. Maski wanem rot, 'inverse tan' fomula i stap yet θ = arctan(x) long olgeta taim.
Raitim wanpela veliu bilong apdetim wanwan step hariap.
Hausait Long Yusim Dispela Inverse Tangent Kalkuleita?
Makim desimal o oposit/adjasen input, makim digri o redian, na presim Kalkuletim.
Ol Rot bilong Input
Desimal mod i save kisim ol veliu olsem 0.5, 1, o -2.75.
Oposit / Adjacent mod i brukim tupela sait pastaim na bihain i yusim arctan.
Panel bilong ol risalt i soim planti kain bekim bilong yusim hariap.
Hau long yusim inves tangent long wanpela kalkuleta?
Presim "2nd" o "Shift" ki long wanpela 'scientific calculator' (olsem Casio o TI-84), na bihain presim "tan" baten long kisim tan⁻¹.
- Opim kalkuleta na setim 'angle mode' i go long 'degrees' (DEG) o 'radians' (RAD).
- Presim "2nd" o "Shift." Dispela ki i save kirapim ol narapela wok we i stap antap long wanwan baten. Dispela 'shift tan key' kombinesen em i stap long olgeta Casio, TI-84, na Sharp model. Oltaim setim 'angle mode' bilong yu long DEG o RAD pastaim long yu presim, long wanem, wankain input i save givim ol narapela narapela namba bihainim 'mode'.
- Presim "tan" ki. Displei i soim "tan−1(" o "atan(".
- Raitim veliu na presim "=".
Piksa aninit i soim ol stretpela baten bilong presim long wanpela TI-84 saientifik kalkuleta.
Painim tan⁻¹(1) = 45° long wanpela TI-84 kalkuleta
Hau long Kalkuletim Inverse Tangent Sapos yu no gat Kalkuleta?
Yusim arctangent Taylor series expansion long skelim arctan(x) long han: arctan(x) = x − x3/3 + x5/5 − x7/7 + … Dispela series i save bung taim |x| ≤ 1.
- Taylor Series (Maclaurin series). arctangent series aproksimesen tul i yusim x − x3/3 + x5/5 − x7/7. Moa toktok i save givim bikpela stretpela mak.
- Ol angle veliu we yumi save long en. Tingim ol samting yu save kisim: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- CORDIC Algorithm. Dispela 'hardware-level' rot i save skelim arctangent long rot bilong ol 'angle rotation' planti taim.
Yu ken makim hamas tok yu laik putim insait. Lukim hau aproksimesen i go long trupela veliu.
Inverse Tangent Graf
arctan(x) graf em i wanpela S-sep kev we i wok long go antap na i go long as na i go klostu long ±π/2.
- Em i gat ol 'horizontal asymptotes' long y = -π/2 na y = π/2.
- Em i narakain, olsem na arctan(-x) = -arctan(x).
- Em i save go antap long lephan i go long raithan.
Hover antap long graf long sekim ol stretpela veliu.
Tangent Tebol
Ol tan inves veliu long 0°, 30°, 45°, 60°, na 90° i save kamap long klostu olgeta trigonometri kos na i gutpela long tingim. Klikim wanpela lain bilong tebol long putim dispela standet veliu i go insait long kalkuleta.
| x | arctan(x) Digri | arctan(x) Redian | π Fraksen |
|---|---|---|---|
| −∞ | −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 |
Notesen bilong Inves bilong Tangent
Notesen bilong inves bilong tangent i kisim 3-pela standet fom: tan⁻¹(x), arctan(x), na atan(x).
- tan⁻¹(x) Em i save kamap long ol 'physical calculator'.
- arctan(x) Standet long fomal matematiks.
- atan(x) Programing na sofwet notesen.
Sampela sumatin i kolim olsem 'anti tangent' bikos em i save senisim wanem samting 'tangent' i save mekim, tasol dispela i no standet matematikel tok.
Klikim wanwan 'notation' long soim we em i kamap long 'math', 'programming', na 'calculator'.
tan⁻¹(x) em i nambawan 'notation' long ol 'physical calculator'. Supaskript -1 i soim "inves fanksen," i no "1 / tan(x)".
Painim tan−1 bilong ol Negetiv Namba
Tan−1 bilong ol negatif namba i save givim bek wanpela negatif angle. Bikos arctangent em i wanpela 'odd function', arctan(-x) = -arctan(x).
- arctan(-1) = -45° o -π/4 radians
- arctan(-√3) = -60° o -π/3 radians
Wanem em i tan⁻1 bilong -1?
Tan−1 bilong -1 em -45° (-π/4 radians o -0.7854 radians).
Putim wanpela negatif namba long lukim hau arctan i makim ol negatif input i go long ol negatif angle.
FAQ
Ansa long ol askim we planti man i save askim long 'inverse tangent'.
Ya, tan⁻¹ em standard matimatikal notasen bilong inverse tangent, tu kolim arctangent olsem arctan. Lig bilong ⁻¹ i no min 1/tan (husat em kotanjent). Namel long, tan⁻¹(x) i askim: 'Wanem engkel i gat wanpela tangent i wankain long x?' Olsem, tan⁻¹(1) = 45° long wanem tan(45°) = 1. Yu ken tu lukim em rait olsem arctan(x) o atan(x) long programing tokples.
Tangent fanksen i kisim engkel na bringim bek resio bilong bung wantaim sait long klostu sait insait long retpela traingel. Inverse tangent (arctan) i mekim bek: em i kisim resio na bringim bek engkel. Olsem, tan(45°) = 1, olsem arctan(1) = 45°. Tangent i gat domain bilong olgeta real namba xcept odd multiples bilong 90°, hap inverse tangent i laikim olgeta real namba na autim ol engkel namel long −90° na 90° (−π/2 igo long π/2 redian).
Inverse tangent baten i stap antap long tan ki long planti saientifik kalkuleita. Long kisim em, presim 2nd o Shift ki pastaim, nau presim tan baten. Skrin bai soim tan⁻¹ o arctan. Long graf kalkuleita olsem TI-84, presim 2nd nau TAN. Long Casio kalkuleita, presim SHIFT nau tan.
Yusim Taylor seris expansen: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... long |x| ≤ 1. Long komun valyu, memoraisim ol bikpela engkel: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Yu ken tu yusim CORDIC algorithm. Long valyu ausait long [−1, 1], yusim identity arctan(x) = π/2 − arctan(1/x) long x > 0.
Inverse tangent bilong 1 em 45° (o π/4 redian). Dispela long tan(45°) = 1. Insait long retpela traingel we bung wantaim na klostu sait i wankain, engkel em 45°.
Tan i tanim engkel igo long resio (bung wantaim/klostu), hap inverse tan (arctan) i tanim resio igo bek long engkel. Tan i periodic na ken kamapim olgeta real namba, hap arctan oltaim i bringim bek wanpela spesol engkel long renj (−90°, 90°).
Ya, yusim fomula =ATAN(valyu) long Excel. Dispela i bringim bek risol long redian. Long tanim igo long digri, yusim =DEGREES(ATAN(valyu)). Excel tu sapotim =ATAN2(x, y) long tupela agyument arctangent.
Tanem iPhone bilong yu igo long landskep luksave long soim saientifik kalkuleita. Tapim 2nd baten long senis igo long inverse fanksen. Tan baten bai senis igo long tan⁻¹. Putim valyu bilong yu na tap tan⁻¹.
Insait long retpela traingel, inverse tangent bilong resio bung wantaim/klostu i wankain olsem engkel long dispela kona. Sapos bung wantaim = 3 na klostu = 4, olsem arctan(3/4) ≈ 36.87°.
I gat 6 komun aplikesen: (1) Nativesen na GPS long bearing engkel, (2) Ensiniaring long slop engkel, (3) Fisis long fos vektor, (4) Kompyuta grafis long rotesen, (5) Elektrikal ensiniaring long fes engkel, (6) Estronomi long elevasen engkel.
Tru long tan(θ) = sin(θ)/cos(θ). Sapos θ = arctan(x), olsem sin(θ) = x/√(1+x²) na cos(θ) = 1/√(1+x²). Derivat bilong arctan(x) em 1/(1+x²).
Ya. Slop resio em wankain olsem bung wantaim ova klostu insait long retpela traingel. Putim yu go antap olsem bung wantaim sait na yu ron olsem klostu sait na tul bai bringim bek engkel bilong inklinesen long digri na redian.
Dispela tul i wokim spesol long arctangent. Sapos yu nidim wanpela ful inverse trig kalkuleita i kavaim arcsin na arccos wantaim arctan, yu bai nidim wanpela braitpela inverse trigonometri tul.