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.
Inverse Tangent Kalkuleta
Bihain long olgeta kalkulesen, traiengol i save kamap nupela na bai yu ken lukim olsem ฮธ = arctan(opposite / adjacent).
Graf i makim input bilong nau bai yu ken skelim namba wantaim angle bilong en.
Inverse Tangent em i wanem samting?
Inverse tangent, ol i raitim olsem tanโปยน(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(ฮธ) = oposit / klostu, olsem na arctan(oposit / klostu) i givim angle ฮธ.
Domen bilong en em olgeta namba tru, na bikpela mak bilong en em (-ฯ/2, ฯ/2) o (-90ยฐ, 90ยฐ).
Muvim 'slider' long lukim olsem wanem wanpela 'real input' i go long wanpela 'angle' namel long -90ยฐ na 90ยฐ.
Hau long Kalkuletim Inves Tangent?
Yusim ฮธ = 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/ฯ long kisim ol digri, o multiplaim wanpela digri veliu long ฯ/180 long senisim i go bek long 'radian'. Maski wanem rot, 'inverse tan' fomula i stap yet ฮธ = arctan(x) long olgeta taim.
Raitim wanpela veliu bilong apdetim wanwan step hariap.
Hau long yusim dispela inves tangent kalkuleta?
Yu mas makim wanpela desimal o oposit/adjasen input, makim ol digri o redian, na presim Kalkuletim.
Ol Rot bilong Input
Desimal mod i save kisim ol veliu olsem 0.5, 1, o -2.75.
Opposite / Adjacent mode 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 tanโปยน.
- 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 "tanโ1(" o "atan(".
- Raitim veliu na presim "=".
Piksa aninit i soim ol stretpela baten bilong presim long wanpela TI-84 saientifik kalkuleta.
Painim tanโปยน(1) = 45ยฐ 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 โ x3/3 + x5/5 โ x7/7 + โฆ Dispela series i save bung taim |x| โค 1.
- Taylor Series (Maclaurin series). arctangent series aproksimesen tul i yusim x โ x3/3 + x5/5 โ 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) = 0ยฐ, arctan(1) = 45ยฐ, arctan(โ3) = 60ยฐ.
- 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 Graph
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 ยฑฯ/2.
- Em i gat ol 'horizontal asymptotes' long y = -ฯ/2 na y = ฯ/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 0ยฐ, 30ยฐ, 45ยฐ, 60ยฐ, na 90ยฐ 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) Ol digri | arctan(x) Radians | ฯ Hap |
|---|---|---|---|
| −∞ | −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: tanโปยน(x), arctan(x), na atan(x).
- tanโปยน(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'.
tanโปยน(x) em i nambawan 'notation' long ol 'physical calculator'. Supaskript -1 i soim "inves fanksen," i no "1 / tan(x)".
Painim tanโ1 bilong ol Negetiv Namba
Tanโ1 bilong ol negatif namba i save givim bek wanpela negatif angle. Bikos arctangent em i wanpela 'odd function', arctan(-x) = -arctan(x).
- arctan(-1) = -45ยฐ o -ฯ/4 radians
- arctan(-โ3) = -60ยฐ o -ฯ/3 radians
Wanem em i tanโป1 bilong -1?
Tanโ1 bilong -1 em -45ยฐ (-ฯ/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.
Ol FAQs
Ansa long ol askim we planti man i save askim long 'inverse tangent'.
Yes, tanโปยน em i standet matematikel notesen bilong inves tangent, ol i kolim tu arctangent o arctan. Supaskript โป1 i no min olsem 1/tan (em i 'cotangent'). Tasol, tanโปยน(x) i askim: 'Wanem angle i gat tangent i wankain olsem x?' Olsem, tanโป1(1) = 45ยฐ bikos tan(45ยฐ) = 1. Yu ken lukim tu olsem ol i raitim olsem arctan(x) o atan(x) long ol programing tokples.
Tangent fanksen i kisim wanpela angle na i givim bek wanpela reshio bilong oposit sait i go long adjasent sait insait long wanpela rait traiengol. Inves tangent (arctan) i mekim rives: em i kisim wanpela 'ratio' na givim bek 'angle' bilong en. Olsem, tan(45ยฐ) = 1, olsem na arctan(1) = 45ยฐ. Tangent i gat wanpela domen bilong olgeta ril namba tasol ol 'od multiples' bilong 90ยฐ, tasol inves tangent i save kisim olgeta ril namba na i save kamapim ol angle namel long โ90ยฐ na 90ยฐ (โฯ/2 i go long ฯ/2 radians).
Baten bilong 'inverse tangent' i stap antap long 'tan' ki long planti ol 'scientific calculator'. Long kisim, presim namba tu o Shift ki pastaim, na bihain presim tan baten. Displei bai soim tanโปยน o arctan. Long ol 'graphing calculator' olsem TI-84, presim 2nd na bihain TAN. Long Casio kalkuleta, presim SHIFT na tan.
Yusim Taylor series expansion: arctan(x) = x โ x3/3 + x5/5 โ x7/7 + ... bilong |x| โค 1. Long ol komon veliu, tingim ol ki angle: arctan(0) = 0ยฐ, arctan(1/โ3) = 30ยฐ, arctan(1) = 45ยฐ, arctan(โ3) = 60ยฐ. Yu ken yusim tu CORDIC algorithm. Long ol veliu ausait long [โ1, 1], yusim aidentiti arctan(x) = ฯ/2 โ arctan(1/x) long x > 0.
Inves tangent bilong 1 em 45ยฐ (o ฯ/4 radians). Dispela i kamap bikos tan(45ยฐ) = 1. Insait long wanpela rait traiengol we tupela sait i stap klostu na sait i stap klostu i wankain, angle em i 45ยฐ.
Tan i save senisim wanpela angle i go long wanpela 'ratio' (oposit/adjacent), na 'inverse tan' (arctan) i save senisim wanpela 'ratio' i go bek long wanpela 'angle'. Tan em i 'periodic' na em inap long kamapim wanem kain 'real namba', tasol arctan i save givim wanpela 'angle' insait long 'range' (-90ยฐ, 90ยฐ).
Yes, yusim fomula =ATAN(value) insait long Excel. Dispela i givim bek risal long ol 'radians'. Long senisim i go long ol digri, yusim =DEGREES(ATAN(value)). Excel i sapotim tu =ATAN2(x, y) bilong tupela-argument arctangent.
Tanim iPhone bilong yu i go long 'landscape orientation' bilong soim 'scientific calculator'. Taitim namba tu baten long senis i go long ol inves fanksen. Tan baten bai senis i go long tanโ1. Putim veliu bilong yu na paitim tanโ1.
Insait long wanpela 'right triangle', 'inverse tangent' bilong 'ratio oposite/adjacent' i wankain olsem 'angle' long dispela 'vertex'. Sapos opposite = 3 na adjacent = 4, orait arctan(3/4) โ 36.87ยฐ.
I gat 6-pela komon aplikesen: (1) Nevigesen na GPS bilong ol 'bearing angles', (2) Enjiniaring bilong ol 'slope angles', (3) Fisiks bilong ol 'force vectors', (4) Komputa grafik bilong 'rotation', (5) Elektrikel enjiniaring bilong ol 'phase angles', (6) Astronomi bilong ol 'elevation angles'.
Long rot bilong tan(ฮธ) = sin(ฮธ)/cos(ฮธ). Sapos ฮธ = arctan(x), orait sin(ฮธ) = x/โ(1+xยฒ) na cos(ฮธ) = 1/โ(1+xยฒ). Derivativ bilong arctan(x) em 1/(1+xยฒ).
Yes. Wanpela 'slope ratio' em i wankain olsem 'opposite' antap long 'adjacent' insait long wanpela 'right triangle'. Putim 'rise' bilong yu olsem narapela sait na 'run' bilong yu olsem narapela sait na tul i givim bek 'angle of inclination' long tupela digri na 'radian'.
Dispela tul em ol i wokim stret bilong arctangent. Sapos yu nidim wanpela ful inves trig kalkuleta we i karamapim arcsin na arccos wantaim arctan, yu bai nidim wanpela bikpela inves trigonometri tul.