Enn kalkilatris tanzant invers (osi koni kouma enn kalkilatris tanzant arcus) kalkil arctanzant (atan) ninport ki nimero reel e retourn ang ki so tanzant egal a sa valer-la. Ki ou pe trouv ang enn lapant par rant dan rise and run kouma opoze ek adjacent, ou sinpleman konverti enn rapor tanzant an degre ou radian, sa angle finder-la donn ou rezilta instantaneman. Met enn desimal ou rapor bann kote opoze / adjasan depi enn triyang drwat, swazir ant bann degre ek bann radian, e gagn bann rezilta instantanie. Sa kalkilatris arc tan-la osi desinn enn diagram triyang interaktif, tras enn grafik arctan(x), ek afis enn tablo tanzant konpleโtou seki neseser pou bann kalkil trigonometri, kalkil, ek navigasion dan enn sel plas.
Tanzant Invers Kalkilatris
Rezilta
Finn kalkile arctan(1)
45°
Degre 45°
Bann radian 0.7854 rad
Bann gradien 50 grad
ฯ Fraksion π/4
Triyang drwat interaktif
Apre sak kalkil, triyang-la met azour pou ki ou kapav trouve ki ฮธ = arctan(opoze / akote).
Graf tanzant inverse
Graf-la mark input aktyel pou ki ou kapav konpar nimero-la avek so ang.
Ki ete tanzant invers?
Tanzant invers, ekrir kouma tanโปยน(x), arctan(x), ou atan(x), retourn ang ki so tanzant egal a x. Dan bann liv Eropeen ek Alman sa mem fonksion-la aparet kouma arcus tangens ou arcus tangens. Lor serk inite, arctan retourn ang ki koresponn a ninport ki valer tanzant toutlong serk-la.
Dan enn triyang drwat, tan(ฮธ) = opoze / adjasan, alor arctan(opoze / adjasan) donn ang ฮธ.
So domenn se tou bann nimero reel, e so ranze prinsipal se (-ฯ/2, ฯ/2) ou (-90ยฐ, 90ยฐ).
Interaktif: Domenn ek Ranze arctan(x)
Bouz kurser-la pou gete kouma ninport ki input reel map ver enn ang ant -90ยฐ ek 90ยฐ.
Kouma pou kalkil tanzant invers?
Servi ฮธ = arctan(x) kan x enn valer desimal ou enn rapor.
- Idantifie valer x.
- Servi enn kalkilatris siantifik ou enn fonksion atan() pou kalkil arctan(x).
- Konverti rezilta-la si ou bizin bann degre olie bann radian. Miltipliy rezilta radian par 180/ฯ pou gagn bann degre, ouswa miltipliy enn valer degre par ฯ/180 pou konverti an radian. De tout fason, formil tan inverse res ฮธ = arctan(x) toutlong.
Interaktif: Kalkil etap par etap
Tap enn valer pou met sak letap azour toutswit.
1Rantre: x = 1
2arctan(1) = 0.7854 rad
3Konverti: 0.7854 ร 180/ฯ = 45°
Kouma pou servi sa kalkilatris tanzant inverse-la?
Swazir enn desimal ou enn input opoze/adjasan, swazir bann degre ou bann radian, ek pez lor Kalkile.
Metod Input
1
Valer desimal
Mod desimal aksepte bann valer kouma 0.5, 1, ou -2.75.
2
Vizavi / Adjasan
Mod opoze / adjasan diviz 2 kote-la avan e apre aplik arctan.
Panel rezilta montre plizier format repons pou enn itilizasion rapid.
Kouma servi tanzant inverse lor enn kalkilatris?
Pez lakle โ2ndโ ou โShiftโ lor enn kalkilatris siantifik (kouma Casio ou TI-84), apre pez bouton โtanโ pou gagn akse a tanโ1.
- Alim kalkilatris-la ek met mod ang lor degre (DEG) ouswa radian (RAD).
- Pez โ2emโ ou โMaj.โ Sa lakle-la aktiv bann fonksion segonder ki inprime lao sak bouton. Sa konbinezon lakle shift tan-la li iniversel atraver bann model Casio, TI-84, ek Sharp. Touletan met ou mod ang lor DEG ou RAD avan pez li, parski mem input retourn diferan nimero depandan lor mod-la.
- Pez tous โtanโ. Afis-la montre โtanโปยน(โ ou โatan(โ.
- Tap valer-la ek pez โ=โ.
Gid Viziel: Rod tanโ1 lor enn Kalkilatris
Zimaz anba montre bann bouton exakt pou peze lor enn kalkilatris siantifik TI-84.
Trouv tanโปยน(1) = 45ยฐ lor enn kalkilatris TI-84
Kouma pou kalkil tanzant invers san enn kalkilatris?
Servi arctangent Taylor series expansion pou aproxime arctan(x) par lame: arctan(x) = x โ x3/3 + x5/5 โ x7/7 + โฆ Sa seri-la konverze kan |x| โค 1.
- Seri Taylor (seri Maclaurin). Zouti aproksimasion seri arctangent servi x โ x3/3 + x5/5 โ x7/7. Plis term donn enn presizion pli ot.
- Bann valer ang koni. Memoriz bann rezilta komin: arctan(0) = 0ยฐ, arctan(1) = 45ยฐ, arctan(โ3) = 60ยฐ.
- Algoritm CORDIC. Sa metod onivo hardware-la kalkil arctangent atraver bann rotasion ang repete.
Interaktif: Aproksimasion Seri Taylor
Swazir komie term pou inklir. Gete kouma aproximasion-la konverz ver vre valer.
Graf tanzant inverse
Graf arctan(x) se enn kourb an form S ki pe ogmante e ki pas par lorizinn e apros ยฑฯ/2.
- Li ena bann asinpt orizontal a y = -ฯ/2 ek y = ฯ/2.
- Li drol, alor arctan(-x) = -arctan(x).
- Li touletan ogmante depi gos ziska drwat.
Interaktif: arctan(x) Grafik
Pas lor grafi-la pou inspekte bann valer exakt.
Tab tanzant
Bann valer inverse tan a 0ยฐ, 30ยฐ, 45ยฐ, 60ยฐ, ek 90ยฐ aparet dan preske tou bann kour trigonometri e li vo lapenn gard zot dan memwar. Klik lor ninport ki lalign latab pou met sa valer standar-la dan kalkilatris.
| x | arctan(x) Degre | arctan(x) Bann radian | ฯ Fraksion |
|---|---|---|---|
| −∞ | −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 |
Notasion pou linvers tanzant
Notasion pou linvers tanzant pran 3 form standar: tanโปยน(x), arctan(x), ek atan(x).
- tanโปยน(x) Komen lor bann kalkilatris fizik.
- arctan(x) Standar dan matematik formel.
- atan(x) Programasion ek notasion lozisiel.
Ena zelev ki apel li anti-tanzant dan enn fason informel parski li ranvers seki tanzant fer, mem si sa pa enn terminolozi matematik standar.
Interaktif: Konparezon Notasion
Klik lor sak notasion pou met an evidans kot li aparet dan matematik, programmasion, ek kalkilatris.
tanโปยน(x) se notasion pli komen lor bann kalkilatris fizik. Let -1 indik โfonksion inverse,โ pa โ1 / tan(x)โ.
Rod tanโปยน bann nimero negatif
Tanโปยน bann nimero negatif retourn enn ang negatif. Parski arctangent se enn fonksion bizar, arctan(-x) = -arctan(x).
- arctan(-1) = -45ยฐ ou -ฯ/4 radians
- arctan(-โ3) = -60ยฐ ou -ฯ/3 radians
Ki ete tanโ1 pou -1?
Tanโ1 -1 se -45ยฐ (-ฯ/4 radian ou -0.7854 radian).
Interaktif: Explorer Valer Negatif
Met ninport ki nimero negatif pou gete kouma arctan map bann input negatif a bann ang negatif.
arctan(-1) = -45° = -π/4 rad
arctan(1) = 45ยฐ ↔ arctan(-1) = -45ยฐ
FAQ
Repons a bann kestion komin lor tanzant inverse.
Wi, tanโป1 se notasion matematik standar pou tanzant invers, ki apel osi arctanzant ou arctan. Siperskript โปยน pa vedir 1/tan (ki kotanzan). Okontrer, tanโปยน(x) demande: 'Ki ang ena enn tanzant egal a x?' Par exanp, tanโยน(1) = 45ยฐ parski tan(45ยฐ) = 1. Ou kapav osi trouv li ekrir kouma arctan(x) ou atan(x) dan bann langaz programmasion.
Fonksion tanzant pran enn ang e retourn enn rapor kote opoze ar kote adjasan dan enn triyang drwat. Tanzant invers (arctan) fer lekontrer: li pran enn rapor e li retourn ang korespondan. Par exanp, tan(45ยฐ) = 1, alor arctan(1) = 45ยฐ. Tanzant ena enn domenn tou bann nimero reel apart bann miltip enpe 90ยฐ, alor ki tanzant invers aksepte tou bann nimero reel e prodir bann ang ant โ90ยฐ ek 90ยฐ (โฯ/2 ziska ฯ/2 radian).
Bouton tanzant inverse trouv lao lakle tan lor laplipar kalkilatris siantifik. Pou gagn akse ar li, pez 2em ou Shift avan, apre pez bouton tan. Afis-la pou montre tanโปยน ou arctan. Lor bann kalkilatris grafik kouma TI-84, pez 2em apre TAN. Lor kalkilatris Casio, pez SHIFT apre tan.
Servi expansion seri Taylor: arctan(x) = x โ x3/3 + x5/5 โ x7/7 + ... pou |x| โค 1. Pou bann valer komin, memoriz bann ang kle: arctan(0) = 0ยฐ, arctan(1/โ3) = 30ยฐ, arctan(1) = 45ยฐ, arctan(โ3) = 60ยฐ. Ou kapav osi servi algoritm CORDIC. Pou bann valer andeor [โ1, 1], servi lidantite arctan(x) = ฯ/2 โ arctan(1/x) pou x > 0.
Tanzant invers 1 se 45ยฐ (ou ฯ/4 radian). Sa li parski tan(45ยฐ) = 1. Dan enn triyang drwat kot kote opoze ek kote adjasan egal, ang-la se 45ยฐ.
Tan konverti enn ang an enn rapor (opoze/adjasan), alor ki tan inverse (arctan) konverti enn rapor an enn ang. Tan li peryodik e li kapav prodir ninport ki nimero reel, alor ki arctan touletan retourn enn ang inik dan ranze (โ90ยฐ, 90ยฐ).
Wi, servi formil =ATAN(value) dan Excel. Sa retourn rezilta-la an radian. Pou konverti an degre, servi =DEGREES(ATAN(value)). Excel osi soutenir =ATAN2(x, y) pou de-argiman arctangent.
Vir ou iPhone dan oryantasion peizaz pou devwal kalkilatris siantifik. Klik lor 2em bouton pou sanz pou bann fonksion inverse. Bouton tan pou sanze pou vinn tanโปยน. Met ou valer ek tap lor tanโปยน.
Dan enn triyang drwat, tanzant invers rapor opoze/adjasan egal a ang dan sa vertex-la. Si opoze = 3 ek adjasan = 4, lerla arctan(3/4) โ 36.87ยฐ.
Ena 6 aplikasion komin: (1) Navigasion ek GPS pou bann ang portan, (2) Inzenieri pou bann ang lapant, (3) Fizik pou bann vekter lafors, (4) Grafik informatik pou rotasion, (5) Inzenier elektrik pou bann ang faz, (6) Astronomi pou bann ang elevasion.
Atraver tan(ฮธ) = sin(ฮธ)/cos(ฮธ). Si ฮธ = arctan(x), lerla sin(ฮธ) = x/โ(1+xยฒ) ek cos(ฮธ) = 1/โ(1+xยฒ). Derive arctan(x) se 1/(1+xยฒ).
Wi. Enn rapor pant li parey kouma opoze lor adjasan dan enn triyang drwat. Fer rant ou rise kouma kote opoze ek ou kours kouma kote adjasan e zouti-la retourn ang enklinasion an degre ek radian toulede.
Sa zouti-la finn konstrir spesifikman pou arctangent. Si ou bizin enn kalkilatris trig invers konple ki kouver arcsin ek arccos akote arctan, ou pou bizin enn zouti trigonometri invers pli larz.