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 konple—tou seki neseser pou bann kalkil trigonometri, kalkil, ek navigasion dan enn sel plas.
Tanjant Envers Kalkilater
Rezilta
Finn kalkile arctan(1)
45°
Degre 45°
Radian 0.7854 rad
Gradian 50 grad
Fraktyon π π/4
Triyang drwat interaktif
Apre sak kalkil, triyang-la met azour pou ki ou kapav trouve ki θ = arctan(opoze / akote).
Graf Tanjant Envers
Graf-la mark input aktyel pou ki ou kapav konpar nimero-la avek so ang.
Ki ete Tanjant Envers?
Tanzant invers, ekrir kouma tan⁻¹(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(θ) = opoze / adjasan, alor arctan(opoze / adjasan) donn ang θ.
So domenn se tou bann nimero reel, e so ranze prinsipal se (-π/2, π/2) ou (-90°, 90°).
Interaktif: Domenn ek Ranze arctan(x)
Bouz kurser-la pou gete kouma ninport ki input reel map ver enn ang ant -90° ek 90°.
Kouma Kalkil Tanjant Envers?
Servi θ = 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/π pou gagn bann degre, ouswa miltipliy enn valer degre par π/180 pou konverti an radian. De tout fason, formil tan inverse res θ = 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 × 180/π = 45°
Kouma Servi Sa Kalkilater Tanjant Envers 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
Opoze / 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 “2nd” ou “Shift” lor enn kalkilatris siantifik (kouma Casio ou TI-84), apre pez bouton “tan” pou gagn akse a tan−1.
- Alim kalkilatris-la ek met mod ang lor degre (DEG) ouswa radian (RAD).
- Pez “2em” ou “Maj.” 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 “tan”. Afis-la montre “tan⁻¹(” ou “atan(”.
- Tap valer-la ek pez “=”.
Gid Viziel: Rod tan−1 lor enn Kalkilatris
Zimaz anba montre bann bouton exakt pou peze lor enn kalkilatris siantifik TI-84.
Trouv tan⁻¹(1) = 45° 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 − x3/3 + x5/5 − x7/7 + … Sa seri-la konverze kan |x| ≤ 1.
- Seri Taylor (seri Maclaurin). Zouti aproksimasion seri arctangent servi x − x3/3 + x5/5 − x7/7. Plis term donn enn presizion pli ot.
- Bann valer ang koni. Memoriz bann rezilta komin: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- 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 Tanjant Envers
Graf arctan(x) se enn kourb an form S ki pe ogmante e ki pas par lorizinn e apros ±π/2.
- Li ena bann asinpt orizontal a y = -π/2 ek y = π/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.
Tablo Tanjant
Bann valer inverse tan a 0°, 30°, 45°, 60°, ek 90° 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) Radian | Fraktyon π |
|---|---|---|---|
| −∞ | −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: tan⁻¹(x), arctan(x), ek atan(x).
- tan⁻¹(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.
tan⁻¹(x) se notasion pli komen lor bann kalkilatris fizik. Let -1 indik “fonksion inverse,” pa “1 / tan(x)”.
Rod tan⁻¹ bann nimero negatif
Tan⁻¹ bann nimero negatif retourn enn ang negatif. Parski arctangent se enn fonksion bizar, arctan(-x) = -arctan(x).
- arctan(-1) = -45° ou -π/4 radians
- arctan(-√3) = -60° ou -π/3 radians
Ki ete tan−1 pou -1?
Tan−1 -1 se -45° (-π/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) = 45° ↔ arctan(-1) = -45°
Kesyon Souvan
Repons a bann kestion komin lor tanzant inverse.
Wi, tan⁻¹ se notasyon matematik standar pou tanjant envers, ousi apele arctangent oswa arctan. Ekspozan ⁻¹ pa vedir 1/tan (ki se kotanjant). O kontrer, tan⁻¹(x) dimande: 'Ki lang ki ena en tanjant egal ar x?' Par egzanp, tan⁻¹(1) = 45° parski tan(45°) = 1. Ou kapav ousi trouv li ekri kouma arctan(x) oswa atan(x) dan langaz programasyon.
Fonksyon tanjant la pran en lang ek retourn en rapo ant kote opoze ek kote adjasan dan en triyang drwat. Tanjant envers (arctan) fer linvers: li pran en rapo ek retourn lang ki koresponn. Par egzanp, tan(45°) = 1, alor arctan(1) = 45°. Tanjant ena en domeinn tou nimero reel eksepte miltip enpar 90°, tandi ki tanjant envers aksept tou nimero reel ek donn bann lang ant −90° ek 90° (−π/2 ziska π/2 radian).
Bouton tanjant envers la asize lor bouton tan lor laplipar kalkilater syantifik. Pou akse li, pez bouton 2nd oswa Shift an premie, apre pez bouton tan. Lekran pou montre tan⁻¹ oswa arctan. Lor kalkilater graf tel ki TI-84, pez 2nd apre TAN. Lor kalkilater Casio, pez SHIFT apre tan.
Servi ekspansyon seri Taylor: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... pou |x| ≤ 1. Pou bann valer kouran, memorize bann lang kle: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Ou kapav ousi servi algorit CORDIC. Pou bann valer andeor [−1, 1], servi lidantite arctan(x) = π/2 − arctan(1/x) pou x > 0.
Tanjant envers 1 se 45° (oswa π/4 radian). Sa parski tan(45°) = 1. Dan en triyang drwat kot kote opoze ek adjasan egal, lang-la se 45°.
Tan konverti en lang an en rapo (opoze/adjasan), tandi ki tan envers (arctan) konverti en rapo retourn an en lang. Tan se periodik ek li kapav prodwir nenport nimero reel, tandi ki arctan touzour retourn en lang inik dan seri (−90°, 90°).
Wi, servi formil =ATAN(valer) dan Excel. Sa retourn rezilta an radian. Pou konverti an degre, servi =DEGREES(ATAN(valer)). Excel ousi siport =ATAN2(x, y) pou arctangent de-argiman.
Tourn ou iPhone an oryantasyon peizaz pou revele kalkilater syantifik. Tap bouton 2nd pou sanz an fonksyon envers. Bouton tan pou sanz an tan⁻¹. Antre ou valer ek tap tan⁻¹.
Dan en triyang drwat, tanjant envers rapo opoze/adjasan egal lang kot sa sommet-la. Si opoze = 3 ek adjasan = 4, alor arctan(3/4) ≈ 36.87°.
Ena 6 aplikasyon kouran: (1) Navigasyon ek GPS pou ang direksyon, (2) Enzenyori pou ang pant, (3) Fizik pou vekter lafors, (4) Grafik ordinater pou rotasyon, (5) Enzenyori elektrik pou ang faz, (6) Astronomi pou ang elevasyon.
Atraver tan(θ) = sin(θ)/cos(θ). Si θ = arctan(x), alor sin(θ) = x/√(1+x²) ek cos(θ) = 1/√(1+x²). Derive arctan(x) se 1/(1+x²).
Wi. En rapo pant se mem parey ar opoze lor adjasan dan en triyang drwat. Antre ou monte kouma kote opoze ek ou desann kouma kote adjasan ek zouti-la retourn ang lenklinezon an degre ek an radian.
Sa zouti-la finn fet spesyalman pou arctangent. Si ou bezwen en kalkilater trigonometri envers konple ki kouver arcsin ek arccos ansam avek arctan, ou pou bezwen en zouti trigonometri envers pli larz.