Inverse tangent calculator (a wɔsan frɛ no arcus tangent calculator) bu arctangent (atan) a ɛwɔ nɔma ankasa biara mu na ɛsan de angle a ne tangent yɛ pɛ saa bo no. Sɛ́ ebia worehwehwɛ ɔkwan a ɛkɔ soro no anim denam nkɔanim ne mmirikatu a wobɛhyɛn mu sɛ ɛne ne ho bɔ abira na ɛbɛn so, anaasɛ woredan tangent ratio akɔ digrii anaa radians kɛkɛ no, saa anim hwehwɛfo yi ma wunya nea efi mu ba no ntɛm ara. Hyehyɛ decimal anaa afã horow a ɛne wɔn ho wɔn ho bɔ abira / a ɛbɛn ho nsusuwii fi ahinanan nifa so, paw digrii ne radian, na nya nea efi mu ba ntɛm ara. Saa arc tan akontabuo yi nso yɛ nkitahodiɛ ahinanan mfonini, yɛ arctan(x) graph no, na ɛkyerɛ tangent pon a ɛdi mũ —biribiara a ɛhia ma trigonometry, calculus, ne akwantuo akontabuo wɔ beaeɛ baako.
Inverse Tangent a ɛyɛ nea ɛkɔ akyiri Nkontaabu afiri
Akontaabu biara akyi no, ahinanan no yɛ foforo sɛnea ɛbɛyɛ a wubetumi ahu sɛ θ = arctan(a ɛne no bɔ abira / ɛbɛn).
Graf no hyɛ mprempren input no agyirae sɛnea ɛbɛyɛ a wubetumi de nɔma no atoto ne anim.
Dɛn ne Inverse Tangent?
Inverse tangent, a wɔakyerɛw no sɛ tan⁻¹(x), arctan(x), anaa atan(x), san de angle a ne tangent yɛ pɛ x. Wɔ Europa ne German adesua nhoma ahorow mu no, saa dwumadi koro yi ara pue sɛ arcus tangens anaa arkus tangens. Wɔ unit kurukuruwa no so no, arctan san de anim a ɛne tangent bo biara a ɛwɔ kurukuruwa no ho hyia no ba.
Wɔ ahinanan nifa mu no, tan(θ) = a ɛne ne ho bɔ abira / a ɛbɛn, enti arctan(a ɛne ne ho bɔ abira / a ɛbɛn) ma anim θ.
Ne domɛn nyinaa yɛ akontaahyɛde ankasa, na ne kwan titiriw ne (-π/2, π/2) anaa (-90°, 90°).
Fa slider no kɔ baabi foforo na hwɛ sɛnea input ankasa biara map kɔ anim a ɛda -90° ne 90° ntam.
Ɔkwan Bɛn so na Wobu Inverse Tangent?
Fa θ = arctan(x) di dwuma bere a x yɛ decimal value anaa ratio.
- Kyerɛw bo a ɛsom x.
- Fa nyansahu mu akontaabu afiri anaa atan() dwumadie di dwuma fa bu arctan(x).
- Dane nea efi mu ba no sɛ wuhia digrii mmom sen sɛ wubehia radians a. Fa radian aba no bɔ 180/π na woanya digrii, anaa fa digrii bo bi bɔ π/180 na woasan adan akɔ radian mu. Ɔkwan biara so no, inverse tan formula no kɔ so tra hɔ θ = arctan(x) wɔ ne nyinaa mu.
Type value bi na fa anammɔn biara update ntɛm ara.
Ɔkwan Bɛn so na Wɔde Saa Inverse Tangent Calculator Yi Di Dwuma?
Paw decimal anaa opposite/adjacent input, paw degrees anaa radians, na mia Calculate.
Akwan a Wɔde Hyehyɛ Nsɛm Mu
Decimal mode gye nsusuwii te sɛ 0.5, 1, anaa -2.75 tom.
Opposite / Adjacent mode no di kan kyekyɛ afã 2 no mu na afei ɛde arctan di dwuma.
Nea efi mu ba no kyerɛ mmuae ahorow pii a wɔde bedi dwuma ntɛmntɛm.
Sɛnea Wɔde Inverse Tangent Di Dwuma wɔ Calculator So?
Mia “2nd” anaa “Shift” safoa no so wɔ nyansahu mu akontaabu afiri bi so (te sɛ Casio anaa TI-84), afei mia “tan” bɔtn no so na woanya tan−1.
- Dane calculator no na fa angle mode no si degrees (DEG) anaa radians (RAD) so.
- Mia “2nd” anaa “Shift” so. Saa safoa yi ma dwumadi ahorow a ɛto so abien a wɔatintim wɔ bɔtn biara atifi no yɛ adwuma. Saa shift tan key nkabom yi yɛ amansan nyinaa de wɔ Casio, TI-84, ne Sharp nhwɛso ahorow nyinaa mu. Bere nyinaa fa wo angle mode no to DEG anaa RAD ansa na woamia so, efisɛ input koro no ara san de nɔma ahorow ba a egyina mode no so.
- Mia “tan” safoa no so. Ɔyɛkyerɛ no kyerɛ “tan−1(” anaa “atan(”.
- Type value no na mia “=” so.
Mfonini a ɛwɔ aseɛ ha yi kyerɛ bɔtn pɔtee a ɛsɛ sɛ womia wɔ TI-84 nyansahu mu akontabuo so.
Hwehwɛ tan−1(1) = 45° wɔ TI-84 akontaabu afiri so
Sɛnea Wobebu Inverse Tangent a Wonni Calculator?
Fa arctangent Taylor series ntrɛwmu no di dwuma de bɛyɛ arctan(x) denam nsa so: arctan(x) = x − x3/3 + x5/5 − x7/7 + ... Saa series yi hyia bere a |x| ≤ 1.
- Taylor Ntoatoaso (Maclaurin nsɛm a ɛtoatoa so) .. arctangent series approximation adwinnade no de x − x3/3 + x5/5 − x7/7 di dwuma. Nsɛmfua pii ma pɛpɛɛpɛyɛ a ɛkorɔn.
- Angle Values a Wonim. Fa nea efi mu ba a ɛtaa ba no gu wo tirim: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- CORDIC Algorithm a Wɔde Di Dwuma. Saa hardware-level kwan yi bu arctangent denam angle rotations a wɔtaa yɛ no so.
Paw nsɛmfua dodow a wode bɛka ho. Hwɛ sɛnea bɛyɛ no hyia kɔ nokware bo no so.
Inverse Tangent Graph a Wɔde Kyerɛw Nsɛm
arctan(x) graph no yɛ S-shaped curve a ɛkɔ soro a ɛfa mfiase no mu na ɛbɛn ±π/2.
- Ɛwɔ asymptotes a ɛkɔ soro wɔ y = -π/2 ne y = π/2.
- Ɛyɛ nwonwa, enti arctan(-x) = -arctan(x).
- Ɛkɔ soro bere nyinaa fi benkum kɔ nifa.
Fa wo nsa hyɛ graph no so na hwɛ gyinapɛn ahorow pɔtee.
Tangent Table a ɛwɔ hɔ
Ɛkame ayɛ sɛ tan inverse values a ɛwɔ 0°, 30°, 45°, 60°, ne 90° no pue wɔ trigonometry adesua biara mu na ɛfata sɛ wode wo ho to so sɛ wobɛkae. Klik table row biara so na fa saa standard value no gu calculator no mu.
| x | arctan(x) Abodin krataa ahorow | arctan(x) Radians a ɛwɔ hɔ | π Nkyekyɛm ketewaa bi |
|---|---|---|---|
| −∞ | −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 |
Nkyerɛwde a wɔde kyerɛw Inverse of Tangent
Nkyerɛwde a wɔde kyerɛw tangent a ɛdannan no fa gyinapɛn ahorow 3: tan⁻¹(x), arctan(x), ne atan(x).
- tan⁻¹(x) . Ɛtaa ba wɔ honam fam akontaabu mfiri so.
- arctan(x) . Standard wɔ akontaabu a wɔde di dwuma wɔ ɔkwan a ɛfata so.
- atan(x) . Programming ne software nkyerɛwde.
Asuafo binom frɛ no anti tangent wɔ ɔkwan a ɛnyɛ ɔkwan pa so efisɛ ɛdan nea tangent yɛ no, ɛwom sɛ eyi nyɛ akontaabu mu nsɛmfua a wɔahyɛ da ayɛ de.
Klik nkyerɛwde biara so na twe adwene si baabi a epue wɔ akontaabu, nhyehyɛe, ne akontaabu mfiri mu.
tan⁻¹(x) ne nkyerɛwde a wɔtaa de di dwuma wɔ honam fam akontaabu mfiri so. Nkyerɛwde a ɛwɔ soro -1 kyerɛ “inverse function,” ɛnyɛ “1 / tan(x)”.
Hwehwɛ tan−1 a ɛfa Nkontaabu a Ɛnyɛ Asɛm ho
Nnɔmba a ɛnyɛ papa no tan−1 no san de anim a ɛnyɛ papa ba. Esiane sɛ arctangent yɛ adwuma a ɛyɛ nwonwa nti, arctan(-x) = -arctan(x).
- arctan(-1) = -45° anaa -π/4 radian
- arctan (-√3) = -60° anaa -π/3 radians
Dɛn ne tan−1 a ɛwɔ -1 mu?
Tan−1 a ɛwɔ -1 mu no yɛ -45° (-π/4 radians anaa -0.7854 radians).
Fa nɔma biara a ɛnyɛ papa hyɛ mu na hwɛ sɛnea arctan de nsɛm a ɛnyɛ papa no map kɔ anim a enye.
FAQs
Nsɛmmisa a wɔtaa bisa fa inverse tangent ho mmuae.
Yiw, tan−1 ne akontaabu mu nkyerɛwde a wɔahyɛ da ayɛ ma inverse tangent, a wɔsan frɛ no arctangent anaa arctan. Nkyerɛwde a ɛwɔ soro −1 no nkyerɛ 1/tan (a ɛyɛ cotangent). Mmom no, tan⁻¹(x) bisa sɛ: ‘Ahinanan bɛn na ɛwɔ tangent a ɛne x yɛ pɛ?’ Sɛ nhwɛso no, tan−1(1) = 45° efisɛ tan(45°) = 1. Wubetumi nso ahu sɛ wɔakyerɛw no sɛ arctan(x) anaa atan(x) wɔ nhyehyɛe kasa mu.
Tangent dwumadie no fa ahinanan na ɛsan de ɔfã a ɛne no bɔ abira no ne ɔfã a ɛbɛn no ratio wɔ ahinanan a ɛyɛ pɛ mu. Inverse tangent (arctan) no yɛ reverse: ɛfa ratio na ɛsan de angle a ɛne no hyia no ba. Sɛ nhwɛso no, tan(45°) = 1, enti arctan(1) = 45°. Tangent wɔ dodow ankasa nyinaa domain gye odd multiples a ɛyɛ 90°, bere a inverse tangent gye akontaahyɛde ankasa nyinaa tom na ɛde angles a ɛwɔ −90° ne 90° (−π/2 kosi π/2 radians) ntam ba.
Inverse tangent button no te tan key no atifi wɔ nyansahu mu akontaabu mfiri dodow no ara so. Sɛ wopɛ sɛ wokɔ mu a, di kan mia 2nd anaa Shift key no so, afei mia tan button no so. Ɔyɛkyerɛ no bɛkyerɛ tan−1 anaa arctan. Wɔ graphing calculators te sɛ TI-84 so no, mia 2nd afei TAN. Wɔ Casio akontaabu mfiri so no, mia SHIFT afei tan.
Fa Taylor ntoatoaso ntrɛwmu no di dwuma: arctan(x) = x − x3/3 + x5/5 − x7/7 + ... ma |x| ≤ 1. Sɛ wopɛ gyinapɛn ahorow a wɔtaa de di dwuma a, kyere afã atitiriw no gu wo tirim: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Wubetumi nso de CORDIC algorithm no adi dwuma. Sɛ wopɛ gyinapɛn ahorow a ɛwɔ [−1, 1] akyi a, fa nkyerɛkyerɛmu arctan(x) = π/2 − arctan(1/x) di dwuma ma x > 0.
Inverse tangent a ɛyɛ 1 no yɛ 45° (anaasɛ π/4 radians). Eyi te saa efisɛ tan(45°) = 1. Wɔ ahinanan nifa a afã horow a ɛne ne ho bɔ abira ne nea ɛbɛn no yɛ pɛ mu no, ahinanan no yɛ 45°.
Tan dane anim bi kɔ ratio (a ɛne no bɔ abira/ɛbɛn), bere a inverse tan (arctan) dane ratio bi san kɔ anim. Tan yɛ bere ne bere mu na ebetumi ama dodow ankasa biara aba, bere a arctan san de anim soronko bi ba bere nyinaa wɔ kwan no mu (−90°, 90°).
Yiw, fa fomula =ATAN(value) di dwuma wɔ Excel mu. Eyi san de nea efi mu ba no ba wɔ radians mu. Sɛ wopɛ sɛ wodan kɔ digrii mu a, fa =DEGREES(ATAN(value)) di dwuma. Excel nso boa =ATAN2(x, y) ma abien-akasakasa arctangent.
Dannan wo iPhone no kɔ asase a ɛkyerɛ kwan so na ama woada nyansahu mu akontaabu afiri no adi. Klik 2nd button no so na dan kɔ inverse functions so. Tan bɔtn no bɛsesa ayɛ tan−1. Hyehyɛ wo bo no na pia tan−1.
Wɔ ahinanan nifa mu no, inverse tangent a ɛwɔ ratio a ɛne no bɔ abira/ɛbɛn no yɛ pɛ angle a ɛwɔ saa vertex no so. Sɛ ɛne no bɔ abira = 3 na ɛbɛn = 4 a, ɛnde arctan(3/4) ≈ 36.87°.
Nneɛma 6 na wɔtaa de di dwuma: (1) Navigation ne GPS a wɔde yɛ bearing angles, (2) Engineering ma slope angles, (3) Physics ma force vectors, (4) Kɔmputa so mfonini a wɔde di akɔneaba, (5) Electrical engineering ma phase angles, (6) Astronomy ma elevation angles.
Ɛdenam tan(θ) = sin(θ)/cos(θ) so. Sɛ θ = arctan(x) a, ɛnde sin(θ) = x/√(1+x²) ne cos(θ) = 1/√(1+x²). Nea efi arctan(x) mu ne 1/(1+x²).
Yiw. Slope ratio yɛ pɛ ne opposite over adjacent wɔ right triangle mu. Hyɛ wo sɔre no mu sɛ ɔfã a ɛne no bɔ abira na wo mmirikatu no hyɛ mu sɛ ɔfã a ɛbɛn no na adwinnade no san de anim a ɛkɔ fam no ba wɔ digrii ne radians nyinaa mu.
Wɔasisi saa adwinnade yi ama arctangent titiriw. Sɛ wuhia inverse trig calculator a edi mũ a ɛkata arcsin ne arccos so wɔ arctan nkyɛn a, anka wubehia inverse trigonometry adwinnade a ɛtrɛw.