Choŵerengera chopingasa cha tangent (chomwe chimatchedwanso kuti arcus tangent calculator) chimasonkhanitsa arctangent (atan) cha nambala yeniyeni iliyonse ndi kubweza ngodya yomwe tangent yake ikufanana ndi mtengowo. Kaya mukupeza ngodya ya malo otsetsereka polowera mmwamba ndikuthamanga moyandikana ndi moyandikana, kapena kungotembenuza chiyerekezo cha tangent kukhala madigiri kapena ma radian, chopeza ngodyachi chimakupatsani chotsatira nthawi yomweyo. Lowetsani decimal kapena chiyerekezo cha mbali zotsutsana / zoyandikana kuchokera pamakona atatu kumanja, sankhani pakati pa madigirii ndi ma radian, ndikupeza zotsatira pompopompo. Chowerengera cha arc tan ichi chimajambulanso chithunzi cha makona atatu, chimajambula arctan(x) graph, ndikuwonetsa tebulo lathunthu-chilichonse chofunikira pa trigonometry, calculus, ndi navigation navigation pa malo amodzi.
Inverse Tangent Calculator
Pambuyo pa kuwerengera kulikonse, makona atatu amasintha kuti muwone kuti θ = arctan(motsutsana / moyandikana).
Grafu imayika zomwe zalowetsedwapo kuti mutha kuyerekeza nambala ndi ngodya yake.
Kodi Inverse Tangent ndi chiyani?
Tengenti yopingasa, yolembedwa ngati tan⁻¹(x), arctan(x), kapena atan(x), imabweretsa ngodya yomwe tanjenti yake ikufanana ndi x. M'mabuku aku Europe ndi ku Germany ntchito yomweyi imawoneka ngati arcus tangens kapena arkus tangens. Pa bwalo la mayunitsi, arctan amabweza ngodya yomwe imafanana ndi mtengo uliwonse wozungulira bwalolo.
Mu makona atatu kumanja, tan(θ) = moyang'anizana / moyandikana, kotero arctan(motsutsana / moyandikana) amapereka ngodya θ.
Dera lake ndi manambala enieni, ndipo mndandanda wake waukulu ndi (-π/2, [π/2) kapena (-90°, 90°).
Sunthani chotsetserekera kuti muwone momwe mamapu enieni amalowera kukona pakati pa -90° ndi 90°.
Momwe Mungawerengere Inverse Tangent?
Gwiritsani ntchito θ = arctan(x) pamene x ndi chiwerengero cha decimal kapena chiŵerengero.
- Dziwani mtengo wa x.
- Gwiritsani ntchito chowerengera chasayansi kapena atan() ntchito kuti muwerengere arctan(x).
- Sinthani zotsatira ngati mukufuna madigiri m'malo mwa ma radian. Chulukitsani zotsatira za radian ndi 180/π kuti mupeze madigirii, kapena chulukitsani madigirii ndi π/180 kuti mubwerere ku ma radian. Mulimonse momwemo njira yosinthira tani imakhalabe θ = arctan(x) ponseponse.
Lembani mtengo kuti musinthe sitepe iliyonse pompopompo.
Momwe Mungagwiritsire Ntchito Ma Calculator A Inverse Tangent?
Sankhani mawu owerengeka kapena otsutsana/oyandikana nawo, sankhani madigirii kapena ma radian, ndikudina Calculator.
Njira Zolowetsa
Decimal mode amavomereza zinthu monga 0.5, 1, kapena -2.75.
Zotsutsana / Zoyandikana zimagawaniza mbali za 2 poyamba ndipo zimagwiranso ntchito arctan.
Chotsatira gulu limasonyeza angapo mayankho akamagwiritsa ntchito mwamsanga.
Momwe Mungagwiritsire Ntchito Inverse Tangent pa Calculator?
Dinani batani la “2nd” kapena “Shift” pa chowerengera cha sayansi (monga Casio kapena [TI-84), kenako dinani batani la “tan” kuti mupeze tan⁻¹.
- Yatsani choŵerengera ndikukhazikitsa madigiri (DEG) kapena ma radian (RAD).
- Dinani "2nd" kapena "Shift". Kiyiyi imayambitsa ntchito zina zosindikizidwa pamwamba pa batani lililonse. Kuphatikizika kwa kiyi wa tan kumeneku kumachitika paliponse pamitundu yonse ya Casio, TI-84, ndi Sharp. Nthawi zonse ikani makona anu kukhala DEG kapena RAD musanayikanize, popeza kulowetsa komweko kumabweretsa manambala osiyanasiyana malinga ndi mawonekedwe.
- Dinani batani la "tan". Chiwonetserocho chikuwonetsa "tan⁻¹(" kapena "atan(".
- Lembani mtengo ndikusindikiza "="".
Chithunzi chili m'munsichi chikuwonetsa mabatani enieni oti musindikize pa TI-84 chowerengera chasayansi.
Kupeza tan⁻¹(1) = 45° pa TI-84 calculator
Momwe Mungawerengere Inverse Tangent Popanda Calculator?
Gwiritsani ntchito arctangent Taylor kukulitsa mndandanda kuti muyerekeze arctan(x) pamanja: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + … Mndandanda uwu ukumana |x| ≤ 1.
- Taylor Series (Maclaurin mndandanda). Chida cha arctanchitsanzo chofananira chimagwiritsa ntchito x − x³/3 + x⁵/5 − x⁷/7. Mawu ochulukirapo amapereka kulondola kwambiri.
- Zodziwika za Angle Values. Lowezani zotsatira zodziwika: arctan(0) = 0°, arctan(1) = 45°, arctan(√3) = 60°.
- Algorithm ya CORDIC. Njira ya mulingo wa hardware iyi imawerengetsera arctangent kudzera m'makona obwerezabwereza.
Sankhani mawu angati oti muphatikizepo. Yang'anani momwe kuyerekezera kukusinthira ku mtengo weniweni.
Chithunzi cha Inverse Tangent
arctan(x) graph ndi njira yowonjezereka yofanana ndi S yomwe imadutsa poyambira ndikuyandikira ±π/2.
- Ili ndi ma asymptotes opingasa pa y = π/2 ndi y = π/2.
- Ndizosamvetseka, kotero arctan(-x) = -arctan(x).
- Nthawi zonse imawonjezeka kuchokera kumanzere kupita kumanja.
Yendani pamwamba pa graph kuti muwone zenizeni zenizeni.
Tangent Table
Miyezo ya tan inverse pa 0°, 30°, 45°, 60°, ndi 90° imapezeka pafupifupi m’maphunziro onse a trigonometry ndipo ndi oyenera kukumbukira. Dinani mzere uliwonse wa tebulo kuti mukweze mtengo wokhazikika mu chowerengera.
| x | arctan(x) Madigiri | arctan(x) Radians | π Gawo |
|---|---|---|---|
| −∞ | −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 |
Chizindikiro cha Inverse of Tangent
Mawu osintha a tangent amatenga mitundu itatu yokhazikika: tan⁻¹(x), arctan(x), ndi atan(x).
- tan⁻¹(x) Zodziwika pa zowerengera zakuthupi.
- arctan(x) Standard mu masamu ofunda.
- atan(x) Mapulogalamu ndi chidziwitso cha mapulogalamu.
Ophunzira ena amachitcha kuti anti tangent chifukwa chimatembenuza zomwe tangent imachita, ngakhale awa si mawu odziwika a masamu.
Dinani mawu aliwonse kuti muwunikire pomwe amawonekera mu masamu, mapulogalamu, ndi ma Calculator.
tan⁻¹(x) ndiye mawu odziwika kwambiri pa zowerengera zakuthupi. Mawu apamwamba -1 akuwonetsa "ntchito yosiyana," osati "1 / tan(x)".
Kupeza tan⁻¹ ya Nambala Zolakwika
The tan⁻¹ ya manambala opondereza amabweza ngodya yotsutsa. Chifukwa arctangent ndi ntchito yachilendo, arctan(-x) = -arctan(x).
- arctan(-1) = -45° kapena π/4 ma radian
- arctan(-√3) = -60° kapena π/3 ma radian
Kodi tan⁻¹ ya -1 ndi chiyani?
Tan⁻¹ wa -1 ndi -45° (-π/4 ma radians kapena -0.7854 radians).
Lowetsani nambala iliyonse yotsutsa kuti muwone momwe arctan amapangira ma angle olakwika.
FAQs
Mayankho a mafunso ofala okhudzana ndi tangent.
Inde, tan⁻¹ ndiye masamu okhazikika a tangent, omwe amatchedwanso arctangent kapena arctan. Mawu apamwamba ⁻¹ sakutanthauza 1/tan (yomwe ndi cotangent). M'malo mwake, tan⁻¹(x) amafunsa kuti: 'Kodi ndi ngodya yotani yomwe ili ndi tanjenti yofanana ndi x?' Mwachitsanzo, tan⁻¹(1) = 45° chifukwa tan(45°) = 1. Mukhozanso kuliwona litalembedwa ngati arctan(x) kapena atan(x) m’zinenero zopanga mapulogalamu.
Ntchito ya tangent imatenga ngodya ndikubwezeretsa chiŵerengero cha mbali ina yoyandikana ndi makona atatu kumanja. Tengenti yopingasa (arctan) imachita mobweza: zimatengera chiŵerengero ndikubwezeretsa ngodya yofananira. Mwachitsanzo, tani(45°) = 1, kotero arctan(1) = 45°. Tangent ili ndi madera a manambala enieni kupatula machulukitsidwe osamvetseka a 90°, pamene tangent yopingasa imavomereza manambala enieni onse ndi ma angles otuluka pakati pa −90° ndi 90° (−[2]] mpaka π/2 ma radian).
Batani lopingasa limakhala pamwamba pa kiyi ya tan pa zowerengera zasayansi zambiri. Kuti muyipeze, dinani 2nd kapena Shift kaye, kenako dinani batani la tani. Chiwonetserocho chidzawonetsa tan⁻¹ kapena arctan. Pa zowerengera zojambula ngati TI-84, dinani 2nd kenako TAN. Pa Casio zowerengera, dinani SHIFT kenako tanizani.
Gwiritsani ntchito kukulitsa mndandanda wa Taylor: arctan(x) = x − x³/3 + x⁵/5 − x⁷/7 + ... kwa |x| ≤ 1. Pazikhalidwe zodziwika bwino, lowezani pamtima makona ofunikira: arctan(0) = 0°, arctan(1/√3) = 30°, arctan(1) = 45°, arctan(√3) = 60°. Mutha kugwiritsanso ntchito algorithm ya CORDIC. Pazinthu zakunja kwa [−1, 1], gwiritsani ntchito chizindikiro arctan(x) = π/2 − arctan(1/x) pa x > 0.
Kutembenuzidwa kwa 1 ndi 45° (kapena π/4 ma radian). Izi zili choncho chifukwa tan(45°) = 1. Mu makona atatu kumanja komwe mbali zotsutsana ndi zoyandikana ndi zofanana, ngodyayo ndi 45°.
Tan amasintha ngodya kukhala chiŵerengero (chotsutsana/choyandikana), pamene tani yosiyana (arctan) imasintha chiŵerengerocho kukhala ngodya. Tan imakhala yanthawi ndi nthawi ndipo imatha kupanga nambala yeniyeni iliyonse, pomwe arctan nthawi zonse imabweza ngodya yapadera (−90°, 90°).
Inde, gwiritsani ntchito fomula =ATAN(value) mu Excel. Izi zimabweretsa zotsatira kukhala ma radian. Kuti musinthe kukhala madigirii, gwiritsani ntchito =DEGREES(ATAN(value)). Excel imathandiziranso =[2]] pamakangano awiri arctangent.
Tembenukirani iPhone yanu kumalo ozungulira kuti muwulule chowerengera chasayansi. Dinani batani lachiwiri kuti musinthe kuzinthu zosintha. Batani la tani lisintha kukhala tan⁻¹. Lowetsani mtengo wanu ndikudina tan⁻¹.
Mu makona atatu kumanja, chopingasa cha tangent cha chiŵerengero choyang'anizana ndi / moyandikana chimafanana ndi ngodya ya vertex imeneyo. Ngati zotsutsana = 3 ndi moyandikana = 4, ndiye arctan(3/4) ≈ 36.87°.
Pali 6 ntchito zofala: (1) Navigation ndi GPS zokhala ndi ngodya, (2) Engineering kwa ngodya zotsetsereka, (3) Physics kwa ma vectors mphamvu, (4) Zithunzi za makompyuta pozungulira, (5) Umisiri wamagetsi pa ngodya za gawo, (6) Astronomy ya ngodya zokwera.
Kudzera tan(θ) = sin(θ)/cos(θ). Ngati θ = arctan(x), ndiye sin(θ) = x/√(1+x²) ndi cos(θ) = 1/√(1+x²). Chochokera ku arctan(x) ndi 1/(1+x²).
Inde. Chiŵerengero cha otsetsereka ndi chofanana ndi chosiyana ndi moyandikana ndi makona atatu akumanja. Lowetsani kuwuka kwanu ngati mbali ina ndikuthamanga kwanu ngati mbali yoyandikana ndi chidacho chimabwezeretsanso mbali ya kupendekera mu madigirii onse ndi ma radian.
Chida ichi chimapangidwira arctangent. Ngati mukufuna chowerengera chokwanira cha trig chophimba arcsin ndi arccos pambali pa arctan, mungafunike chida chokulirapo cha trigonometry.